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:
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.
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”.
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:
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…
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
The Clique (Twenty Øne Piløts fanatic fanbase) is convinced that the nine Bishops of Dema were modelled after the Bourbaki-group.
It is therefore of no surprise to see a Photoshopped version circulating of this classic picture of some youthful Bourbaki-members (note Jean-Pierre Serre poster-boying for Elon Musk’s site),
replacing some of them with much older photos of other members. Crucial seems to be that there are just nine of them.
I don’t know whether the Clique hijacked Bourbaki’s Wikipedia page, or whether they were inspired by its content to select those people, but if you look at that Wikipedia page you’ll see in the right hand column:
Founders
Henri Cartan
Claude Chevalley
Jean Coulomb
Jean Delsarte
Jean Dieudonné
Charles Ehresmann
René de Possel
André Weil
Really? Come on.
We know for a fact that Charles Ehresmann was brought in to replace Jean Leray, and Jean Coulomb to replace Paul Dubreil. Surely, replacements can’t be founders, can they?
Well, unfortunately it is not quite that simple. There’s this silly semantic discussion: from what moment on can you call someone a Bourbaki-member…
But, before the Besse-meeting there were ten ‘proto-Bourbaki’ meetings, the first one on December 10th, 1934 in Cafe Capoulade. These meetings have been described masterly by Liliane Beaulieu in A Parisian Cafe and Ten Proto-Bourbaki Meetings (1934-35) (btw. if you know a direct link to the pdf, please drop it in the comments).
During these early meetings, the group called itself ‘The Committee for the Treatise on Analysis’, and not yet Bourbaki, whence the confusion.
Do we take the Capoulade-1934 meeting as the origin of the Bourbaki group (in which case the founding-members would be Cartan, Chevalley, De Possel, Delsarte, Dieudonne, and Weil), or was the Bourbaki-group founded at the Besse-congress in 1935 (when Cartan, Chevalley, Coulomb, De Possel, Dieudonne, Mandelbrojt, and Weil were present)?
07-1935 is the Besse-congress, 09-1936 is the ‘Escorial’-congress (or Chancay 1) and 09-1937 is the second Chancay-congress. The ten dates prior to July 1935 are the proto-Bourbaki meetings.
Even though Delsarte was not present at the Besse-1935 congress, and De Possel moved to Algiers and left Bourbaki in 1941, I assume most people would agree that the six people present at the first Capoulade-meeting (Cartan, Chevalley, De Possel, Delsarte, Dieudonne, and Weil) should certainly be counted among the Bourbaki founding members.
What about the others?
We can safely eliminate Dubreil: he was present at just one proto-Bourbaki meeting and left the group in April 1935.
Also Leray’s case is straightforward: he was even excluded from the Besse-meeting as he didn’t contribute much to the group, and later he vehemently opposed Bourbaki, as we’ve seen.
Coulomb’s role seems to restrict to securing a venue for the Besse-meeting as he was ‘physicien-adjoint’ at the ‘Observatoire Physique du Globe du Puy-de-Dome’.
Because of this he could rarely attend the Julia-seminar or Bourbaki-meetings, and his interest in mathematical physics was a bit far from the themes pursued in the seminar or by Bourbaki. It seems he only contributed one small text, in the form of a letter. Due to his limited attendance, even after officially been asked to replace Dubreil, he can hardly be counted as a founding member.
This leaves Szolem Mandelbrojt and Charles Ehresmann.
We’ve already described Mandelbrojt as the odd-man-out among the early Bourbakis. According to the Bourbaki archive he only contributed one text. On the other hand, he also played a role in organising the Besse-meeting and in providing financial support for Bourbaki. Because he was present already early on (from the second proto-Bourbaki meeting) until the Chancay-1937 meeting, some people will count him among the founding members.
Personally I wouldn’t call Charles Ehresmann a Bourbaki founding member because he joined too late in the process (March 1936). Still, purists (those who argue that Bourbaki was founded at Besse) will say that at that meeting he was put forward to replace Jean Leray, and later contributed actively to Bourbaki’s meetings and work, and for that reason should be included among the founding members.
What do you think?
How many Bourbaki founding members are there? Six (the Capoulade-gang), seven (+Mandelbrojt), eight (+Mandelbrojt and Ehresmann), or do you still think there were nine of them?
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).
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).
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’).
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.”
“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.
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.
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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