Each math problem was structured in one of three ways. With "high-attachment" syntax, the final operation of the problem applied to a large "chunk" of the earlier part. For instance: 80 -- (5 + 15) / 5, where the final division (/ 5) applies to the previous addition term (5 + 15). With "low-attachment" syntax -- say, 80 -- 5 + 15 / 5 -- the final operation applied to a smaller previous chunk. A third category -- "baseline" problems like 80 -- 5 -- implied neither high nor low attachment.
After each equation, the participant was given a sentence fragment that could be completed with either high or low attachment syntax. For instance -- The tourist guide mentioned the bells of the church that … A high-attachment ending would refer to the entire phrase the bells of the church and might finish with "that chime hourly." Low attachment would link only the church to the completed final clause -- say, "that stands on a hill."
The subjects were variously successful in solving the problems. Their choice of high or low attachment sentence completions also revealed complexities -- some perhaps related to the preference in English for low-attachment syntax.
Still, in significant numbers, high-attachment math problems primed high-attachment sentence completions, and low-attachment problems made low-attachment completions likely.
What does all this mean? Our cognitive processes operate "at a very high level of abstraction," the authors write. And those abstractions may apply in similar fashion to all kinds of thinking -- in numbers, words, or perhaps even music.