#andre weil

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

数学文化 Vol 3 No. 1 Mathematical Culture. Download this issue here. Recent issues (four per year) available for USD 10/yr. About that Prime Number Stuff 素数的那些事儿 Lu Jun (陆俊) English translation of an article in Mathematical Culture (数学文化), vol. 3, no. 1, pp. 29-37. About the author: Lu Jun 陆俊 is a lecturer in the Department of Mathematics at East China Normal University. His field is algebraic…