Visualizing Causal Relations

Visualizing Causal Relations

Abstract

Michotte suggests that causal relationships are perceived directly if certain simple animation techniques are used. Based on his work, we introduce a semiotic method called a visual causal vector that uses animation to produce the perceptual impression of a causal relationship between two graphically represented entities. This work introduces three different visual causal vectors together with preliminary experimental results relating to two of them.

Introduction

The most common representation of causal relationships between entities is a directed graph diagram (Figure 1). But this kind of diagram is also used to represent other kinds of relationships. In Software Engineering alone, directed graphs are used in: flow diagrams, state transitions in automata, and calling sequences in procedural code. Moreover, students often misinterpret static causal graphs (Zapata et al (1999). Although the arrows in the diagram give a strong perceptual sense of some relationship between the entities, the nature of that relationship must be given by some other convention. A number of researchers have applied animation to various problems in information display, ranging from visualizing message passing to discrete multi-dimensional data display (Limoges and Ware, 1989; Stasko, 1993, Bartram, 1997). However, the idea of using animation to convey the concept of a causal relationship between variables has not been explored and it seems promising.

Figure 1. A directed graph is a common way of illustrating relationships between entities.

Perception of causality

When we see a billiard ball strike another and set it in motion we perceive a causal event according to the work of Michotte (translated 1963). Michotte carried out careful studies of the perception of interactions between two patches of light and concluded that the perception of causality can be as direct and immediate as the perception of simple form. Michotte used an apparatus with little mirrors and beams of light. Using this, one rectangular patch of light would be moved from left to right until it just touched a second patch of light then stopped (Figure 2). At about this point in time the second patch of light would be made to move. Depending on the temporal relationships between the moving light events and their relative velocities, observers reported perceiving different kinds of causal relationships Michotte variously categorized as “launching”, “entraining” or “triggering”. More recent developmental work by Leslie and Keeble (1987) has shown that infants at only 27 weeks of age can perceive causal relations such as launching. This would appear to support the contention that such percepts are in some sense basic to perception.

Michotte found that precise timing is needed to achieve perceived causality. For example, he found that for the effect he called launching to be perceived the second object had to move within 70 milliseconds of contact. After this length of time, subjects still perceived the first object to set the second object in motion but the phenomenon was qualitatively different. He called it delayed launching. Beyond about 160 milliseconds there was no longer an impression of causal effect; instead, subjects reported perceptions of unconnected movements of the two objects. Figure 3 reproduces of some of his results. They suggest that for causality to be perceived visual events must be synchronized within at least one sixth of a second. Given that in many data visualization systems animation often only occurs at about 10 frames per second this means that events should be frame accurate for clear causality to be perceived.

Figure 2. Michotte studied the perception of causal relationships between two patches of light that moved always along the same line but with a variety of velocity patterns.

Figure 3. From Michotte (1963). The graph shows how different kinds of causal interaction a are perceived depending on the delay between the arrival of one object and the departure of the other.

Based on Michotte’s work we have developed a new visualization construct that we call a visual causality vector (VCV). A VCV is a graphical device that conveys the sense that a change in one entity has caused a change in another entity. We believe there is scope for a richly expressive vocabulary of VCVs that articulate variations on the simple expression of causality. In exploring this design space we have constructed three different metaphors to express different kinds of causal relationship: the pin-ball metaphor, the wave metaphor and the prod metaphor. We describe each metaphor together with some of the opportunities for expression afforded by each. Finally we report some empirical results concerning temporal contingencies required for the pin-ball metaphor.

Pin-Ball metaphor

In the pin-ball metaphor the VCV is a ball that moves from one object to another causing the second object to change. The nodes, when struck, oscillate using a sync function: (sin(t)/t). For the motion of the ball, we use linear interpolated motion between the points.

Figure 4. In the pin-ball metaphor when the VCV is a ball that strikes the target node. The latter is set in motion with a damped oscillation as shown. Note the path is stretched out vertically only to show how the target node moves over time; the motion of the node is strictly horizontal.

For example, a ball may be able express quantity by its diameter and kinetic energy by the product of mass and velocity squared, although the extent to which these quantities are perceived by human subjects is debatable. Gilden and Proffitt (1994) have shown that relative masses of two colliding bodies are estimated heuristically from relative motion (as opposed to size) and this may provide a method for parameterizing the causal effect.

Prod Metaphor

In the prod metaphor a rod extends from one entity to prod a second entity and set it in motion. We use the same sync function to represent the causal effect on the node.

Figure 5 In the prod metaphor the VCV is a rod that extends and strikes the node.

Wave metaphor

The wave metaphor is based on a wave like function animated along an arc (Figure 6). The impact of a wave on a node is shown by a circular component of the node that “floats” as the wave arrives. This metaphor can be parameterized in many ways. The height or speed of the wave can be used to denote the amount of causal power. Waves above and below a line may be able to express positive and negative causal links. A wave that dies out can be used to illustrate weak causal links.

Figure 6. A sequence of arc states animated using the wave metaphor. When the VCV wave strikes the target node it floats up as shown.

Experiment: Temporal contingencies of causality perception.

To validate our approach we designed an experiment to determine whether Michotte’s findings applied to our VCVs. For our preliminary work to concentrated on the pin-ball metaphor. In addition to simply replicating Michotte with this metaphor we extended his experimental paradigm in one significant respect. Michotte investigated only the perceptual consequences of a target object beginning to move after a collision. However, it might be the case that causality can also be perceived reliably if a target node begins to move slightly before the arrival of the VCV. Varying the movement asynchrony in both a negative and positive sense around the time of impact allows for more meaningful estimation of the temporal window required for causality to be reliably perceived.

