I was recently contacted by another graduate student for advice on how to deal with feeling bogged down by theoretical and mathematical detail while working on a journal paper. This is a problem that I have a lot actually, I don’t think I’ve gotten it all solved, but I have developed a number of strategies for getting through it.
The most general one is somewhat circular, but more proactive. I’ve put significant effort toward learning to be a better researcher, learner, writer, and generally productive person. I’ve read some books and countless articles on these types of matters. This of course isn’t the best in the moment before a deadline solution, to try to consume all of these materials at once and then magically be able to get your work done, but slowly working through these materials over the course of time has made me lose less time and get less worried when I face these struggles. I maybe face them less often or maybe with about the same frequency, but lose less time with each occurrence and I do more complex and more theoretical work than I did at the beginning of graduate school. This strategy can help a little immediately as well. When I get really stuck I pause and spend 20-30 minutes reading whatever’s next on my ‘get better at x’ list or the book I’m currently working through. After a few minutes of a productive feeling distraction, I often have a better idea of how to proceed. This used to be my first strategy, I’d spend a few minutes reading and learning about things I could try until I found one that sounded like a good strategy to try. Recently this has fallen lower on my list, because the ones below get me back on track. I think this is the most important strategy and that it should the first one I mention here, because even though the strategies below help me they may not help you so learning about as many strategies and trying them out until you settle into your own toolbox of strategies is the most important.
Start Typing. Don’t Stop.
I open a separate space (for me, 750words.com which I’ve mentioned previously or writebox is the new one I’ve just started occasionally) somewhere where the project isn’t there, I have no context and zero pressure for formatting or even correct grammar or spelling. I start typing and don’t stop until I reach a predetermined goal. I most often require myself to push through this exercise until I reach 750 words, sometimes though I go much longer, other times to get there I write some pretty redundant things (not literally repetitive though, that’s cheating), but having a minimum I must reach require me to reach some level of breadth or depth. This strategy has a few different sub-components that I’ve pulled together from other places, but in general, getting whatever ideas, or stumbling blocks, that are on my mind out and in writing helps me move on. The separate space is important for me because there’s no pressure for what I write to fit into a project or distraction of the existing text. I have no problem writing non stop with varying tone, audience or topic, when it’s not in a project, just what I need out of my way: a note on what I’m stuck on to my adviser, a new draft of how it could go, another version of the same paragraph from a different perspective, etc. Then when I’m done, I copy and paste anything useful into the project.
Most often, I start writing about what I’m having trouble writing, coding or figuring out and why, maybe with a friend or my adviser in mind as the audience. Sometimes that takes a while, but at the end I at least feel better and usually have an idea. Usually, after about a paragraph, I have an idea for how to fix the thing or explain whatever it is I’m having trouble with. I start to then draft the writing I need, maybe halfway through a paragraph I have a better way to say something, so I just write the second option next. Later, I can pick and choose the best aspects of each way, or maybe after I can try to write out a justification for each and use those to decide. This is nonstop writing, no revising; clean up and sorting is for after.
Other times I try to write out instructions to myself for what to do or the new questions I have to research in order to progress. When stuck with writing specifically, I’ve found that writing out the objectives for the section I’m having trouble with, “by the end of this section the reader should …” helps a lot. One of my favorite get unstuck freewriting exercises it to write out the material as a script of a talk I might give if I were talking to children or other lay people. This text of course, won’t be useful to directly copy and paste into a manuscript, but often helps me figure out how to write for the manuscript.
Sometimes, struggling through work just has to happen. Staring at the problem, thinking about it every imaginable way, reading and rereading, writing and rewriting. Doing this endlessly, however wouldn’t move anything progress, so I do a lot of my work using the pomodoro technique, I’ve mentioned it previously (http://www.sarahmbrown.org/5-academic-tools/”>here. I set a timer for 25 minutes and have to stay on task for those 25 minutes, no e-mail, texts, calls, social media, anything. I also pick a single specific task on a specific project (ex: write section 1.4, reorganize chapter 2, etc) that I have to work on the whole time. If I truly finish in less time, I can move onto something that’s a natural succession, but if I’m stuck I have to stay and keep trying until that 25 minutes is up. Then 5 minute break and repeat. After 4 take a longer break. The 25 minutes is often long enough I get myself unstuck, but short enough I don’t feel like I’m wasting time and I also stop and move on before I actually mull too long.
Visualize: Digitally, Not Mentally
I’m a very visual learner, so writing is hard for me. Explaining and learning things with diagrams and tables is easier for me; when I’m troubleshooting code I generate figures at intermediate steps to see how the data changes to check that it’s working. When I think through how ideas relate, I think of them that way. Sometimes, I draft slides or paper figures for a section when I’m having trouble with or the whole thing if I’m having trouble with organization. For equations, while a specific equation might be hard to understand and explain, an annotated plot of it might easier. Thinking about how to visualize content for quick understanding that’s necessary for good slides, helps me figure out how to explain it in text. Also, then I feel like I’m making progress, I’ve at least got the figures for the paper or the slides for later ready in advance. The slides, I can zoom out on and see a story board of the whole project which helps provide perspective that is useful for organization.
For really abstract theory, try to think of an analogy that could work to explain the concept to a child. That process helped a lot with a large collaborative project. We needed to explain the mathematical (systems theory) definition of state for an audience of psychologists. We tried a few different analogies until we got one that was simple enough to cover what we needed. That is included in the paper as a box/sidebar, but also it helped us really refine the right words to use to provide the base definition in the main text of the paper. We have a long list of failed candidate analogies we brainstormed in meetings, but each one got us closer to one that actually worked. This can be worked into a free-writing exercise but I more often do it with a table. I make a row for each aspect and a column for the analogy and then fill in the boxes with what about each analogy relates to that aspect of the concept. I often add rows as I go and sometimes it takes some other figure-like form, but the idea is to relate the work to something that’s more broadly understandable. Giving yourself new ways to think about it, will help you not only write it down for others to understand, but can even give you new ideas about how to approach the problem or extend your result.