Tag: Dema

Clancy and Nancago

Published May 3, 2024 by lievenlb

Later this month, 21 pilots‘ next album, “Clancy”, will be released, promising to give definite answers to all remaining open questions in Dema-lore.

By then we will have been told why Andre Weil and the Bourbaki group show up in the Trench/Dema tale.

This leaves me a couple of weeks to pursue this series of posts (see links below) in which I try to find the best match possible between the factual history of the Bourbaki group and elements from the Dema-storyline.

Two well-known Bourbaki-photographs seem important to the pilots. The first one is from the september 1938 Dieulefit/Beauvallon Bourbaki congress:

At the time, Bourbaki still had to publish their first text, they were rebelling against the powers that be in French mathematics, and were just kicked out of the Julia seminar.

In clikkies parlance: at that moment the Bourbakistas are Banditos, operating in Trench.

The second photograph, below on the left, is part of a famous picture of Andre Weil, supposedly taken in the summer of 1956.

At that time, Bourbaki was at its peak of influence over French mathematics, suffocating enthusiastic math-students with their dry doctrinal courses, and forcing other math-subjects (group theory, logic, applied math, etc.) to a virtual standstill.

In clique-speech: at that moment the Bourbakistas are Bishops, ruling Dema.

Let me recall the story of one word, associated to the Bourbaki=Bishops era which lasted roughly twenty years, from the early 50ties till Bourbaki’s ‘death’ in 1968 : Nancago.

From the 50ties, Nicolas Bourbaki signed the prefaces of ‘his’ books from the University of Nancago.

Between 1951 and 1975, Weil and Diedonne directed a series of texts, published by Hermann, under the heading “Publications de l’Institut mathematique de l’Universite de Nancago”.

Bourbaki’s death announcement mentioned that he “piously passed away on November 11, 1968 at his home in Nancago”.

Nancago was the name of a villa, owned by Dieudonne, near Nice. Etc. etc.

But then, what is Nancago?

Well, NANCAGO is a tale of two cities: NANcy and ChiCAGO.

The French city of Nancy because from the very first Bourbaki meetings, the secretarial headquarters of Bourbaki, led by Jean Delsarte, was housed in the mathematical Institute in Nancy.

Chicago because that’s where Andre Weil was based after WW2 until 1958 when he moved to Princeton.

Much more on the history of Nancago can be found in the newspaper article by Bourbaki scholar par excellance Liliane Beaulieu: Quand Nancy s’appelait Nancago (When Nancy was called Nancago).

Right, but then, if Nancago is the codeword of the Bourbaki=Bishops era, what would be the corresponding codeword for the Bourbaki=Banditos era?

As mentioned above, from 1935 till 1968 Bourbaki’s headquarters was based in Nancy, so even in 1938 Nancy should be one of the two cities mentioned. But what is the other one?

In 1938, Bourbaki’s founding members were scattered over several places, Jean Delsarte and Jean Dieudonne in Nancy, Szolem Mandelbrojt and Rene de Possel in Clermont-Ferrand, and Andre Weil and Henri Cartan in Strasbourg. Claude Chevalley was on a research stay in Princeton.

Remember the Bourbaki photograph at the Beauvallon meeting above? Well, it was taken in september 1938 when the Munich Agreement was reached.

Why is this relevent? Well, because Strasbourg was too close to the German border, right after the Munich agreement the Strasbourg Institute was ordered to withdraw to the University of Clermont-Ferrand.

Clermont-Ferrand lies a bit south of Vichy and remained in WW2 in the ‘free zone’ of France, whereas Strasbourg was immediately annexed by Germany.

For more on the importance of Clermont-Ferrand for Bourbaki during 1940-1942 see the article by Christophe Eckes and Gatien Ricotier Les congrès de Clermont-Ferrand de 1940, 1941 et 1942.

That is, all Bourbaki members where then either affiliated to Nancy or to Clermont-Ferrand.

