The brain has a problem. Information can only enter it through sensory apparatuses: the eyes, ears, nose, tongue, and skin. And the information that enters the brain is fairly simple. The brain therefore has an enormous task: to take sparse inputs and transform them into extremely complex cognitive representations. For example, the retina that coats the back of the eye is made of a two dimensional sheet of light-sensitive neurons, like the sensor in a camera. When a person looks at a cup, what she sees is the result of a 2D projection of the image onto her retinas. Somehow, her brain manages to convert the 2D input from the retina into a 3D representation. That is, despite the fact that the information that is sent to the visual cortex is 2D, the brain extracts 3D information from it, by using clues like light, shadow, or perspective.

This kind of simple-to-complex transformation is not unique to inferring the 3D shape of objects. The mind also works to infer social variables - such as causality and animacy - from simpler inputs, such as actions and movements.

For example, imagine two circles, one red and one green, several inches apart but along the same line. The red circle moves in a straight line until it collides with the green circle. Thanks to physics, we know that when that happens, the red circle stops moving, and the green circle starts moving in the same direction that the red circle had previously been moving.

Now imagine the same two circles. The red circle begins moving towards the green circle, just as before. This time, before it can collide with it, the green circle moves away.

The two scenarios are very similar, but in one case the green circle's motion was the direct result of a physical impact, while in the second scenario, it was not. Despite the fact that the retinal input from these two displays are extremely similar, you can't help but think of the circles as "alive" in the second scenario. You might assume that the red circle "wants" to catch the green one, and that the green circle "wants" to run away. Under certain conditions, even 2D shapes can be interpreted as animate social agents rather than simple intentionless objects. In other words, you have imbued the red and green circles with desires and intentions. You have granted them minds.

This phenomenon was perhaps most famously investigated in 1944 by Smith College experimental psychologists Fritz Heider and Marianne Simmel. In their first experiment, the psychologists simply instructed their female undergraduate subjects to "write down what happened" in the movie above. (The rest of this post will only make sense if you watch the video above!)

Most of the thirty four subjects interpreted the shapes in the movie as animate characters. Thirty two described them as people, and two described the shapes as birds. The experimenters provide an example of a common interpretation:

A man has planned to meet a girl and the girl comes along with another man. The first man tells the second to go; the second tells the first, and he shakes his head. Then the two men have a fight, and the girl starts to go into the room to get out of the way and hesitates and finally goes in. She apparently does not want to be with the first man. The first man follows her into the room after having left the second in a rather weakened condition leaning on the wall outside the room. The girl gets worried and races from one corner to the other in the far part of the room. Man number one, after being rather silent for a while, makes several approaches at her; but she gets to the corner across from the door, just as man number two is trying to open it. He evidently got banged around and is still weak from his efforts to open the door. The girl gets out of the room in a sudden dash just as man number two gets the door open. The two chase around the outside of the room together, followed by man number one. But they finally elude him and get away. The first man goes back and tries to open his door, but he is so blinded by rage and frustration that he can not open it. So he butts it open and in a really mad dash around the room he breaks in first one wall and then another.

They also provide an unusually elaborate interpretation made by one subject:

The first thing we see in this little episode is triangle number-one closing the door of his square. Let's insist that the action of the play is on a two-dimensional surface (not that it makes much difference) and we will undoubtedly start calling the square in which the triangle number- one seems to make his dwelling, a house, which infers three dimensions. But we are not sticking to the theme of our story. Triangle number-one shuts his door (or should we say line) and the two innocent young things walk in. Lovers in the two-dimensional world, no doubt; little triangle number-two and sweet circle. Triangle-one (here-after known as the villain) spies the young love. Ah! ... He opens his door, walks out to see our hero and his sweet. But our hero does not like the interruption (we regret that our actual knowledge of what went on at this particular moment is slightly hazy, I believe we didn't get the exact conversation), he attack striangle-one rather vigorously (maybe the big bully said some bad word).

