Aha moments as percolation transitions

There is the occasional interdisciplinary physics paper that I find insightful and this is one of them: Nonuniversality for crossword puzzle percolation, by Alexander Hartmann of the Carl von Ossietzky University of Oldenburg, published in Physical Review E (link open access preprint: link).

It makes intuitive sense that getting to an Aha moment, in many domains of life, is akin to reaching a percolation threshold beyond which everything suddenly flows. In the case of crossword puzzles, the percolation analogy is quite literal and that makes it a phenomenal case study in Aha-ing that can be analyzed with the superpower of statistical physics (I may be biased here). One finding of interest to physicists is that the i.i.d. version is similar to 2D percolation (not surprising) but that correlations between words (what the author calls the game variant) leads to non universal behavior with the critical exponent depending on the details of the underlying structure. Of course, correlated percolation is reminiscent of explosive percolation, a continuous but unusual transition with weird finite-size scaling.

Is the brain a gigantic biological crossword puzzle? Half-kidding, the other half is missing.