EXPLAINING THE BEHAVIOR OF TRIANGLES

In 1944 Fritz Heider and Marianne Simmel published the results of a novel experiment conducted at Smith College in Northampton, Massachusetts. In “An experimental study of apparent behavior” Heider and Simmel (1944) prepared a brief film depicting the movements of a two triangles and a circle in and around a shape made to look like a room with a door. The film was shown to 114 undergraduate women at Smith College divided into three experimental groups. In the first, subjects were given the general instruction to “write down what happened in the picture.” In the second, subjects were instructed to interpret the movements of the figures as actions of persons and to answer ten questions in a written questionnaire. The third group was shown the film in reverse, by running the filmstrip backwards through the projector, and asked a subset of the same questions.

The Heider–Simmel film, which is today readily viewable on online video websites, is not particularly remarkable as a piece of animated cinematography. Compared to Walt Disney's films of the same era, including Pinocchio, Fantasia, and Bambi, the film must have appeared anachronistic even to the original Smith College subjects. Each frame in the film was produced as a photo of geometric shapes cut from cardboard and placed on a horizontal translucent-glass plate illuminated from above. The careful placement of the shapes in each frame created a narrative stream of events, evidenced only by the silent trajectories of each shape and its position in relation to the others. As expected, the subjects in the three experimental groups interpreted these events as a coherent narrative and described them in terms of the interrelated behaviors of three intentional characters, in and around a room defined by four walls and a door. Somewhat surprising is the degree to which these descriptions attributed mental states to these nondescript shapes. Heider and Simmel provide the following as representative of the descriptions produced by the first experimental group:

The rest of this book is heavy on logic; that's what the word “Formal” in the title means. But we believe the book has value beyond the formalization, in the systematic development of the content of the theories, and we would not like to see readers put off by their lack of familiarity or comfort with logic. The logic we use is neither deep nor especially complicated. So we have included an appendix on first-order logic that gives a gentle introduction to all the logic one needs for understanding the axioms in this book.

Even those comfortable and familiar with logicmay find it profitable to look over Sections 7 and 8 of the appendix. Section 7 presents our view that commonsense theories are not to be built up by definitions resting ultimately on a set of primitive concepts, in a kind of “Euclidian” program. Rather every predicate is, in a sense, a primitive, but they all occur in axioms that constrain their possible meanings more or less tightly. The most fundamental concepts in commonsense knowledge cannot be defined precisely with necessary and sufficient conditions. The most we can hope for is to characterize them as precisely as possible with lots of necessary conditions and lots of sufficient conditions. Then Section 8 presents the most common patterns we use in the axioms, and it should reduce their perceived complexity for the reader.

The focus of this book is commonsense psychology. But this is a very complex domain, and it rests on a number of other nonpsychological domains. Before talking about belief, we have to talk about logic. Before doing goals and plans, we need a theory of causality. We can't axiomatize scheduling until we handle time. In Part II we develop these and other background theories.

The theories, one per chapter, fall into two broad categories. Some provide required mathematical infrastructure that will be needed everywhere or argue for fundamental ontological commitments necessary for getting any effort to encode commonsense knowledge off the ground. In Chapter 5 we reify “eventualities”, or states and events, by treating them as first-class individuals in the logic. In Chapter 7 we make a similar move with typical elements of sets, or reified universally quantified variables.

Suppose we are watching a workman doing his job.He looks around for his toolbox, and when he finds it, he opens it and takes out a hammer and nails. He pounds one nail after another into boards. Each step in this repetitive action is itself a repetitive action, hitting the nail with the hammer again and again until it is flush with the wood. He sweats, and from time to time as the sweat drips into his eyes, he takes out a handkerchief and wipes his brow. Five o'clock comes, and he puts his tools away and goes home. He comes back the next morning at nine o'clock for a day of similar tasks.

The workman has a goal he is trying to achieve, and he breaks this into subgoals that eventually bottom out in individual actions and bring him closer to the satisfaction of the goals. He needs to have certain tools and resources to do his job, and to have these, he needs to know where they are – resource preconditions and knowledge preconditions. He generally engages in repetitive actions because each repetition brings him a little closer to his goal. Situations arise and have to be dealt with immediately. To do his job, he has to be able to see, and when something interferes with this, he must somehow counteract it. His job is embedded in a larger structure of plans for his life as a whole, and this has to be aligned with periodic regularities of his physical and social environment. Thus, the fine structure of his actions emerges from his manipulations of the causal structure of the world as organized in his plans.

We as observers see individual actions happening one after the other.We make sense of them in part by recognizing similarities in successive actions and thereby recognizing repetitions.We see an action happening occasionally and realize it happens only when some condition arises.We thereby recognize conditional events.We see that some actions happen only at particular times or for particular durations. By these means we recognize the temporal structure of complex events, but we have not really interpreted his actions until we understand the causal structure implicit in them, that is, until we have recognized the plan he is executing.