why do you think they added the extra symbols to the logo? like a protective layer? like a jumpsuit? idk
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.”
Considering the importance of predecessors on Trench (the mention of “succession” in Neon Gravestones, and the importance placed on ancestors in that song and Legend), considering the importance of the vials as empty things that are worshipped, considering the fact that the Bourbaki group was interested in using mathematics to incontrovertibly prove (think Implicit Demand) metaphysical notions like the existence of God using concepts like the empty set - I would not be surprised if the logo change really was This Deep.
