Kinematic mental simulations in abduction and deduction

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 an environment of a single railway track and a siding. This environment is akin to a universal Turing machine, but it is simple enough for nonprogrammers to use. Participants solved problems that required use of the siding to rearrange the order of cars in a train (experiment 1). Participants 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, participants 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.

Keywords: cognitive processes; informal programming; problem solving; reasoning.

Fig. 1.

The railway environment with an example of an initial configuration in which a set of cars is on the left side (A) of the track, the siding (B) can hold one or more cars while other cars are moved to the right side of the track (C). The program allows individuals to select a car (e.g., the highlighted “E” car) and to move it and all of the cars in front of it to the siding or the right track.

Fig. 2.

The proportions of correct algorithms in experiment 2 for trains of any length depending on the type of rearrangement and whether the participants carried out problems of trains of any length in the first block (A) or the second block (B).