Saturday, July 19, 2014

Presentaton at the Society for Mathematical Psychology

I'm in Quebec at the Society for Mathematical Psychology meetin
presenting some of my research on crossword puzzle solvers.  The complete slide presentation can be found here.

A highlight of the presentation was the video below, which shows an expert and novice playing the same puzzle. I'll let you guess who is who.


In fact, the novice was actually sped up by a factor of 4.

Below is a brief review of the presentation.

Crossword play involves memory search using cues from two dimensions: orthographic (letters) and semantic (clues). We hypothesize that this is done largely through associations in memory.  That is, parts of the clue or parts of the letter 'remind' you of many possible answers, and your job is to wade through all the possibilities that come to mind to until you find the answer.  As such, these cues provide two complementary roles:
1. They activate memory, 'spreading' activation out to many possible candidate answers.
2. From the active candidates, they then winnow down and select the best one.

These two processes are fundamental to many kinds of expert decisions.  Cues in the environment lead you to possible courses of action, but then you need to evaluate those courses of action against these cues.

In terms of crossword solving, we developed a computational model that tries to account for both clue difficulty and orthographic difficulty.  One way to try to solve a clue is to use semantic associations.  That is, look at the clue, and try to think of everything that comes to mind, and check each candidate against the letter constraints.  A second way is to focus on the orthographic constraints, and check those candidates against the semantic clue.  It turns out these two models make fundamentally different predictions about the affect of difficulty.  To illustrate this we developed a computer model of crossword clue solving.  We used Matt Ginsberg's database to feed the model, and have it solve clues of varying difficulty (either easy or hard clues, and by varying the number of letters given)

Below shows the results of the model.  On the left are the results when you use letter-patterns to try to solve a clue.  Each line is a word of a different length, and the horizontal axis shows the number of present letters. Here, longer words are typically moor difficult, but it gets easier as you have more and more letters.  In contrast, on the right shows the semantic route. Here, it does not matter how many letters you have, but rather the difficulty of the clue matters more.

To test this, we conduct an experiment on crossword experts  Below shows some of those results.  Note that we see a combination of the two models.  When only a few letters are available, experts appear to use semantic-route solutions and produce a difficulty effect.  When most letters are available, the semantic difficulty effect goes away as they shift to an orthographic strategy.

If you want to be good at solving crossword puzzles, here is what this tells you.  You want to be solving on the right side of these curves--when most letters are known.  This makes the clue sort of irrelevant, and hard clues are not that hard.  However, to get there, you need to be good on the left side.  In contrast to experts who were above 50% accurate at solving clues with only one letter hint, novices are down at around 20%.  Experts get this way because they retain and can access a lot of semantic associations, both within the crossword domain and outside.  Even though they are really good at semantic associations, it is still more difficult than completing a word that is mostly solved.  So the key is to work toward solving clues that are mostly already solved.

We are working on publishing these and other results, so stay tuned here for more discussion.

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