In this experiment, subjects were given two sets of simple, identical, and half-finished patterns in Figure 2 to complete. One set, they were told, contains the first half of a ball's rolling paths and the other set, they were told, contains half-finished strokes by an artist on a canvas. If the conception of mechanical events has to follow mechanical constraints, it was expected that much more variations would occur in the responses (drawings) of the subjects to the second stimulus than in those to the first one.
Subjects: One hundred and eighty undergraduate students who were enrolled in a General Psychology class participated in this experiment. 57% of these students were female and 43% of them were male. The average age was 20. The experiment was carried out in subject groups of different sizes, ranging from a small group of 3 students to a psychology class of 109 students.
Stimuli: Four different computer-drawn patterns were the stimuli for this experiment. Each pattern, with a black dot on its left marked by a letter A, occupies only the left half of a 7cm×7cm box on the paper. The four boxed patterns were shown to the subjects on a regular 8.5in×11in paper in the form of a 2×2 matrix. On top of the paper and above the four patterns is the instruction about the stimuli to the subjects. The instruction differs from condition to condition in the experiment, but the four computer-drawn patterns remain exactly the same throughout the experiment.
Procedure: Before the experiment, the 180 sets of stimuli were shuffled into random order. At the beginning of the experiment, the subjects were given an information sheet with three requirements of the experiment written on it: 1) the experiment is not a test; 2) use their gut-feeling to answer the questions; 3) do not go back to any completed answer. The experimenter read out loud these requirements to the subjects. In the experiment, the subjects were first given the visual-instructed stimuli, in which the subjects were instructed that "on a canvas, an artist put his brush at point A and started drawing something. The following are his half-finished drawings. Please finish them as quickly as you can". After finishing their responses to the visual-instructed stimuli, the subjects were then given the mechanical-instructed stimuli, in which the subjects were instructed that "a ball (either a ping-pong ball or a lead ball; see below) is rolling, starting at position A, with trajectories as shown in the following diagrams. Only incomplete paths are shown in these diagrams. Please complete the ball's paths as quickly as you can". Upon finishing their responses to the mechanical-instructed stimuli, subjects had completed this experiment.
Design: The Visual-instructed condition and the Mechanical-instructed condition formed a within-subject design. Further, the Visual-instructed condition was tested before the Mechanical-instructed condition for every subject in the experiment. (The design here was not a counterbalanced one because 1) the conditions were distinguished solely by the instructions given to the subjects while the stimuli (incomplete patterns) remained exactly the same and 2) the two responses of a subject were judged or measured completely relative to each other. See below) The Mechanical-instructed condition was further divided into two subconditions: Lead-ball condition and Ping-pong-ball condition. The total 180 students were randomly divided into two groups, the Lead-ball group and the Ping-ping-ball group, with 90 students in each group, being tested independently on the mechanical-instructed lead-ball stimuli and the mechanical-instructed ping-pong-ball stimuli (both after being tested on the visual-instructed stimuli). So, the Lead-ball condition and the Ping-pong-ball condition formed a between-subject design. Note, the conditions of this experiment were manipulated only through the written instructions on the stimulus page, because the four incomplete patterns were the same under all conditions.
Three independent blind judges were asked to classify the responses of each subject into being either mechanical (i.e., consisting of a ball's rolling paths) or visual (i.e., consisting of patterns other than a ball's rolling paths). The two responses of every subject, one to the mechanical stimuli and the other to the visual stimuli, were simultaneously shown to one judge at a time, one on the left hand and another on the right hand of the experimenter. The side of presentation was randomized across conditions and between the judges. The responses were shown to the judges without any of the original instructions about the tasks, i.e., the judges had no information about which stimuli belong to the Visual-instructed condition and which to the Mechanical-instructed (either the Lead-ball or the Ping-pong-ball) conditions.
Obviously, four types of judgements can be made on all the responses if they were presented to the judges individually: 1) a response to the visual-instructed stimuli is judged as consisting of visual patterns; 2) a response to the visual-instructed stimuli is judged as consisting of mechanical patterns; 3) a response to the mechanical-instructed stimuli is judged as consisting of mechanical patterns; 4) a response to the mechanical-instructed stimuli is judged as consisting of visual patterns. Clearly , only 1) and 3) are correct, because the judgments are then consistent to the experimental stimulus conditions. 2) and 4) are incorrect, because the judged categories, either mechanical or visual, do not match the stimulus categories.
