I recently published a paper on kinematic mental simulations in PNAS. The paper is with Monica Bucciarelli, Robert Mackiewicz, and Phil Johnson-Laird, and it examines how reasoners without any background in computer science or logic can construct mental “algorithms” in a systematic way, akin to recipes or driving directions.
Here’s the abstract:
We present a theory, and its computer implementation, of how mental simulations underlie the abductions of informal algorithms and deductions from these algorithms. Three experiments tested the theory’s predictions, using a novel environment of a single railway track and a siding. This environment is akin to a universal Turing machine, but it is simple enough for non-programmers to use. They solved problems calling for them to use the siding to rearrange the order of cars in a train (Experiment 1). They abduced and described in their own words algorithms that solved such problems for trains of any length; and, as the use of simulation predicts, they favored while-loops over for-loops in their descriptions (Experiment 2). Given descriptions of loops of procedures, they deduced the consequences for given trains of six cars, doing so without access to the railway environment (Experiment 3). As the theory predicts, difficulty in rearranging trains depends on the numbers of moves and cars to be moved, whereas in formulating an algorithm and deducing its consequences it depends on the Kolmogorov complexity of the algorithm. Overall, the results corroborated the use of a kinematic mental model in creating and testing informal algorithms, and showed that individuals differ reliably in the ability to carry out these tasks.