## [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!

I reading code and learning Basic to be more interesting.

This explains the nuclear reactor.

@ Switch Master:“I reading”? Curse you iPhone!

And then there’s me who can barely comprehend trigonometry…

I understood some of those words.

Now I am imagining Larisa in full-plate armour marching up to Shinichi Mochizuki and hitting him over the head with a rubber chicken. >:=)Monty Python)>

Or Yuna sitting in front of a large fishbowl, scribbling complex equations and measurements…

Larisa: *marches up to bowl, points finger* Let there be light!

Fishbowl: *Big Bang, universe starts forming*

Yuna:

Dilettante!!!D-:>:=)>

Little girls who are grounded until the end of eternity don’t get to stay up late listening to things that may or may not actually be complex mathematical proofs.

I love the look on on Ye-Thuza’s face for this one as she’s reading…. almost wish we could have gotten a soundbite to go along with it.

Hilarious!

I think that’s what happened when someone working alone for a long time. They are too deeply entrentched in their world they start making up words to represent something. I think that Japanese guy need to do it live to help people to actually understand.

For me? I’m hopeless in math, so I just sit here gawking at that theory and drool.

*head explodes*

My…head…hurts

Hm… i need to look up that notation… Seems kinda weird… But the math in here is probably not harder than what I had in my 2nd year in university…

I was wondering if I just hadn’t learned that yet. Nope, completely incomprehensible. Good to know. (Math grad student here).

This comic proves Sandra’s comment about which family is weirder in the previous strip…

This reminds me of a quote about a theoretical physics paper which claimed (more or less) to describe the conditions before the big bang: “Scientifically, it’s clearly more or less complete nonsense, but these days that doesn’t much distinguish it from a lot of the rest of the literature.” – Dr. Peter Woit.

Agreeing that some of that notation just looks plain wrong. Operators are meaningless without their operands correctly placed, and the notation here includes certain operators without operands in the proper places.

If it looks like gibberish, even to the members of the target community, then perhaps it is indeed gibberish. I would not put it past a previously unknown individual to create a ridiculously complex piece of nonsense cobbled together from bits and pieces that might or might not make sense on their own, for the express purpose of watching the greater community scratch its collective head.

I read that first as a ‘do tell’ hodge theatre. ‘How does this Hodge-podge work?’ ‘Do tell’

What’s the big deal? The logic is as plain as day when you take into account Frobisher’s quantum modal vibrations. I’ve seen it often assert itself as a 6th order plenum intersection of the connifling vector into parallel Branes. String theory predicts both hollow convex and concave Hodge Theater constructs where Heisenberg’s uncertainty principle applies both positively and negatively. The beauty of this theorem manifests itself when implemented in the fabrication of the Alludium-Fosdex space torque modulator which was patented in the late ’80s by Marvin Martian. Hope this clears up any misunderstanding incurred.

Sincerely,

The Doctor

I keep reading it as “DO-tell Hodge theater.”

Ah, ninja’ed.

Sir Read-a-Lotwrote:It’s worth pointing out that Peter Woit has an axe to grind. He’s a mathematician (not a physicist) who’s been complaining for years about today’s physicists not being as bright as… basically him. He wrote a popular book attacking physics and ever since then the media has treated him as the go-to expert on physics issues despite the fact that he really has no particular distinction in that field beyond being an unusualy loud troll.

That said, the event you’re referring to, the Bogandov Affair, has been pretty widely agreed to be a rare case of peer review failure. A nonsense paper slipped through. It happens. I doubt very much that Woit’s assertion that most of modern physics publications are nonsense has any truth to it at all. He’s pretty famous for his over-the-top trash-talking.

Mochizuki is a genius. His proof is almost certainly not nonsense, but it might turn out to be incorrect. The reason nobody can understand it is that he has developed a whole theory on his own without explaining it very well to his audience. Louis de Branges’ claimed proof of the Riemann Hypothesis has the same problem: he’s a well-known genius, but he developed all the theory on his own and doesn’t make an effort to explain it to his audience, so his proof has been ignored despite the fact that it is almost certainly not nonsense.

bogwomblerwrote:Huh?

