Tag: bourbaki

TØP PhotoShop mysteries

Published August 11, 2023 by lieven

Suppose you’re writing a book, and for the duration of that project you keep a certain photo as your desktop-background. I guess we might assume that picture to be inspirational for your writing process.

If you PhotoShopped it to add specific elements, might we assume these extra bits to play a crucial role in your story?

Now, let’s turn to Twenty One Pilots and the creation process of their album Trench, released on October 5, 2018

We know from this tweet (from August 19th, 2018) that Tyler Joseph’s desktop-background picture was a photoshopped version of the classic Bourbaki-1938 photo on the left below, given it Trench-yellow, and added a bearded man in the doorway (photo on the right)

And we know from this interview (from September 5th, 2018) that, apart from the bearded man, he also replaced in the lower left corner the empty chair by a sitting person (lower photo).

The original photo features on the Wikipedia page on Nicolas Bourbaki, and as Tyler Joseph has revealed that Blurryface‘s real name is Nicolas Bourbaki (for whatever reason), and that he appears in the lyrics of Morph on Trench, this may make some sense.

But, of the seven people in the picture only three were founding members of Bourbaki: Weil, Diedonne and Delsarte. Ehresmann entered later, replacing Jean Leray, and Pison and Chabauty were only guinea pigs at that moment (they later entered Bourbaki, Chabauty briefly and Pison until 1950), and finally, Simonne Weil never was a member.

There’s another strange thing about the original picture. All of them, but Andre and Simone Weil, look straight into the camera, the Weil’s seem to be more focussed on something happening to the right.

Now, TØP has something with the number 9. There are nine circles on the cover of Blurryface (each representing one of a person’s insecurities, it seems), there are nine towers in the City of Dema, nine Bishops, etc.

So, from their perspective it makes sense to Photoshop two extra people in, and looking at the original there are two obvious places to place them: in the empty doorway, and on the empty chair.

But, who are they, and what is their significance?

1. The bearded man in the doorway

As far as I know, nobody knows who he is. From a Bourbaki point of view it can only be one person: Elie Cartan.

We know he was present at the 1938 Bourbaki Dieulefit/Beauvallon meeting, and that he was kind of a father figure to Bourbaki. Among older French mathematicians he was one of few (perhaps the only one) respected by all of Bourbaki.

But, bearded man is definitely not Elie Cartan…

If bearded man exists and has a Wikipedia page, the photo should be on that page. So, if you find him, please leave a comment.

Previous in this series I made a conjecture about him, but I’m not at all sure.

2. Why, of all people, Szolem Mandelbrojt?

We know from this Twentyonepilots subReddit post that the man sitting on the previously empty chair in none other than Bourbaki founding member Szolem Mandelbrojt, shopped in from this other iconic early Bourbaki-photo from the 1937 Chancay-meeting.

Let me tell you why this surprises me.

Szolem Mandelbrojt was atypical among the first Bourbaki-gang in many ways: he was the only one who didn’t graduate from the ENS, he was a bit older than the rest, he was the only one who was a full Professor (at Clermont-Ferrand) whereas the others were ‘maitre de conference’, he was the only one who didn’t contribute actively in the Julia seminar (the proto-Bourbaki seminar) nor much to the Bourbaki-congresses either for that matter, etc. etc.

Most of all, I don’t think he would feel particularly welcome at the 1938 congress. Here’s why.

(Jacques Hadamard (left), and Henri Lebesgue (right))

From Andre Weil’s autobiography (page 120):

Hadamard’s retirement left his position open. I thought myself not unworthy of succeeding him; my friends, especially Cartan and Delsarte, encouraged me to a candidate. It seemed to me that Lebesgue, who was the only mathematician left at the College de France, did not find my candidacy out of place. He even let me know that it was time to begin my ‘campaign visits’.

But the Bourbaki-campaign against a hierarchy of scientific prizes instituted by Jean Perrin (the so called ‘war of the medals’) interfered with his personal campaign. (Perhaps more important was that Mandelbrojt did his Ph.D. under Hadamard…)

Again from Weil’s autobiography (page 121):

Finally Lebesque put an end to my visits by telling me that he had decided on Mandelbrojt. It seemed to me that my friends were more disappointed than I at this outcome.

In the spring of 1938, Mandelbrojt succeeded Hadamard at the College de France.

There’s photographic evidence that Mandelbrojt was present at the 1935 Besse-congress and clearly at the 1937-Chancay meeting, but I don’t know that he was even present at Chancay-1936. (Edit May 2024: He was present in 1936)

The only picture I know of that meeting is the one below. Standing on bench: Chevalley’s nephews, seated Andre Weil and Chevalley’s mother; standing, left to right: Ninette Ehresmann, Rene de Possel, Claude Chavalley, Jacqueline Chavalley, Mirles, Jean Delsarte and Charles Ehresmann.

