post of little interest to anyone except possibly ursule.

[aryanhwy]

I have a recipe for writing papers that has served me quite well over the last four years. It allows me to pick a topic and churn out a ~15 page paper in about 4 weeks from start to finish; this includes doing all relevant background reading. However, the recipe is not entirely unproblematic, and as I follow it currently, I think I have identified two struggle points:

- When to introduce the formal language.
- When to introduce the implicit principles.

Both of these have the same issues: On the one hand, I keep hoping to arrange the paper such that the formal language is introduced in its entirety, and then it is applied to the specific problem I am dealing with. Likewise, a sense of decorum in me wants me to make explicit all of the implicit principles first, and then just refer back to them in the cases where they are used.

However, awkwardness arises in terms of justification. If I introduce the language and the implicit principles before I discuss the justification for my choice of language or for why I believe the implicit principles exist/are being used, then the end result seems sort of mystifying: Why these principles? Why this language? How did the author (a reader might wonder) come up with these? Yet if I try to discuss the justifications first, then I end up introducing both the principles and the language piecemeal, which is both frustrating, potentially unclear, and inelegant.

Worse, if I discuss the implicit principles before I've introduced the formal language, then I have to write them again, in the formal language, once the language has been introduced, and this seems needlessly duplicative. But since the justification for the formal language often consists in the necessity of being able to express concepts used in the implicit principles, if the justification is to come before the introduction, then I have to put the implicit principles first.

I feel like I'm stuck in a sort of vicious circle that I'm never quite sure how to get out of. Often times I just impale myself on one of the horns, and deal with the consequences, but I'm never entirely happy with the result.

This is probably not a situation that anyone reading this journal usually finds themselves in, with perhaps the exception of ursule, but if anyone has any advice, I'd appreciate it.

Comments

[badgersandjam.livejournal.com]

I introduce terms as necessary, or where they would make a good link in discussion. I don't think I've ever (except when writing a chapter on theory) ever defined them in one lump, then used them.

If a term is used heavily by a particular critic or theorist, I introduce it as a useful tool when I discuss that critic, and then happily continue to use it (referring backwards to and onwards from) in other parts of the discussion.

I've never had bad feedback doing that, FWIW

[aryanhwy.livejournal.com]

One contributing factor in the competition amongst ideals here is the traditional mathematical paper goes:

- definitions
- lemmas
- minor theorems
- corollaries
- main theorem

You might sometimes find definitions scattered in between the lemmas and stuff, but more often, they're as close to the beginning as is possible, because they're fundamentally presupposed by many of the other results.

[ursula]

Some advice I've heard about mathematical paper-writing, which I think is very striking but have not quite figured out how to practice, is that a good introduction to a math paper does something: it states the main theorem and describes its most interesting implications, or works out an example that demonstrates the method of proof, or illustrates the question that the main theorem will eventually answer, rather than just telling you who else has worked on this problem and what will be in the rest of the paper.

[ursula]

I think the papers I'm writing are much more experimental and less proof-oriented than yours are (and progress much more slowly; "I tried to do this for four weeks and it didn't work, so I tried something else" is pretty normal for me). In your shoes I'd try bouncing ideas off q10, who does formal linguistics.

[aryanhwy.livejournal.com]

Mine are experimental only in so far as I sometimes go through a lot of scratch paper working through proofs (often with many mistakes)! I think part of what is fueling some of my competing desires is that I want to present my results as if I didn't waste all of that paper, but actually knew from the start what the right things to prove are and how to prove them.

I'll drop q10 a line if you think he/she won't mind!

[ursula]

I think he enjoys theoretical discussions of this sort!

My guess is that in many cases you would be best off breaking down the implicit principles into several different categories, and then dealing with the principles AND formalisms of each category in turn. (I suspect struggling up front with what category fits where will produce a better paper in the end; that's how things seem to go for me, anyhow.)

[lumineaux.livejournal.com]

I do run into the same problems, but I'm not sure if any of the fixes when writing legal papers carry over to what you are doing. I will ponder it though.

[q10.livejournal.com]

I don't have any real wisdom on this. Here in linguistics, you have to give a lot of the motivating intuitions first, at least if you have any serious formalism, because plunging into the formalism without that loses too much of the audience. I definitely find that frustrating, but I think maybe it's not all a bad thing. There's something to be said for stating clearly and in ordinary prose what you're thinking and what you're trying to do, and, really, even quite mathematically literate people often don't absorb new stuff on the first presentation. As in many areas of life, a little redundancy is not always a bad thing.

So the best I can do is to say you have to accept a littler redundancy, and that, all things being equal, it's better if by the time you're unloading piles of formal definitions, people have at least a fuzzy idea of what you hope to accomplish. Beyond that, I don't have much. I'm not actually that good at this part, as the mix of clueless reviewer comments and ‘this is trivial and redundant’ reviewer comments accompanying various article rejections will attest.

[aryanhwy.livejournal.com]

Ah yes, "trivial and redundant", reviewereese for "this was immediately obvious to me and thus would be to everyone else". What I have found is that what people find "trivial" varies immensely!

Thanks for returning to this and sharing your thoughts. I actually gave a talk based on the paper I'm working on right now last Thursday, in a working session in my group, and that helped me clarify a bit more how to arrange things in this particular case. I don't always organize talks the same was as the papers they're based on, but while speaking I came across a few places where I definitely felt "I wish I had my formal language now so that I could say clearly and precisely what would be confusing to say in natural language". So for the time being I've introduced the bulk of the language upfront -- all the bits which are going to be familiar to my readers -- with a note that we will add to it as needed throughout the paper, when I introduce concepts and definitions that are *not* so familiar.

[q10.livejournal.com]

Yeah... I always want to write back to the reviewers ‘Yeah, I thought P was trivial too, but every time i said “well, obviously P”, i got a lot of blank stares, which made me think that maybe spelling out the reasons explicitly wouldn't be such a terrible contribution after all’.

[aryanhwy.livejournal.com]

every time i said “well, obviously P”, i got a lot of blank stares

Or worse, referees complaining that "P is by no means obvious or trivial, and a proof of it would be desired".