Our VCVs differ from Michotte’s experimental stiimuli in several ways . In Michotte’s study, the first moving patch of light typically stopped moving and remained visible when the second patch moved off. In ours, the pin-ball VCV continued moving to the center of the target node and then disappeared. Also none of Michotte’s studies used anything resembling our oscillatory motion of the nodes.

Method

The monitor that we used had about 36 pixels per cm. All animations were done at 60 frames/second. The velocity of the pin-ball VCV was 5.6 cm per second and the length of the path to the center of the target node was 3.9 cm. The diameter of the pin-ball VCV was 0.44 cm. and the diameter of the target node was 0.56 cm.

The variation of the sync function used to vibrate the node was

Xdisplacement = sin(20t)*80/(4.0+60t)

where t is in seconds and the displacement is in pixels. This yields a function with a maximum amplitude of motion of about 0.25 cm. and a starting velocity of a little more than 7.0 cm/sec. The motion is rapidly damped so that after one second the amplitude is reduced by 85%

Responses and Instructions

Our experiment allowed four responses: 1) The ball had a direct causal effect on the node. 2) There was some other (unspecified) relationship between the motion of the ball and the motion of the node. 3) There was no relationship between the motion of the ball and that of the node. 4) Repeat the trial. Responses were made with a menu selection.

A pilot experiment revealed that some subjects saw a causal relationship between VCV and node motion when there was temporal synchrony between the start of the pin-ball VCV’s motion and the node motion. This occurred at a relative time to contact of approximately –0.7 seconds. Since we were interested in effects relating to temporal synchrony between the arrival of the pin-ball VCV at the end of its motion path, we asked our observers to ignore this interesting effect.

Trials

There were two parts to the experiment. In the first, the intervals tested ranged above and below the time to contact in intervals of 1/6 sec. The range tested was between +/- 5/6 sec in steps of 1/6 sec. The second part was designed to measure perception more precisely about the point of contact. The range tested was between +/- 1/4 sec with intervals of 1/20 sec.

Trials were given in blocks so that subjects saw each time relative-to-contact interval twice in a random order. There were two blocks for the broad range and two blocks for the narrow range.

Subjects

The 5 subjects were all male volunteers.

Figure 7. Perceived effect is plotted against the delay between the arrival of the ball and the start of the node's vibration.

Results

Figure 7 shows averaged results from five subjects. Since the broad-range and narrow-range results closely agreed, we have combined them. The x-axis shows the time relative to contact where contact is defined as the moment that the front edge of the ball VCV makes contact with the node. As can be seen a direct causal relationship was only perceived if the node started to vibrate a short while after the ball made contact with it. The half width of the causal interval was about 0.25 seconds. For convenience in later discussion we call this perceptual phenomena a p1 response.

Figure 7 illustrates a bimodal distribution in which some relationship was perceived. that could not be characterized as “directly causal”. We call the first peak a p2 response. This has a maximum at about – 80 msec and tails off to zero before –900 msec. The second broader peak occurs when vibration is delayed. We call this a p3 response and as shown this effect is more reliable and decays much more slowly. It is reported almost 100 percent of the time from about 350 msec to 500 msec and is still at about the 50% level at the end of the interval we tested.

Phenomenology

Several researchers have questioned the accuracy of the terms Michotte used to describe the phenomenology of causality (Boyle, 1960; Beasely, 1968). Our experiences confirm this. People we show the effects to often look rather puzzled when we use terms such as “launching” or “triggering”. The are two possible reasons for this. It might be the case that the phenomena are robust but we do not have terms in everyday language to describe them. Alternatively, the phenomena themselves may not be well defined perceptually or cognitively.

To better understand these issues we carried out an informal follow-up study to find out if subjects could verbally characterize what they perceived. To do this we repeatedly showed our observers examples in at the peak of p1 (+80 msec), at the peak of p2 (-80 msec) and at the peak of p3(+400 msec). We also presented the –700 msec effect that we had asked them to ignore during the initial experiment. We recalled four of the subjects and engaged them in a dialogue to try to find out if there were any common descriptive terms that they used reliably. We began by asking them what they saw, without suggesting terminology, then introduced Michotte’s terms and some of our own to see if there was any agreement. The result were clear-cut only for p1 which the observers described as “hitting”. In describing p3 observers did not show any enthusiasm for Michotte’s terms launching or triggering, instead they preferred the term “delayed effect”. The p2 effect was described even more hesitantly. This is not surprising since the p2 effect was the least reliable. Two of the subjects described it as though a force field ahead of the VCV pushed the node to start it moving.

The effect that occurred when the VCV started (as opposed to ended) its movement path in synchrony with the node vibrating was sometimes seen as a kind of reverse causality, or sometimes it was perceived as if there were a third latent variable or agent influencing both events in some causal way.

Conclusion

Our contributions, thus far, are as follows.

• The concept of a visual causal vector has been introduced as a way of visualizing causal relationships.

• Three different VCV metaphors have been constructed.
• A preliminary experiment confirms that the perception of causality is highly dependent on temporal synchrony between the arrival of the VCV and changes in the node. Two phenomenologically different impressions can be reliably obtained, corresponding to the impression caused by hitting, and a kind of delayed effect. We have preliminary evidence for a third that acts when there is near synchrony between the VCV beginning its motion and the oscillatory motion of the node.

References

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