Of all possible people, Szolem Mandelbrojt would be the miscast at the 1938-meeting. So, why did they shop him in?

– convenience: they had an empty chair in the original picture, another Bourbaki-photo with a guy sitting on such a chair, so why not shop him in?

– mistaken identity: in the subReddit post the sitting guy was mistakenly identified as Claude Chevalley. Now, there is a lot to say about wishing to add Chevalley to the original. He is by far the most likeable of all Bourbakis, so if these nine were ever supposed to be the nine Bishops of Dema, he most certainly would be Keons. But, Chevalley was already in the US at that time, and was advised by the French consul to remain there in view of the situation in Europe. As a result, Chevalley could not obtain a French professorship before the early 50ties.

– a deep hidden clue: remember all that nonsense about Josh Dun’s ‘alma mater’ being that Ukrainian building where Nico and the niners was shot? Well, Szolem Mandelbrojt’s alma mater was the University of Kharkiv in Ukraine. See this post for more details.

3. Is it all about Simone Weil?

If you super-impose the two photographs, pinning Mandelbrojt in both, the left border of the original 1938-picture is an almost perfect mirror for both appearances of Simone Weil. Can she be more important in all of this than we think?

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Dema2Trench, AND REpeat

Published August 4, 2023 by lieven

There’s this band Twenty One Pilots and they’ve woven a complicated story around some of their albums, notably Blurryface, Trench, and Scaled and Icy.

Since Trench, an important component of that story is the Bourbaki group, so I’m just curious whether the few things I know about them can help to clarify parts in the TØP- storyline.

Pretty pointless, I know, as no artistic project will follow blindly historical facts. But hey, as long as I discover new things I’ll keep going.

The story’s about a City of Dema, ruled by nine Bishops installing a terror regime called Vialism, and a land outside the city walls, called Trench, to which citizens would like to escape.

Think of Dema as an extremely toxic environment from which you need to escape to a safe place, let’s call it Trench.

Sadly, too often survivors from abusive settings later on create their own toxic environment, abusive to others.

So, Dema-escapees to Trench should always be wary of the danger of creating a new Dema for others.

It is very hard to break these Dema2Trench cycles of violence. That’s probably why the map of the City of Dema is circular.

Let’s start with these two photos not (yet) in the Dema-lore:

Both pictures are of the French mathematician Gaston Julia.

Julia graduated from the ENS in 1914, so was among the worst victims of the military regime Lavisse installed at the ENS. He was mobilised but hadn’t yet completed his second year of military training. That was shortened to just 5 months, after which we has send as a second lieutenant to the war.

In January 1915 he was seriously wounded in his face, had to undergo a series of operations and for the rest of his life he resigned himself to wearing a leather strap around the area where his nose had been.

He ran a weekly seminar from 1933 till 1939, the Seminaire Julia, to which the Bourbaki core members contributed a vast number of lectures.

Until 1937-38 (so just before the Dieulefit Bourbaki congress) the Bourbakis felt happy citizens of Julia’s Seminar/Dema. But then they discovered his political agenda and were expelled from it, or escaped from it depending on the version.

Jean Leray convinced Julia that it was a terrible mistake to let his seminar run by Bourbaki, and that things would go much better if he ran it. Julia expelled Bourbaki from the seminar, changed its name to ‘ Cercle mathématique de l’École normale supérieure’ and moved the venue from the IHP to the ENS. The attendants of this seminar were younger and less international that in the preceding years, hence more malleable to his political ideas.

Another reason for the break-up between Bourbaki and Julia was that they reproached him of attending in June 1937 the festivities of the bicentennial of the University of Gottingen, which were seen as pure propaganda for the Nazi-regime.

During WW2, Julia collaborated with the occupying Nazi-regime in that he tried to find French mathematicians to contribute to the Zentralblatt. After the war he was briefly suspended for this.

Much more on the Julia seminar and the break-up with Bourbaki can be read in the thesis by Gatien Ricotier ‘Projets collectifs et personnels autour de Bourbaki dans les années 1930 à 1950’, and Michele Audin’s book on the Julia Seminar.

Let us compare Julia’s photographs to these two in Dema-lore:

Is it a coincidence that Clancy in Trench has a scar on his nose? Is it a coincidence that the black paint on some of the Bishop’s faces looks a lot like Julia’s mask?

Can it be that victims of one Dema-era become Bishops in a next era?

This repetitiveness of Dema-environments also indicates the importance of Bishop Andre. Recall that all the Bishops’ names (except for Nico) come from concatenations of word-parts in the lyrics of the songs on the Blurryface album.

