Mental Maze Solving

Abstract

Abstract We sought to determine how a visual maze is mentally solved. Human subjects (N = 13) viewed mazes with orthogonal, unbranched paths; each subject solved 200-600 mazes in any specific experiment below. There were four to six openings at the perimeter of the maze, of which four were labeled: one was the entry point and the remainder were potential exits marked by Arabic numerals. Starting at the entry point, in some mazes the path exited, whereas in 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 regression model. RT increased as a function of key parameters of the maze, namely the length of the main path, the number of turns in the path, the direct distance from entry to termination, and the presence of an exit. The dependence of RT on the number of turns was present even when the path length was fixed in a separate experiment (N = 10 subjects). In a different experiment, subjects solved large and small mazes (N = 3 subjects). The former was the same as the latter but was scaled up by 1.77 times. Thus both kinds of mazes contained the same number of squares but each square subtended 1.77° of visual angle (DVA) in the large maze, as compared to 1 DVA in the small one. We found that the average RT was practically the same in both cases. A multiple regression analysis revealed that the processing coefficients 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 processing coefficients for number of turns and exit status were practically the same in the two cases. Finally, the eye movements of three subjects were recorded during maze solution. They consisted of sequences of saccades and fixations. The number of fixations in a trial increased as a linear function of the path length and number of turns. With respect to the fixations themselves, eyes tended to fixate on the main path and to follow it along its course, such that fixations occurring later in time were positioned at progressively longer distances from the entry point. Furthermore, the time the eyes spent at each fixation point increased as a linear function of the length and number of turns in the path segment between the current and the upcoming fixation points. These findings suggest that the maze segment from the current fixation spot to the next is being processed during the fixation time (FT), and that a significant aspect of this processing relates to the length and turns in that segment. We interpreted these relations to mean that the maze was mentally traversed. We then estimated the distance and endpoint of the path mentally traversed within a specific FT; we also hypothesized that the next portion of the main path would be traversed during the 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 the path where the mental traversing ended, so that “the eyes would pick up where the mental traversal left off.” In this way, a portion of the path would be traversed during a fixation and successive such portions would be strung 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 distance of mental traverse and the distance along the path between the current and the next fixation spot. Indeed, we found that these distances were practically the same and that the endpoint of the hypothesized mental path traversing was very close to the point where the eye landed by the saccade to initiate a new mental traversing. This forward progression of fixation points along the maze path, coupled with the ongoing analysis of the path between successive fixation points, would constitute an algorithm for the routine solution of a maze.