Mental maze solving

We sought to determine how a visual maze is mentally solved. Human subjects (N = 13) viewed mazes with orthogonal, unbranched paths; each subject solv ed 200-600 mazes in any specific experiment below. There were four to six o penings at the perimeter of the maze, of which four were labeled: one was t he entry point and the remainder were potential exits marked by Arabic nume rals. Starting at the entry point, in some mazes the path exited, whereas i n others it terminated within the maze. Subjects were required to type the number corresponding to the true exit (if the path exited) or type zero (if the path did not exit). In all cases, the only required hand movement was a key press, and thus the hand never physically traveled through the maze. Response times (RT) were recorded and analyzed using a multiple linear regr ession model. RT increased as a function of key parameters of the maze, nam ely the length of the main path, the number of turns in the path, the direc t distance from entry to termination, and the presence of an exit. The depe ndence of RT on the number of turns was present even when the path length w as fixed in a separate experiment (N = 10 subjects). In a different experim ent, subjects solved large and small mazes (N = 3 subjects). The former was the same as the latter but was scaled up by 1.77 rimes. Thus both kinds of mazes contained the same number of squares but each square subtended 1.77 degrees of visual angle (DVA) in the large maze, as compared to 1 DVA in th e small one. We found that the average RT was practically the same in both cases. A multiple regression analysis revealed that the processing coeffici ents related to maze distance (i.e., path length and direct distance) were reduced by approximately one-half when solving large mazes, as compared to solving small mazes. This means that the efficiency in processing distance- related information almost doubled for scaled-up mazes. In contrast, the pr ocessing coefficients for number of turns and exit status were practically the same in the two cases. Finally, the eye movements of three subjects wer e recorded during maze solution. They consisted of sequences of saccades an d fixations. The number of fixations in a trial increased as a linear funct ion of the path length and number of turns. With respect to the fixations t hemselves, eyes tended to fixate on the main path and to follow it along it s course, such that fixations occurring later in time were positioned at pr ogressively longer distances from the entry point. Furthermore, the time th e eyes spent at each fixation point increased as a linear function of the l ength and number of turns in the path segment between the current and the u pcoming fixation points. These findings suggest: that the maze segment from the current fixation spot to the next is being processed during the fixati on time (FT), and that. a significant aspect of this processing relates to the length and turns in that segment. We interpreted these relations to mea n chat the maze was mentally traversed. We then estimated the distance and endpoint of the path mentally traversed within a specific FT; we also hypot hesized that the next portion of the main path would be traversed during th e ensuing FT, and so on for the whole path. A prediction of this hypothesis is that the upcoming saccade would land the eyes at or near the locus on t he path where the mental traversing ended, so that "the eyes would Dick up where the mental traversal left off." In this way, a portion of the path wo uld be traversed during a fixation and successive such portions would be st rung together closely along the main path to complete the processing of the whole path. We tested this prediction by analyzing the relations between the path dista nce of mental traverse and the distance along the path between the current and the next fixation spec. Indeed, we found that these distances were prac tically the same and that the endpoint of the hypothesized mental path trav ersing was very close to the point where the eve landed by the saccade to i nitiate a new mental traversing. This forward progression of fixation point s along the maze path, coupled with the ongoing analysis of the path betwee n successive fixation points, would constitute an algorithm for the routine solution of a maze.