ANDRE comes from ‘..AND REpeat’ in Fairly local:

Tomorrow I’ll keep a beat
And repeat yesterday’s dance

In view of this, let’s have another look at the two Bourbaki-related photographs that appeared in the run up to the Trench-album:

On the left is the photo of the Dieulefit/Beauvallon 1938 meeting, which is on the Bourbaki Wikipedia page, and was on the desktop of Tyler Joseph.

On the right a photo of Andre Weil together with a girl, according to Wikipedia the picture dates from 1956. I’m pretty certain it was taken in the summer of 1957, and that the girl is Mireille Cartan, the second youngest daughter of Henri Cartan. Not that any of this matters, TØP-wise. A clipping of the girl was among the material originally posted at the dmaorg.info site.

In 1938, Andre Weil was a victim of Lavisse’s Dema. His year was the last one getting a military training to become reserve officers in the French infantry/artillery (as were Cartan, Dieudonne and Delsarte).

When France would mobilise they were forced to return to Dema (military service) and lead their bataljons as second lieutenants into war. All of them, except for Weil, did this.
Weil escaped to Trench (Finland), and was taken back to Dema, and imprisonment.

In 1957, Bourbaki dominated much of French mathematical life, and certainly its influence in Paris was suffocating for aspiring math-students. A good read on this is Jacques Roubaud’s Mathematique.

Bourbaki has turned French mathematics (and beyond) into its own Dema, and Andre Weil certainly was one of the more important Bishops of it.

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Where’s Bourbaki’s Dema?

Published July 15, 2023 by lieven

In this series I’m trying to figure out why the Bourbaki-group was an inspiration for the storyline of Trench, the fifth studio album by American musical duo Twenty One Pilots (or TØP).

Trench-lore centers around the city of Dema, ruled by nine Bishops enforcing Vialism (a fake religion asking people to take their own lives to glorify Dema).

It is an unfortunate coincidence that the city of Dema in the movie-clip of Nico and the Niners was inspired, and shot in Kyiv and Charkiv, Ukraine (the clip is from 2018).

I’ve just found out that Dema is situated in my country… (NATN was made in Kyiv and Charkiv, Ukraine)
by u/Sasha0503 in twentyonepilots

Here’s the corresponding ‘beyond the movie’-clip, from which we learn (or rather are told) that the movie’s ‘city of Dema’ was shot in ‘the former Ukranian high-school’ of Josh Dun (he even calls it his ‘Alma Mater’), all in quotes because I don’t buy any of it, but take it as a desperate hint to identify Dema.

In the Trench movie-clips, Josh Dun is always cast as a Bandito, and last time we saw that also the Bourbaki-gang is likely to be close to the Banditos. Dema is supposed to be the Alma Mater of (at least some of) the Banditos. Hold that thought.

As for the connection between the City of Dema and the Bourbaki-group, we only have one piece of solid information:

That the Bourbaki-group named themselves after Nico=Nicolas Bourbaki clearly resonates with Twenty Øne Pilots who got their name from the 1947 play ‘All My Sons’ by American playwright Arthur Miller.

But the crucial info is: “The story of Dema happened before them”, so the story of Dema with the Bishops and Vialism happened before the Bourbaki-group. An extra piece of evidence that there is no way the Bourbaki-group are the nine Bishops of Dema.

So, what happened before the Bourbaki-group?

Mathematically, their direct predecessors were David Hilbert, Emil Artin, Emmy Noether and her boys, in short German mathematicians from the 1920’s and early 1930’s.

Several of the Bourbaki founding members studied in Germany (Weil in Gottingen in 1927, Chevalley in Hamburg in 1931 and Marburg in 1932, and Ehresmann in Gottingen in 1930).

They were inspired by Hilbert’s program (We must know, we will know), and set out to introduce the German style of writing and doing mathematics in France.

So, a first candidate (also given the Bauhaus-like architecture of Dema) might be ‘German Mathematicians’, or in German, DEutscher MAthematiker = DEMA.

But one can hardly argue that there was a self-destructive attitude (like Vialism) present among that group, quite the opposite.

Still, one can ask why German mathematics was that strong in the 1920’s, compared to the French. France and Germany took different approaches with their intelligentsia during WW1: while Germany protected its young students and scientists, France instead committed them to the front, owing to the French culture of egalitarianism.

Remember that the album is called Trench, and the dirtiest trench-war in all of human history was WW1. Hold that thought.

But, how does this help us in identifying Dema.

A few months before the release of Trench, a website was launched containing letters (from a character named Clancy) and some photos (including part of a photo of Andre Weil). That website’s URL still is dmaorg.info.

On the rear of the boat in the movie-clip Saturday, we see ‘030904 DMA ORG’ (the 030904 is simplistic code for CID, believed to mean ‘Clancy Is Dead’).

