I know there is a rule against putting author notes as a separate chapter, but I personally think there is enough fiction here for me to get away with it. You won't report me, right? [smiles unconvincingly] Without further ado, then, I present to you...the

Appendix

General Notes
Until now, I have managed to avoid author notes. I had always considered that it would detract from the professionalism I was trying to achieve. Then I realized: Dude, this is fanfiction.

There has been a couple of people asking me about the Infinitesimals Priority Dispute, and even a few guesses. Unfortunately, these guesses were wrong because the truth was too random! In fact, it is the Avatar version of the dispute about who invented calculus. Now that I've posted an annotation for Dr. Best's The Infinitesimals Dispute, the "secret" is out! For more details, see below.

I know that this is not a conventional annotated bibliography. Apart from the lack of proper citations, the annotations are way too long. I explain these anomalies as follows: scholarship in the Avatar World evolved differently. They don't care which publisher published a book. As long as they can get a hold of the title and author (and edition, if need be), scholars there are fine. As for the annotations, I give here an excerpt from...the

Preface to the 11th Edition of the Annotated Bibliography of the Avatar

[...] The recent earthquake in Ba Sing Se and the subsequent destruction of countless priceless manuscripts have placed the Bibliography in a unique position: it is now the sole record of many, many lost documents. In it are preserved, in the form of our annotations, the last vestiges of much lost knowledge. In light of this sad development, the editorial board has implemented a new policy. We have decided to expand the annotations where appropriate, to form a better summary and evaluation of each document. It is hoped that this policy will aid in the preservation of knowledge should any such event occur again. [...]

In other words, the Annotated Bibliography evolved over time into something quite different from what its title implies (and also quite different from what it started out as). And no, I did not pull the above excerpt out of my ass. I was going to put it in the Preface to the 20th Edition, but decided not to. Anyways, my final justification is this: artistic licence.

Speaking of which, I completely made up the lives of the Gaang after the war. It is all original. I usually make it up on the spot, but I try to be consistent. As for events before and during the war, I try to be as faithful as possible to canon as a matter of course...which leads me to the numbering of the Avatars that some readers may have noticed. I estimated the number of Avatars (assuming there is a finite number of them) by estimating the number of Avatar statues found in the sanctuary of the Southern Air Temple. My estimate gave me about 310. Assuming an average lifespan of about 75 years, this sets the time of the First Avatar at well over 20,000 years ago. You are welcome to debate with me on this; I only did this because I needed a number.

It may be of interest that the Avatar Hong sometimes referred to (and whom I made up) was a bookworm of an Avatar who took up a position as a professor of history instead of keeping balance in the world the conventional way. I have placed him at seven reincarnations after Aang—he is the second Fire Nation Avatar after Avatar Roku.

Avatar Aang: Collected Letters
Letter 194 began as follows: "To the idiot who sits on the throne of Ba Sing Se: What the hell have you been doing?..."

Life of Avatar Aang
You may interpret "hundred-and-sixties" to refer to Aang's biological age or his chronological age. It matters not to me.

My Husband, the Avatar
If you're wondering whether I really think Katara wrote porn about her relationship with Aang: no.

Sab-I Luoman is…well…sound it out.

A Cabbage Merchant Remembers
Ga'ai-shi, the name I gave to the Cabbage Merchant, is an anomalous transliteration of the Cantonese word for "street market".

Lives of the Avatars
See the Preface if you don't remember this one.

The Cave of Two Lovers, Wan Shi Tong's Library and Energybending: A Critical Analysis of the Available Evidence
1/8 Riwu-Monkey is to be read as "the first day of the eighth month of the year Riwu-Monkey". This is taken from the reading on the calendar in Wan Shi Tong's planetarium when Sokka and Aang finds the date of the next eclipse. In Chinese it would be much better intelligible: 氜武猴年八月一日. Riwu, or 氜武, is a year-name that appears to be paired with an animal from the Chinese zodiac to give the name of a particular year. In accordance with this, I took "Yuanzheng" from another reading on the dial and randomly paired it with the Serpent to give "Yuanzheng-Serpent".

