Thursday, November 14, 2013

The many stages of writing a paper, and how to close the deal.

[tl;dr] Producing a piece of research for publication has many stages, and each stage has different needs, requiring different ways of operating. Learning these stages is a key developmental step for a graduate student. In what follows, I describe this process.

Caveat: this is obviously customized to more theoretical-style work, although I'll talk about how experimental evaluation fits in, in the context of my work. So YMMV.

From my conversations with students (mine and others), I think this accurately describes how students think a paper gets written:

  1. Advisor produces problem miraculously from thin air. 
  2. Come up with solution.
  3. Write down solution
  4. Advisor makes annoying and mystifying edit requests on irrelevant introductory stuff, while throwing out long complicated proofs (or experiments) student has spent many hours sweating over.
  5. Make final edits and submit paper.
Most student figure out  how to do 2) , and eventually learn how to do 3) (which is itself a topic for another post). 5) is probably the first thing students learn how to do: fix typos, edit latex, and generally do yak-shaving.

But step 4) is perhaps the most mysterious part of the writing process for a new researcher, and the least structured. I call it "closing the deal" and it's really about going from a bag of results to an actual submittable paper. 

Let me elaborate.

1) Coming up with a problem.
    Of course coming up with a problem is the essence of the research process ("it's about the questions, not the answers", he shrieks). This takes experience and vision, and can often be changed by things you do in stage 4. I'll say no more about it here.

2) Solving a problem.
    This is the stage that everyone knows about. That's what we do, after all - solve problems ! This is where we drink lots of coffee, live Eye of the Tiger montages, get inspiration in our sleep, and so on. 

   It often happens that you don't exactly solve the problem you set out to attack, but you make many dents in it, solving special cases and variants. It's important to be flexible here, instead of banging your head against a wall head-on. At any rate, you either exit this stage of the project completely stuck, with a complete solution, or with a collection of results, ideas and conjectures surrounding the problem (the most typical case)

3) Writing it all down.
   Again, I could spend hours talking about this, and many people better than I have. It's a skill to learn in and of itself, and depends tremendously in the community you're in.

4) Closing, or getting to a submission.
    But this is the part that that's often the most critical, and the least understood. I call it "closing the deal": getting from 80% to 100% of a submission, and it requires a different kind of skill. The overarching message is this:
A paper tells a story, and you have to shape your results - their ordering, presentation, and even what you keep and what you leave out - in order to tell a consistent and clear story. 
(before people start howling, I'm not talking about leaving out results that contradict the story; that would be dishonest. I'm talking about selecting which story to tell from among the many that might present themselves)

So you have a bag of results centering around a problem you're trying to solve. If the story that emerges is: "here's a problem that's been open for 20 years and we solved it", then your story is relatively easy to tell. All you have to do is explain how, and using what tools. 

But in general, life isn't that easy. Your results probably give some insights into the hard core of the problem: what parts are trivial, what directions might be blocked off, and so on. 

Now you need to find/discover the story of your paper. You can't do this too early in the research process: you need to explore the landscape of the problem and prove some results first. But you shouldn't wait too long either: this stage can take time, especially if the story changes.

And the story will change. One way of thinking about what you need for a conference submission is a relatively tight, compelling and interesting story. While the loose ends and unexplored directions are probably the thing most interesting to you and your research, they are best left to a conclusions section rather than the main body. What the body should contain is a well-thought out march through what you have discovered and what it says about the problem you're solving. In doing so, you will find yourself making decisions about what to keep, and what to leave out, and how to order what you keep. 

And so, speculations need to be made into concrete claims or triaged. Experiments need to be run till they tell a definite story. Introductions need to be made coherent with the rest of the paper. There's also an element of bolt-tightening: making the bounds as tight as possible, stating claims as generally as makes sense for the overarching story (if your story is about points in the plane, then stating some claims in a general metric space might not always make sense). 

And all of this has to be done to serve the overarching story that will make the most compelling paper possible. The story can change as new results come in, or expand, or sometimes even die, (but this latter is rare). But there is this constant drumbeat of "am I getting closer to a submission with a nice story with each step".

Telling a good story is important. For someone to appreciate your paper, cite it, or even talk about it (whether it's accepted, or on the arxiv) they have to be willing to read it and retain its results. And they'll be able to do that if it tells a clear story, which is not just a union of results. 
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