#bourbaki

❤️ Leonor and Sofía ❤️

La mort de Bourbaki

Dans la lignée dadaïste de sa naissance, le faire-part de décès suivant fut publié pour annoncer la « mort » de Nicolas Bourbaki :

« Les familles Cantor, Hilbert, Noether ; les familles Cartan, Chevalley, Dieudonné, Weil ; les familles Bruhat, Dixmier, Samuel, Schwartz ; les familles Cartier, Grothendieck, Malgrange, Serre ; les familles Demazure, Douady, Giraud, Verdier ; les familles filtrantes à droite et les épimorphismes strictes, mesdemoiselles Adèle et Idèle ;

ont la douleur de vous faire part du décès de M. Nicolas Bourbaki, leur père, frère, fils, petit-fils arrière-petit-fils et petit-cousin respectivement pieusement décédé le 11 novembre 1968, jour anniversaire de la victoire, en son domicile de Nancago. La crémation aura lieu le samedi 23 novembre 1968 à 15 heures au cimetière des fonctions aléatoires, métro Markov et Gödel. On se réunira devant le bar « aux produits directs », carrefour des résolutions projectives, anciennement place Koszul.

Selon les vœux du défunt, une messe sera célébrée en l'église Notre-Dame des problèmes universels, par son éminence le Cardinal Aleph 1 en présence des représentants de toutes les classes d'équivalence et des corps algébriquement clos constitués. Une minute de silence sera observée par les élèves des Écoles normales supérieures et des classes de Chern.Car Dieu est le compactifié d'Alexandroff de l'univers, Grothendieck IV, 22. »

So I know this is probably not what you were expecting but I am going to attempt to explain what I think the logo change means using math.

*deep breath*

So as we know, Andre Weil, founder of the Bourbaki group, introduced and popularized the use of the Ø symbol to denote an empty set in mathematics. it’s important to understand that Ø isn’t exactly the same as nothing - it is, as its wikipedia article says, “rather […] a set with nothing inside it and a set is always something. This issue can be overcome by viewing a set as a bag—an empty bag undoubtedly still exists.” This is familiar to us as twenty one pilots fans - empty vessels; negative space. Sort of makes you wonder whether Tyler’s recent “can you touch a hole” comment was maybe Deeper Than Previously Thought, but I digress. 

Here’s where it gets interesting, and where I think the logo comes in. If I’m understanding this correctly, it is possible to add value to an empty set, because all natural numbers are a reflection of the empty set. The following excerpt is from an article called “World as the Empty Set”: 

“First of all it is important to differentiate Ø from {Ø}. Former is the empty set (which contains no elements) and the latter is the set containing the empty set as its member. So {Ø} is one member set and more than just that, {Ø} is the one itself. As we previously mentioned, every natural number has its immediate successor (for one that is two, for two - three; generally, successor of n is equal to n+1). Even more, we define natural numbers as a collection of these successors […] Therefore, every natural number is actually a set containing its predecessor as the element.” 

The author is essentially saying that while the set Ø is empty, if you put that inside a set of its own, {Ø}, that set is not empty because it contains one element - the empty set. Therefore, the elements in the set are equal to one. Similarly, {{Ø}} is a set that has two elements and is equal to two, and {{{Ø}}} is equal to three, and so follow all natural numbers. 

I think the relationship between |-/ and ||-// is the same as the relationship between Ø and {Ø}. I think that by putting an extra two lines around the original logo - something that Tyler has said he and Mark created as an empty symbol that later became filled with meaning - he is adding value to it. He’s is creating a set that contains an element, instead of containing nothing. He’s filling the vessel. 

The author also follows her discussion of this succession pattern with this: “And finally, what is one? One is the first natural number, and the only number without a predecessor. {Ø} carries the code of all existence - the empty set.” 

*Note* I didn't come up with all this myself I'm mostly just relaying information and adding my own theories...

In 20th century France there was a group of 9 mathematicians that went under the collective pseudonym of Nicolas Bourbaki. This may be where we get the name Nico. The 'de facto' or early leader of this group's name was Andre Weil. If you go to his wikipedia page we find this picture.

Doesn't that boy to the side look familiar?

Andre Weil is also well known in the clique for inventing the symbol ø, mathematically this symbol means empty set. Andre Weil and his group of nine are also known for proving the existence of God.

"God exists since mathematics is consistent, and the Devil exists since we cannot prove it." -Andre Weil

This may have to do with Josh and Tyler's personal beliefs, and even the reason they use the ø symbol.

Sources: https://www.reddit.com/r/theoryonepilots/comments/8f10ev/the_9/

https://en.wikipedia.org/wiki/André_Weil

I actually really think your original interpretation is still valid, and not at all mutually exclusive from the story tyler has presented - especially when you think about it in terms of how the Bourbaki group actually functioned. there were 9 main members of the group, but none of them were actually Bourbaki. Nicolas Bourbaki was a name they all used, shared, passed around, published collectively under. In that sense, Nicolas Bourbaki really was like a ghost - he didn’t exist, but it was a persona that any of the 9 could take on, and because there were really 9 people’s ideas and minds behind it, the name had more more power.