The Rise of Firelord Zuko
The reason Zuko's acts before his coronation were not included in Firelord Ozai: Rise, Reign, Downfall (Ozai's official biography) is because that book was too full of criticisms of Ozai for there to be any room for Zuko. I think. Also, Irah is not the same as Ilah. I like to imagine that Zuko wanted to name a child after his uncle.

One example of the inconsistency of the RFNHA's work: they praise Sokka's ingenuity in the beginning and end of The Rise of Firelord Zuko, but damn him up and down for being a plagiarist in the middle part. That's what you get when you get a government organization to write a biography!

Son of the Avatar: A Diary
The original title of Jinzu's diary was "Meditations and Discourses on Human Nature from First Principles, in which is shown that the Desire and Will to Live, or to Perpetuate Oneself by any Method, is the cause by which Humans, and in general all Living Beings possessed of Sentience or not, act in the way we observe them to; and in which is exposed as an overarching Fallacy of Human Thought the Notion that there can be any Distinction made between True and False Knowledge, it being shown that the Human Mind, and in general any thing capable of Thought, is to a great Degree completely incapable of distinguishing between Truth and Falsity; and from these and other First Principles, set on the ground of impervious Logic, the closest tool available to Human Beings of acquiring Knowledge, it is finally shown that Existence itself is a Grand Fallacy, there being, in truth, nothing existing at all except Nothingness itself". No word of a lie.

With this instalment, all of Aang and Katara's children except the first and last ones have been named. Can you guess the names of the oldest and youngest of their children?

If you are wondering what happened to the recipe after it was found: Katara had wished for the recipe to be passed down to her eldest daughter, and left her a secret note to that effect. Her daughter simply took the recipe after it was found and forgot to tell anyone about it. As for the unrecognizable handwriting…your guess is as good as mine!

Four Variations on "It's a Long, Long Way to Ba Sing Se"
I always thought Aang would make a great musician; that, as well as the song "It's a Long, Long Way to Ba Sing Se", inspired me to write this one. I figure, though, that good ol' angsty Zuko would make a better one!

The Avatar Returns
In a fit of madness, induced by my first watching of The Ember Island Players, I wrote a title page, a "Foreword from the Librettist" and the first few lines of a libretto for an opera entitled The Avatar Returns in response to Pu-on Tim's crappy play. I then told my friends I'd write an Avatar opera. Unfortunately (or fortunately, rather), that opera went nowhere. However, the Foreword and the beginning of the opera are still sitting on my hard drive. Now I can put them to use!

A leitmotif is a distinctive musical theme or other "coherent musical idea, clearly defined so as to retain its identity if modified on subsequent appearances, whose purpose is to represent or symbolize a person, object, place, idea, state of mind, supernatural force or any other ingredient in a dramatic work" (Grove Music Online). The music of Avatar is so ridiculously full of them, one could almost figure out the action just by listening to the music! The "Avatar leitmotif", of course, is the four-note sequence that shows up anytime anything distinctly Avatar-related comes up. At the very end of the very last episode, it's that leitmotif that ends it all. To me, Avatar just isn't Avatar without it.

I know someone else—I think their pen name was samtana—calls them idées fixes. That is another name for leitmotifs, but I don't like calling them that. It smacks too much of Berlioz. Berlioz sucks—his most famous idée fixe, from his Symphonie fantastique, is not nearly as distinctive as the ones in Avatar. In fact, no matter how many times I listen to that demented piece I never hear it! But that's just me.

Remembering Toph Beifong
Well, not everyone could have a happy ending! Poor Toph, going out with her students to prove to herself she wasn't actually in love with Sokka…

Almost Firelord: Princess Azula's Life
I wonder how Azula would feel if she knew that, despite all her accomplishments, barely anyone remembers her?

The Virtues of Vegetarianism
The Epoch Times is a real newspaper. Its editorial policies can be…questionable.

Energybending
I realize this is getting slightly old. To be honest, I'm just going through my list of titles while I figure out the details of my next mini-series. Wang Fire, anyone?

Battle for the North Pole
"Now I shall throw some random facts about dimension at you" is an actual quote from one of my professors. He's named Dr. Pei (what a coincidence!), and couldn't teach a kangaroo how to jump if his life depended on it.

