## [0636] Hodge Theater

└ posted on Monday, 24 November 2014, by Novil

Ye Thuza is, of course, reading Shinichi Mochizuki’s infamous paper on „Inter-universal Teichmüller theory“: [1][2][3][4]. According to Mochizuki, it proves the abc conjecture, one of the most important conjectures in number theory. However, nobody has yet been able to verify his proof because it is so bizarre and complicated that nobody understands it.

I found words such as “Hodge theater” and “Inter-universal Teichmüller theory” incredibly funny, so I just had to make a comic about Mochizuki’s work. The blog posts of mathematicians like Caroline Chen about it are also funny to read:

On MathOverflow, an online math forum, […] Andy Putman, assistant professor at Rice University asked: “Can someone briefly explain the philosophy behind his work and comment on why it might be expected to shed light on questions like the ABC conjecture?” […] Or, in plainer words: I don’t get it. Does anyone?

The problem, as many mathematicians were discovering when they flocked to Mochizuki’s website, was that the proof was impossible to read. The first paper, entitled “Inter-universal Teichmüller Theory I: Construction of Hodge Theaters,” starts out by stating that the goal is “to establish an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve… by applying the theory of semi-graphs of anabelioids, Frobenioids, the étale theta function, and log-shells.”

This is not just gibberish to the average layman. It was gibberish to the math community as well.

“Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space,” wrote Ellenberg on his blog.

**Ye Thuza:** The F-symmetry is represented in a DΘ-Hodge theater HT by a category equivalent to the Galois category of fiite étale coverings of X.

**Ye Thuza:** On the other hand, each of the labels referred to above is represented in a DΘ-Hodge theater HT by a D-prime-strip.

**Ye Thuza:** That’s enough inter-universal Teichmüller theory for today. Now sleep tight.
**Yuna:** Unfair! Just when it started to get exciting!

@ Jerry:Can you please explain it to me? I’m still working my way through the prerequisites to whatever class these symbols are first presented in.

@ Dalek:I’m not sure I should answer that. 😉 It’s complicated. You’ll have to find clever girl and ask her. LOL@ Jerry:Ah yes! It is indeed an uncharted realm of humor for the simple reason that no one has as yet created a coordinate system able to express it! 😀The Doctor

McDouggalwrote:She lost me after “The”…

That girl is going to grow up to be a genius, and she will change the world.

…Whether or not it will be a good change is debatable.

It would be interesting to know how exactly she is narrating this special-symbol-superscript-subscript-laden text.

@ bogwombler:It appears to be a Tessaract based coordinate system multiplied by the square root of Minus One.

A couple bottles of 307 Ale are also recommended when trying to wrap the brain around the concepts.

Anyone else think that this is all an elaborate setup for a superhero webcomic? We have elastic Larisa, super smart Yuna, Cloud the swordsman, and Raging Bull of Destruction Sandra.

And Woo.

@ Jerry:I’ll buy that for a dollar! 😉@ TachyonCode:As I understand it, the mathematics community has done exactly that – sought clarification. It has not been forthcoming. Therefore I maintain my original assertion, with a slight modification:

All of your knowledge does nobody but you any good unless you can clearly express that knowledge so that it can be passed on in understandable form.

Not only this, but your death will also be the death of that knowledge unless you succeed in passing it on in a form which others can understand.

Others may rediscover your knowledge, but that is irrelevant and does not disprove my point.

The symmetry of the type found in the (finite field of size l with addition/subtraction and multiplication/division as the two operators) is fundamentally identical to a subset in a (complex set of things with associated operations/properties fulfilling some conditions) which consists of elements that can be mapped to elements of some other set.

The story is starting in medea res. I took a gander at the papers in question and noticed that one of the four papers (or 167 pages, if you will) was spent on the construction of the D-theta+-ell theater (can someone better at math than me tell me how to pronounce it?). The readers are expected to be familiar with the concepts by the time they get to this claim (whether or not that happens in practice is a different question).

To whoever suggested breaking the proof down to first-order axioms using computers, I think there are two problems with this:

1) We can’t even know for certain that the set of axioms we are using is consistent (see Godel’s incompleteness theorem)

2) There are way too many definitions to cover.

Is anybody else’s brain working after reading this?

@ Bisqwit:I’m pretty sure some symbols denote words (or phrases), purely from grammatical context.

@ Borson:Probably “Dee theta plus minus ell”. It’s identifiable quite well even this way.

The Solution to this is, of course 42.

@ Melkior:Comprehension is dependent on the context of the body of knowledge the person you’re trying to communicate your own to, not only your own ability to communicate.

Any assertion, no matter how obvious, is doomed to being lost if a) you can’t communicate clearly, b) clear communication is lost on the ignorant.

It is the job of the ignorant to seek education, regardless of who they have to ask for clarification.

It is the job of those who possess knowledge to share it, and to struggle alongside the ignorant for a means of communicating it with ease.

A failure of communication, therefore, cannot be defined

onlyby the lack of effectiveness of the ones who possess knowledge – it is a mutual failure on their partandon the part of the ignorant. Or, it is no one’s fault at all, and thus isn’t a failure of effort so much as it is theoppositeof an inevitable occurrence.I started reading this and was like… huh, this sounds somewhat like real math, not like normal math-gobblygook from media. What’s going on here? And then I read the last panel and realized what it was and that you had just taken the paper. Well done.

I have no idea why, but this has to be my favorite comic out of all of them. It might have something to do with Ye Thuza’s expressions in the first two panels, or the fact I still can’t figure out how the heck you’re supposed to read those gobbledygook equations, or whatever they are.

I also started reading the first paper, don’t ask me why, and I wasn’t aware someone could use the word ‘hodge’ that many times in just a few paragraphs. No wonder it gets people so confused…