To be honest, the problem I see with his proof isn’t just the lingo, but the arrangement of the sentences. It might be a translation issue, but the sentences are almost Shakespearean in their structure. In addition, number theory tends to give really long and unreadable names to concepts that are very similar (even moreso than most other branches of math).

In plainspeak: The paper sounds like Shakespeare wrote an essay explaining all the phrases he invented which hardly existed at the time. Except he wrote it using said phrases. Also imagine the essay didn’t flow well at all, to the point where you didn’t know what was explaining what. That’s the English major equivalent to this proof.

@ Switch Master:I’m pretty sure he made most of that up, considering “Alludium-Fosdex” a.k.a. the ‘shaving cream atom’ was central to the plot of Duck Dodgers, a cartoon short from 1953. Also there’s no such thing as a ‘connifling vector.’ And lastly, most of the things he mentions that are actually words are used incorrectly.

This actually illustrates a very important fact:

It makes not the slightest difference that you understand what you’re talking about. If nobody else understands what you’re talking about, then you might just as well be speaking nonsense.

Or, to put it another way:

Clarity of expression is key to transfer of knowledge. If you fail at clarity of expression, all of your knowledge is worthless.

@ mrdoomydoom:Ya think! 😉 Tongue imbedded firmly in cheek. LOL8

@ Switch Master:It’s complicated.

The Doctor.

@ Melkior:That sounds like a political normal talk. Now one under stand them so…

Melkiorwrote:Let me disagree with the sentiment here. Mochizuki’s already done the most important step: Publishing his results. If people want it badly enough, it can be deciphered. Calling that “worthless” seems to me to be insulting to him and very ill-considered of you.

I’m not saying the ability to explain yourself to other people isn’t extremely valuable – in science as much as anywhere – I just object to the tone.

Okay, between this and the working cold fusion reactor, Yuna is scaring me.

It’s all Greek to me. (Points if you get it.)

Hey, if anyone hasn’t figured me out yet, I like to poke fun and wind people up. Tickle, tickle! 😀

Crestlingerwrote:And the first mathematical expression reads “Fix it” ;3

Ye lost me at “The”.

@ bogwombler:Are you The Doctor in disguise?

Anyone else think “Frobenoids” sound like they were created by the Wizard of Frobozz after he was exiled by Lord Dimwit Flathead the Excessive?

Tsunamiwrote:Dante? (The Italian poet, not the videogame character)

@ Switch Master:bogwombler just chained arbitrary words from math or physics as an example to DanialArin’s comment. (And maybe to see if someone would take it seriously. Though IMO it’s quite obvious that quantum mechanics doesn’t go into number theory. ^^)

Uh…

What the heck is she talking about? Math was never my strong point.

@ Tsunami:Cassius in Julius Caesar? At least I think it was that character…

Math is Sandra’s strongest subject, but here Yuna is completely overshadowing her. It also makes strip 243 lose some of its points, at least in my mind. Not a big deal though.

Are anabelioids people who look like they should be called Annabel, but aren’t?

Two thoughts:

First, the statement that no one in the math community can understand this anymore than laymen can reminds me of a line from the Sherlock Holmes stories; Professor Moriarty was said to have written “

The Dynamics of an Asteroid, a book which ascends to such rarefied heights of pure mathematics that it is said that there was no man in the scientific press capable of criticizing it.”Second, Yuna’s interest and apparent understanding of this topic brings to mind one of the testing scenes from the first Men in Black movie, when Edwards, not yet “J,” blew away the image of a little girl because she was carrying a thick physics textbook — and he knew that a girl that age, if she had a book like that, must be up to no good….

Yuna’s unsavory procedures in her quest for cold fusion — destroying

Princess Mononokefigures, ye gods! — reveal that she, too, must be up to no good. Cloud’s little sister is an EVIL mad scientist.If it’s incomprehensible to _read_ those papers, imagine what it’s like to _listen_ to them!

