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.

Logic, probability, and human reasoning

“…Figure I depicts a railway track and the cars, ABCDEF, that have to be rearranged into a new order on the right track (e.g., ACEBDF). Individuals ignorant of programming can create informal programs for solving such rearrangements, even for trains of any number of cars [5]. A computer program, mAbducer, also creates such programs with recursive loops of moves for trains [5].…”

“…In daily life, deductions yield the consequences of rules, laws, and moral principles [2]. They are part of problem solving, reverse engineering, and computer programming [3][4][5][6] and they underlie mathematics, science, and technology [7][8][9][10]. Plato claimed that emotions upset reasoning.…”

Children's creation of algorithms: simulations and gestures

“…The sequence itself represents the temporal order of the events (Johnson-Laird, 1983, Ch. 15;Khemlani et al, 2013).…”

“…They corroborate the intuitive trend too. It is also borne out by a simple universal metric that has been used in psychological studies (e.g., Chater & Vitányi, 2003;Khemlani et al, 2013): Kolmogorov complexity. This measure assesses the complexity of a string of symbols from the length of its shortest possible description in a reference language, such as Common Lisp.…”

“…The ability to devise informal algorithms is crucial for computer programming, and adults who are not programmers are able to devise them (Khemlani, Mackiewicz, Bucciarelli and Johnson-Laird, 2013). It seems reasonable to suppose that the ability has its roots in childhood, but prior to our research no-one knew whether children were able to devise informal algorithms.…”