However, since the two responses of every subject were shown to the judges simultaneously, it was only necessary that the judges were asked to identify, between the two responses of a subject, one response as a ball's rolling patterns. A correct judgment thus required the judges identify as ball-rolling the drawings subjects made under the mechanical instructions, i.e., choose judgment 3) as listed above. For each subject, therefore, only when all three judges had correctly identified as ball-rollings the response of the subject under the Mechanical-instructed condition, would the subject be classified into the mechanical response group (i.e., the mechanically correct group). Any other judgement by any of the three judges would put the subject into the non-mechanical response group (i.e., the mechanically incorrect group).
With such a measurement, the results of this experiment are presented in Figure 3, in which the percentages of mechanically correct responses and the percentages of mechanically incorrect (non-mechanical) responses are shown for both the Ping-pong-ball and the Lead-ball conditions.
Overall, 156 of the 180 subjects (86.7%) were identified uniformly by the three judges as responding mechanically to the mechanical-instructed stimuli and visually to the visual-instructed stimuli, 24 of them (13.3%) were not identified as so. Within the Mechanical-instructed condition, 83 of the 90 subjects (92%) in the Lead-ball group have been judged as responding mechanically to the mechanical stimuli and visually to the visual stimuli, only 7 subjects (8%) were incorrectly identified. In comparison, of the 90 subjects in the Ping-pong-ball condition, 73 (81%) responded mechanically to the mechanical stimuli and visually to the visual stimuli, while 17 (19%) failed to convey the distinction. Obviously, the more the number of subjects responded mechanically to the mechanical stimuli and visually to the visual stimuli, the less the number of subjects who make incorrect responses. With such a measurement, the difference between the number of subjects who responded correctly and the number of subjects who responded incorrectly for the entire sample is significant by the binomial test (p<0.001). Comparison between the Lead-ball condition and the Ping-pong-ball condition with a Chi-square test yields X2=4.81, which means that the difference between the responses under these two conditions is also significant, at the level of p< 0.05. This latter result shows that significantly more ping-pong-ball responses were judged as visual responses than the lead-ball responses were.
The main results of this experiment are 1) subjects responded significantly differently when asked to continue a drawing if they thought they were depicting a mechanical event than when they thought they were completing an abstract pattern; 2) subjects responded significantly differently when told the ball was a lead ball than a ping-pong ball. Let's look at each of these in more detail.
The first result confirms our hypothesis that people's conception of mechanical information follows mechanical constraints and, thus, is different from purely visual conceptions. How do we know the difference between the responses under the two different conditions is caused by knowledge of mechanical constraints in the cognitive system? It can be argued that certain characteristics in the mechanical responses are so unique to the mechanical patterns that the responses to the visual stimuli do not have them. This is why the three independent judges could all come to the same conclusion when being asked to judge which response is mechanical and which is visual. That is, they have to tune into the same information in the responses and use roughly the same criteria in order to make (statistically significantly) the same judgments. Although it is by no means clear what this information is exactly, we can at least conclude from this experiment that it is mechanical, because it (cognitively) distinguishes mechanical patterns from the visual patterns by the subjects and the three judges.
One of judges was interviewed briefly and asked about what rules he was using to make his judgments. His answer was, 'the paths of a rolling ball look simpler than other kinds of patterns'. When further asked what he meant by 'simple', he said 'a rolling ball would not make a lot of sharp turns and would rarely go back to its own starting location'. It seems very plausible that more precise (mathematical) descriptions can be found to capture the mechanical rules or constraints. Is it likely that the cognitive constraints are based on some principles of curvature minimization or differential continuity to a particular order? Maybe, it is the overall pattern that counts; no closure? Or, regularities within the high-order autocorrelations? These, however, are certainly beyond my current concern.
The second result of this experiment shows that the more mass the ball has, the stronger, cognitively, the mechanical constraints seem to be in the subjects' conception of the ball's rolling paths, because the responses by the subjects to the lead-ball stimuli were found to be under stronger mechanical constraints than the responses to the ping-pong-ball stimuli. In other words, people's conceptions of the ping-pong ball, because of its lesser mass, are more similar to their conceptions of free drawings or visual patterns. This is true because significantly more ping-pong-ball responses were judged as visual responses compared to the lead-ball responses (or, visual responses were judged as ping-pong-ball responses significantly more frequently than as lead-ball responses). Therefore, we conclude that, cognitively, the ball's having more mass represents its being more mechanical in motion; The cognitive system not only represents mechanical information as different from other kinds of information, it also represents and distinguishes the different dynamic levels, corresponding to the mass of an object, of mechanical information.
In the next experiment, I will explore in much more detail the role of mass in people's conception of mechanical events.