“The F sub one superscript X plus-minus end-superscript dash symmetry is…”Can you visualize/reconstruct Ye Thuza’s speech-balloon from that?

And, yes, I’ve heard of the Bogandov brothers. First thing that came to my mind.

Caroline Chen though, seems to think Mochizuki is serious; i.e. not playing a joke on the math community, though she considers his unwillingness to explain further unhelpful, to say the least.

Melkiorwrote:The Dada movement would like to leave a ready-made word with you: “No.”

In any event, Confucius had the right of it: “Real knowledge is to know the extent of one’s ignorance.”

Observation is, by definition, chaos; you cannot meet a vacuum in which this chaos is absent, for only in that void are

all observersabsent.Therefore: If you do not understand what someone is talking about,

take responsibilityfor your own little piece of chaos – and.seek clarification@ DanialArin:No, you can easily have an operator algebra without refering to the space that operators act on in your notation. Matrices are a very good example.

As far as reading this stuff goes… sheesh. It’s a good example of how just reading the names and various words that come up lets you gauge the difficulty of whatever is being discussed in an article.

Anything containing the name “Hodge” will likely be too complicated for mere engineers. The word “category” being used repeatedly means only professional pure mathematicians(and some theoretical physicists) will understand it. “Étale” being applied as an adjective to anything means that only a few mathematicians in the finest universities will understand it. Words that when googled lead directly to the author’s wikipedia page mean that only the author himself understands the stuff.

To quote Shakespeare:

“Words. Words, words.”

boson colliderwrote:Words that when googled lead directly to the author’s wikipedia page mean that only the author himself understands the stuff.

Not quite. Saidi and Yamashita, at least, seem to understand it. Though Mochizuki says it took them half a year of study to get to that point. Yamashita is working on a simplified version of the abc conjecture proof that mathematicians are hoping will clarify things a bit.

Melkiorwrote:I agree about transfer of knowledge, but not quite about “all your knowledge is worthless”. Knowledge is useful for plenty more than just explaining things to other people. I’m absolutely terrible at explaining things, but I’ve managed to write all kinds of useful, working software based on ideas that I couldn’t explain to anyone in words.

It would not be unprecedented if his theory was not merely gibberish to laymen and experts, but just plain gibberish. To the point where someone had already created a program that automatically creates a mathematical abstract. And there’s a funny story about that: The output of the program got published in a respected science magazine (I forgot which, was a long time ago when I read about it). It was done to prove that the magazine editor weren’t proof-reading or peer-reviewing their publications, and were simply allowing any paper that looked “sciency”.

To get back to the topic. If this guy’s theory has implications in math, then it should be possible to write it as a first-order logic axiom set, which would allow a computer to verify the validity of his proof. All that would remain, then, is for other mathematicians to analyze the logic and validity of his axioms, and see how they hold up compared to existing axiom sets, lemma, and testable cases.

For instance, it may be discovered that the ABC conjecture (or a corollary, or a generalization) is actually taken as a hidden assumption within the axioms.

There is no need for complex terminology. The beauty of math is that it can be presented in a completely symbolic form, without words. In that form, it has a deterministic and consistent makeup, that can be properly understood even by a slightly intelligent 10-year-old.

So, in short: Don’t be impressed by big arcane buzzwords. The best mathematical theories have always boiled down to the same basic set of symbols.

I’m frankly amazed that no one has yet mentioned the Obvious.

That paper on Inter-universal Teichmüller theory is actualy both True and the qorld’s greatest example of a polylinguistic PUN.

Expressing Puns as Mathmatic formulas is an as yet uncharted form of humor.

This is an amazing blend of the languages of English, Physics and Mathmatics that will go down in history as the final proof that All Mathmatics is actually God making Puns with the Universe.

I’m a calc student and what is this i don’t even

I’m seriously lost.