Compare this to the official email address of the ‘Association des collaborateurs de Nicolas Bourbaki’ which is: bourbaki@dma.ens.fr.

Here, ‘dma’ stands for ‘Département de mathématiques et applications’, one of the fifteen departments of the ENS, the Ecole Normal Superieure in Paris, Rue d’Ulm.

Remember the inspirational, photoshopped photo of the Bourbaki 1938 congress in Dieulefit/Deauvallon:

All seven people in the original picture are ‘normaliens’, that is, their ‘Alma Mater’ is the Ecole Normale Superieure’. All but Simone Weil graduated from the DEpartement de MAthematiques=DEMA, as DMA was called then.

Whence the hypothesis: Bourbaki’s Dema = ENS before and during WW1

It is a conglomerate of buildings and its central courtyard forms a kind of secular cloister around its basin. This space is called “la Cour aux Ernests” in reference to a former director, Ernest Bersot. He had placed red (!) fish (=the Ernests in ENS-slang) in the basin, which have become one of the symbols of the school.

More important to us is that the pond of the Ernests is reached by crossing the “aquarium”, where the ENS war memorial is located, commemorating the 239 (former) ENS-students killed in WW1 on a tatal of about 1400 of them drafted…

From the Wikipedia-page on Nicolas Bourbaki:

“The deaths of ENS students resulted in a lost generation in the French mathematical community; the estimated proportion of ENS mathematics students (and French students generally) who died in the war ranges from one-quarter to one-half, depending on the intervals of time (c. 1900–1918, especially 1910–1916) and populations considered.”

A chilling, and very detailed account of the circumstances that lead to the deaths of about 50% of ENS-student from the period 1910-1913 can be found in the paper Pourquoi les normaliens sont-ils morts en masse en 1914-1918 ? Une explication structurale (Why the normaliens suffered mass-death in 1914-18, a structural explanation) by Nicolas (!) Mariot. Here’s the abstract:

“The École Normale Supérieure d’Ulm is always mentioned when historians summarize the ravages of World War I in France: the institution embodies the commitment of intellectuals at the front. The article offers an interpretation of mortality rates of the School which allows to understand why it is primarily students during schooling (Classes 1910-1913) that are heavily affected. Rather than basing the interpretation on the single assumption of sacrifice, it puts forward arguments pertaining to the history of the school in the immediate pre-war, including the institution of military training after the reform service in 1905, competition with the École Polytechnique to retain the best scientific students, and finally the forced commitment of the ENS students in the infantry.”

Crucial in this is the role of Ernest Lavisse who was the director of the ENS from 1903 till 1919.

Before, normaliens had to serve 12 months in the army, just like all other students. In 1905 the law changed, and under Lavisse’s influence ENS-students were given a heavy military training. From the paper:

“From now on, normalien students, like those of other major military schools, are subject to a two-year service: a first year before their actual entry into rue d’Ulm, which they had to perform in an infantry regiment; a second on leaving, which they can finish as a reserve second lieutenant, but always in the infantry, if they pass the tests. And there is more: because between these two years, the students also follow a fairly heavy military preparation, including theoretical and physical exercises, even on Sundays, organised by two officers seconded full-time for this mission within the walls of the School.”

He also instilled in the ENS-student a radical sense of patriotism, and was a fervent propagandist for l’Union sacrée. From the paper:

“Intellectual mobilisation crystallised in the figures of Lavisse and Durkheim via their famous Letters to all French people distributed in millions of copies across the country. In the fall of 1914, the two founded and took control, respectively as director and secretary of the Committee for Studies and Documents on the War, a propaganda organ for the country’s executives.

Alongside them, eight of the nine other members of the Committee are former students of the School who have become professors at the Sorbonne (Charles Andler, Charles Seignobos, Émile Boutroux, Ernest Denis, Gustave Lanson) or at the Collège de France (Joseph Bédier, Henri Bergson, Jacques Hadamard), without even mentioning the role of editorial secretary held by Lucien Herr, legendary counterpart of Paul Dupuy at the Rue d’Ulm library.”

I would have liked that there were only nine members of the committee, but there were eleven of them…

Anyway, Lavisse and his eight professors created an extremely patriotic environment at the ENS during WW1, encouraging students to go to (the) Trench(es) and give their life for France and the glory of the Ecole. The ENS-monument is the equivalent of the Neon Gravestones in Dema-lore.

Did you spot it too? LAVIsse is almost a perfect anagram for VIALism.

Se non e vero…

Concluding, the best theory I can come up with in order to include the Bourbaki-group in Dema-lore is that their Dema is the ENS in WW1 and preceding years, and that Vialism is the regime installed by Lavisse and the other members from the committee.

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