I do crossword puzzles in pen. I won’t write in an answer until I’m pretty sure it’s correct, but I’ll scribble plausible guesses next to the clue. On more difficult puzzles I’ll do an initial sweep that consists solely of jotting down this marginalia. In this phase I utilize world knowledge (Nixon’s veep’s first name was “Spiro”), language knowledge (a superlative form of strong is “steeliest”), and even meta-knowledge about the puzzle itself (Will Shortz is inordinately fond of “Eero Saarinen”, “Dr. Dre”, and “Jai alai”). I give very little thought to how things will mesh together in the grid though. Aside from letter count, I pay no attention to spelling.
Eventually there will be what I call a gift–one clue that’s so easy that I’m willing to write it in directly. Only then do I start to look for letters that are shared between intersecting horizontal and vertical answers. After a gift or two, I can start filling in the grid, and then my attention shifts from general knowledge of the world to specific knowledge about English spelling. I scan my guesses for low frequency letters that reduce the search space of a perpendicular. Morphology comes into play: I’ll fill in S, EST, and LY endings to answers I still haven’t guessed. I shrug at vowels and crow over Qs. A longshot guess from the far reaches of my trivia knowledge becomes plausible as soon as even a single letter is confirmed by other means. By the end of the puzzle, world knowledge is largely irrelevant. Filling in those last few recalcitrant squares is pure mosaic work.
If you do machine learning, there’s something familiar about all the above. Speech recognition systems, for instance, employ two statistical models–an acoustic model that predicts words given sounds and a language model that predicts words given other preceding words. Each works in concert to reduce the hypothesis space of the other. I usually think of model combination as a machine learning trick, but the crossword puzzle example shows that it is also a purely human reasoning strategy. Leaving aside the mathematics, just being able to consider different kinds of information at the same time is a valuable tool for making our way through the world.