What I learned about research from crossword puzzles

Written by David Mimno

I’ve been doing crossword puzzles daily for many years. Apart from doing a puzzle before grad school exams to warm up my neurons, I never saw much of a connection between puzzles and my day job as a professor of data science. But lately I’ve noticed that many of the habits and attitudes I developed as a solver are also relevant to research. Here’s a summary.

  • You can’t solve hard crosswords, or pursue research, without confidence and persistence. I remember the first time I saw a Saturday New York Times puzzle. I scanned the full set of clues and knew absolutely nothing. Every single square was just as blank as when I started. Today I can do a Saturday puzzle without too much trouble. What has changed is not so much that I can fill in more words at a glance (I can, but only a few). It’s that I don’t stop after that initial pass. I sit with the clues, start working around the few breaks I get, and then start to unravel whole sections. There’s a similar process with research. Even if it’s the flashes of inspiration that get remembered, nothing hard happens without persistence. Inspiration, perspiration, etc, etc, we’ve all heard that before, but what I think is important is to recognize where persistence comes from. It’s not a virtue or a character trait, it’s experience and confidence that give you the optimism to persist, even when nothing is obvious.

  • The back of your mind is as important as the front. Paradoxically, stepping away from a problem can be the most useful tool for persisting. Anyone who has done crosswords knows the bizarre thrill of coming back to an impossible section after a few hours and seeing the answer instantly. Walking, napping, eating lunch, they all help in research too.

  • Have a good eraser. Humility is an advantage. I have occasionally done a Saturday puzzle in pen, but I always end up with some Es that look an awful lot like they began life as As. If I’m solving on paper I like to use a pencil with a big, solid eraser. When doing research it’s easy to get emotionally attached to your ideas, but we need to be open to modifying or even abandoning them when it turns out that our great idea isn’t actually how the world works.

  • Solving a problem is much easier when you have a partial answer. If you know the first letter of a word, you can cut down the number of possible solutions dramatically. It’s the same in research. Fixing as much as possible from the start and then working in the space that’s left keeps you focused. Sometimes, though, this helps the other way: when the letters that are blank can’t possibly be filled with anything correct, you know you need to revisit your assumptions. In machine learning it’s not uncommon to prove that your problem has no solution, yet humans do it unconsciously thousands of times a day. It usually means that your assumptions are wrong.

  • The best way to reduce a solution space is to know something. For both research and crosswords you need to know trivia, obviously, but it has to be the right trivia. Wayne GRETZKY may have been as great a hockey player as Bobby ORR, but only one of them is a short sequence of high-frequency letters. In the same way, knowing lots of facts about math doesn’t necessarily help in machine learning, but knowing specific facts about specific branches of math can help immensely. And just as in puzzles, these facts are interconnected. Knowing one fill word can help me recognize another and another, in the same way that knowing a property of one distribution can imply a whole chain of relationships.

  • The most important thing is that — and this will sound weird, but stay with me — I know the answers. I don’t mean I can fill in everything immediately. But I know the inventory of answers that keep coming up, which makes it much easier to connect them to questions. Clues often have tricky or misleading wordplay. But for example if it has anything to do with mining or the earth, I know there’s a good chance the answer is ORE, and I can work backwards to figure out the pun. In my research field, the same technical answers keep coming up: matrix factorizations, log-linear models, regressions, stochastic gradients. Having a clear inventory of likely answers — even if the real answer isn’t always among them — makes answering much simpler.

In research problems aren’t graded by difficulty, and we don’t have an editor helpfully making sure the clues are “fair”. But crossword skills have helped immensely. Persist, but don’t be afraid to erase. Do your homework so the easy is fast and the hard is easier. Know how to recognize the answers when you hear the questions. Happy solving!

Note: I meet regularly with a small group of Cornell students to work on data science writing and communication. They wanted to try editing my writing for a change, and had some excellent suggestions for this piece. Thank you!