The Infinitesimals Dispute
Finally, it's out! The Infinitesimals Priority Dispute is really just the calculus priority dispute in disguise. When I read about Newton and Leibniz squabbling over who invented calculus first, I was inspired to import it into the Avatar world. But who would be ingenious enough to come up with calculus? Almost immediately the answer came to me: Sokka and Zuko. Out of the many major and minor characters in Avatar, they seemed to me the only viable options. Azula would have been able to do it if she set her mind to it, but she went crazy; probably also the Mechanist, but in my conception he only worked on differential calculus. Besides, a Sokka and Zuko squabble appealed to me.

This is not the place to discuss the principles of calculus, unfortunately. It would take too much space. I leave that task to more competent hands.

You'll notice that some of the mathematical terms I used are different from the ones used in real life. It's a different world, after all. When they develop a concept, who says they have to use the same name for it that we do?

For the convenience of mathematically-minded readers, here is a list of the terms I used and their real-world equivalents (though such readers could probably figure them out anyways):
theory of infinitesimals: calculus
infinitesimal quotient: derivative
continuous summation: (definite) integral

I never did come up with a term for the indefinite integral—it turned out I didn't need it—but I played with "inverse infinitesimal quotient".

I did not assign the roles of Leibniz and Newton to Zuko and Sokka, nor did I attempt to reproduce mathematical history literally. Rather, I thought about what would influence them to invent calculus, and how they would develop it given their personalities. If the history I made up seems unrealistic, that's the reason. Do forgive me, and certainly let me know!

The product rule for derivatives is sometimes called the "Leibniz rule". This inspired me to name the power rule (for integrals) "Zuko's rule".

As a final note, Dr. Best was my calculus professor for my first term in university. He really is the best (pun intended)!

Firelord Zuko and Chief Sokka—Who Had Priority?
You know, I could never write a fanfic without making ridiculous references to remotely related topics. Hence, this whole "Zuko and Sokka invents calculus" thing. There are a number of references to actual mathematicians and quotes in this one. See if you can't identify them!

A Theory of Infinitesimals
Lifespan after angering Suki: if carrying sword and boomerang, 5.7 minutes. If carrying only boomerang, 3.3 minutes. If carrying only sword, 3.1 minutes. If carrying neither, 5.5 seconds.

Avatars and their Animal Friends
Avatar Yinsi came just before Avatar Hong. He was convinced that he was destined to live a life of adventure (which he mostly did), and was also something of a womanizer. (Aang had seven children. Yinsi had seven wives.) So that should give you a sense of timing as to when this book was written... and also why Cheung wrote the book, not Yinsi himself.

And yes, you read right: Momo and family. Turns out a female flying lemur had fallen into the hands of an Earth Kingdom noble, who was attempting to breed a flying turtleduck-lemur. Aang tried to buy her for money, but the nobleman refused. No one really knows how Aang got her in the end, but that nobleman never showed his face during the full moon ever since.

The Fire Temple Defenestrations
Yes, I'm still among the living! It may be four months, but by God I haven't forgotten about this fic! I haven't been posting stuff because I've just gone through a very difficult term. (I'm in physics, and this term they forced quantum mechanics down our throats. You know, Schrödinger's cat that's both alive and dead at the same time, wave-particle duality, that sort of thing... If you think this stuff is conceptually hard, try doing the math!) Hopefully I'll be able to put up another chapter or two during the holidays. But for now, we have actual notes!

By the time this incident takes place, Zuko had pretty much replaced all the ministers with people more-or-less loyal to him. That means Qin, the old War Minister, was tending his little garden in some obscure corner of the Fire Nation when all this happened. Unfortunately, in this particular case it was a bad move replacing the easily-cowed Qin with the not-so-easily-cowed Han. Should have listened to Iroh...

As for the Culture Minister: yes, that's the same Jee who was lieutenant on Zuko's old ship. He was sick of fighting, so when Zuko offered him a job he decided he wanted to organize performances of Pu-on Tim plays instead of fussing over the troops. Unlike many, he actually got a laugh out of The Boy in the Iceberg.


NOTE TO ALL READERS: I am running out of ideas! Please, please, please send in your ideas! I'll credit you for it and everything!

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