There were some common themes. For example, nearly every subject described the interaction between the big triangle and the small triangle as a fight. Most described the big triangle being locked in the "house." The interaction between the big triangle and the circle was usually described as a chase. And the "door" was almost always controlled by the shapes; the shapes were never moved by the door.

Of thirty four subjects, only one described the film in strictly geometrical terms. She wrote:

A large solid triangle is shown entering a rectangle. It enters and comes out of this rectangle, and each time the corner and one-half of one of the sides of the rectangle form an opening. Then another, smaller triangle and a circle appear on the scene. The circle enters the rectangle while the larger triangle is within. The two move about in circular motion and then the circle goes out of the opening and joins the smaller triangle which has been moving around outside the rectangle. Then the smaller triangle and the circle move about together and when the larger triangle comes out of the rectangle and approaches them, they move rapidly in a circle around the rectangle and disappear. The larger triangle, now alone, moves about the opening of the rectangle and finally goes through the opening to the inside. He moves rapidly within, and, finding no opening, breaks through the sides and disappears.

Having verified that humans spontaneously thought of the shapes in their video as animate, Heider and Simmel showed the film to another thirty six undergraduate students. They were explicitly asked to describe the personalities and desires of each of the shapes.

Thirty five of them thought of the big triangle as mean, and used adjectives like aggressive, warlike, belligerent, quarrelsome, angry, bad-tempered, dominant, and irritable. They described it as a bully or as a villain, and they thought it enjoyed "picking on smaller people." Tellingly, it was universally described using male pronouns.

There was slightly more variation when it came to interpretations of the personalities of the small triangle and the circle.

Seventy five percent thought that the circle was afraid, fearful, cowardly, shy, timid, or meek. It was described as a follower, reliant on the small triangle for protection. Sixty one percent described the circle using female pronouns. Only a few described the circle as clever or shrewd.

The small triangle was described by half the participants as heroic, valiant, brave, courageous, or defiant. Many interpreted its actions as the result of resentment at being bullied by the big triangle. The experimenters reason that the small triangle is thought of as brave because, unlike the circle, it hits back and defends itself against the big triangle. Like the circle, a third of participants described the small triangle as clever, brainy, or intelligent. And like the big triangle, the small triangle was almost universally referred to as male.

In both experiments, subjects interpreted individual interactions in fairly routine ways as well. For example, they thought that when the circle and small triangle spun around eachother, it was an expression of joy. And when the circle was trapped in the house with the big triangle, most subjects understood her actions as evasive, reflecting her fear of the bully.

Importantly, the order in which the events were displayed predicted the sorts of personalities and intentions attributed to the shapes. When the experimenters played the movie in reverse for a third set of subjects, their responses were very different from the subjects in the first two experiments.

For example, several times in the video the big triangle and circle move in and out of the house. The motivations behind those actions would differ depending on the order in which the movements occurred. When the shapes' actions were thought of as spontaneous, they might be described as "hiding" or "escaping." But when the actions were interpreted as reactions, the very same motions might be described as "being forced in" or "being lured in." The interpretation of the social interaction would depend on whether the film was played in forward or in reverse. What that means is that the order in which actions occur is critical to the way we interpret motivations, intentions, and desires.

The process through which we attribute mental characteristics to animated circles and triangles is a powerful example of a certain kind of anthropomorphism, a process through which we infer the unobservable mental features of non-human agents as human-like.

Which leads to a chilling question. If it is so easy to imbue geometric shapes with human-like thoughts, feelings, intentions, and desires, how is it equally easy for some people to view others of their own species as decidedly non-human?

Heider F. & Simmel M. (1944). An Experimental Study of Apparent Behavior, The American Journal of Psychology, 57 (2) 243. DOI: 10.2307/1416950

Scholl B.J. & Tremoulet P.D. (2000). Perceptual causality and animacy, Trends in Cognitive Sciences, 4 (8) 299-309. DOI: 10.1016/S1364-6613(00)01506-0

Images: Eye diagram via Ruth Lawson/Wikimedia Commons. Circles diagram modified from Scholl & Tremoulet (2000).