Participants trained on shapes carried the same hidden complexity rule into melodies and touch

A simpler account was available for all of it. Participants could have learned to pick whichever item had more of something, then applied that to whatever came next. Boger and Firestone tested it by swapping in objects that were brighter, larger or more saturated, and the trained rule did not reliably follow ^[7].

The coin game has a second weakness: it pays people for finding a connection, so it can teach the analogy it is meant to detect. One experiment removed the reward. Forty-eight participants judged which of two invented words was more or less complex, two syllables against four, with a shape above each word that they were explicitly told they could ignore ^[8]. When a complex shape sat over a simple word, responses were slower and mistakes more common ^[9].

Pooling the two cross-sense experiments gives 195 participants, and about 53 more of them followed the trained rule than chance predicts ^[1]. One of the ten category pairings did not transfer reliably, and the phys.org account does not say which one ^[2].

Every trial was a choice between two items from the same category ^[2]. A design like that reaches an ordering that survives a change of category and no further: a four-syllable nonsense word and a many-sided shape are never put on one scale, and complexity was built differently in each case, many sides for a shape, varied pitches and rhythms for a melody, two extra syllables for a word ^[14]. One candidate for a quantity that could travel is how compactly a thing can be described, which is roughly what a 2017 paper in PLOS Computational Biology argued when it found people anticipating sequences of spatial locations by using regularities such as symmetry and repetition ^[13].

The last experiment dropped both the rewards and the right answers. A group of 150 participants picked which of two items they found more or less beautiful, comparing pairs within one category at a time ^[10]. People drawn to complex shapes tended to favor complexity in melodies, dot patterns, letter strings and mathematical expressions; the preferences agreed across categories more than chance would predict, though not perfectly ^[11]. That is a correlation among one person's choices in separate tasks. It is consistent with a single shared quantity without on its own demonstrating one. Boger and Firestone wrote that their results suggest "the mind possesses a unified representation" of complexity ^[12].