A catchy codeword for the Bourbaki=Banditos era, similar to Nancago as the tale of two cities, might then be:

CLermont-Ferrand + nANCY = CLANCY.

[For clikkies: rest assured, I’m well aware of the consensus opinion on the origins of Clancy’s name. But in this series of posts I’m not going for the consensus or even intended meanings, but rather for a joyful interplay between historical facts about the Bourbaki group and elements from Dema-lore.]

In this series:

6 Comments

Bourbaki and Dema, two remarks

Published February 26, 2024 by lievenlb

While this blog is still online, I might as well correct, and add to, previous posts.

Later this week new Twenty One Pilots material is expected, so this might be a good time to add some remarks to a series of posts I ran last summer, trying to find a connection between Dema-lore and the actual history of the Bourbaki group. Here are links to these posts:

In the post “9 Bourbaki founding members, really?” I questioned Wikipedia’s assertion that there were exactly nine founding members of Nicolas Bourbaki:

I still stand by the arguments given in that post, but my opinion on this is completely irrelevant. What matters is who the Bourbaki-gang themself deemed worthy to attach their names to their first publication ‘Theorie des Ensembles’ (1939).

But wait, wasn’t the whole point of choosing the name Nicolas Bourbaki for their collective that the actual authors of the books should remain anonymous?

Right, but then I found this strange document in the Bourbaki Archives : awms_001, a preliminary version of the first two chapters of ‘Theorie des Ensembles’ written by Andre Weil and annotated by Rene de Possel. Here’s the title page:

Next to N. Bourbaki we see nine capital letters: M.D.D.D.E.C.C.C.W corresponding to nine AW-approved founding members of Bourbaki: Mandelbrojt, Delsarte, De Possel, Dieudonne, Ehresmann, Chevalley, Coulomb, Cartan and Weil!

What may freak out the Clique is the similarity between the diagram to the left of the title, and the canonical depiction of the nine Bishops of Dema (at the center of the map of Dema) or the cover of the Blurryface album:

In the Photoshop mysteries post I explained why Mandelbrojt and Weil might have been drawn in opposition to each other, but I am unaware of a similar conflict between either of the three C’s (Cartan, Coulomb and Chevalley) and the three D’s (Delsarte, De Possel and Dieudonne).

So, I’ll have to leave the identification of the nine Bourbaki founding members with the nine Dema Bishops as a riddle for another post.

The second remark concerns the post Where’s Bourbaki’s Dema?.

In that post I briefly suggested that DEMA might stand for DEutscher MAthematiker (German Mathematicians), and hinted at the group of people around David Hilbert, Emil Artin and Emmy Noether, but discarded this as “one can hardly argue that there was a self-destructive attitude (like Vialism) present among that group, quite the opposite”.

At the time, I didn’t know about Deutsche Mathematik, a mathematics journal founded in 1936 by Ludwig Bieberbach and Theodor Vahlen.

Deutsche Mathematik is also the name of a movement closely associated with the journal whose aim was to promote “German mathematics” and eliminate “Jewish influence” in mathematics. More about Deutsche Mathematik can be found on this page, where these eight mathematicians are mentioned in connection with it:

Perhaps one can add to this list:

Whether DEutsche MAthematik stands for DEMA, and which of these German mathematicians were its nine bishops might be the topic of another post. First I’ll have to read through Sanford Segal’s Mathematicians under the Nazis.

Added February 29th:

The long awaited new song has now surfaced:

I’ve only watched it once, but couldn’t miss the line “I fly by the dangerous bend symbol“.

Didn’t we all fly by them in our first readings of Bourbaki…

(Fortunately the clique already spotted that reference).

No intention to freak out clikkies any further, but in the aforementioned Weil draft of ‘Theorie des Ensembles’ they still used this precursor to the dangerous bend symbol

Skeletons anyone?

TØP PhotoShop mysteries

Published August 11, 2023 by lievenlb

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 Pisot and Chabauty were only guinea pigs at that moment (they later entered Bourbaki, Chabauty briefly and Pisot 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?

In this series: