Discovery Using Mental Models

In the previous sections, we have dealt with some general approaches to creativity. In the rest of the chapter, we consider some specific cognitive processes that play a key role in creative thinking and discovery. We begin with the issue of simulation using mental models. Many creative thinkers have reported imagining or simulating various states of the world or situations in the generation of new ideas. Einstein reported thought experiments about riding on light beams and standing in plummeting lifts in developing his ideas on relativity. In this section, we consider some research that has been done on trying to characterise this form of simulation using the idea of mental models.

It has been proposed that people understand the world and simulate aspects of it using "naive theories", "folk theories", or "mental models" (see Brewer, 1987; Gentner & Stevens, 1983; Gilhooly, 1995; Norman, 1983; Rips, 1986; Vosniadou & Brewer, 1992). The theory of mental models is used to account for a variety of aspects of behaviour in novel, problem-solving situations (see Johnson-Laird & Byrne, 1991, and Chapter 16 for a slightly different conception used in reasoning research). In the present sense, mental models refer to mostly imagined, dynamic models that we use in everyday life to think about the world. For example, if you are trying to cross a raging torrent without the aid of a bridge, you might imagine trying to jump across at some point or swing on a rope. This simulation of crossing the river is achieved by a mental model.

Mental models of home heating

Kempton's (1986) work is a prime example of the use of mental models. She proposed that when people regulated their thermostats to heat their houses they used one of two models of how a heating system works: a "feedback model" or a "valve model".

According to the feedback model, the thermostat turns the furnace on and off depending on the room temperature. So, when the room is too cold, the thermostat turns the furnace on and when the room is warm enough, it turns the furnace off. The temperature at which the furnace is turned on, is determined by the setting on the thermostat's dial. This model posits that the furnace runs at a constant rate and so the only way that the thermostat can control the amount of heat in a room is by the length of time that the furnace is on. If the dial is adjusted upward only a little bit, the furnace will run for a short time and turn off; if it is adjusted upward a large amount, the furnace must run for a longer period to heat the house sufficiently. Left at one setting, the thermostat will switch the furnace off and on as necessary to maintain the temperature on the dial setting.

In contrast, in the valve model, the thermostat controls the rate at which the furnace generates heat, rather than having a feedback function. So, the furnace runs at variable rates depending on the setting on the dial. To maintain a constant temperature in the house the setting is adjusted so that the amount of heat generated balances the amount being lost. In this model, the thermostat has no specific role as a regulator of heat; indeed, in one sense, it is the person adjusting the thermostat that acts as the regulator. Several other common physical devices operate in a similar manner and are used as analogies for the valve model. For example, as you turn a tap, more water comes out.

These models make different predictions about how heating systems work and about how energy can be saved in the home. However, even though they are elaborate and intriguing, neither of them is technically accurate. The valve model predicts that more fuel is consumed at higher settings than at lower settings. This prediction is correct but for the wrong reasons; the higher fuel consumption is not the result of the valve opening wider, but is due to higher internal temperatures in the house resulting in greater heat loss through walls, windows, and ceilings. Hence, people using the valve model tend to re-adjust their thermostats more frequently and be more efficient energy users. In contrast, the feedback model can, under certain circumstances, lead to fuel wastage. People using the feedback model tend to leave their thermostat settings at a set, often high, level for long periods of time; they assume that the thermostat will turn the heating off when the required temperature is reached. So, the heating is on more than is necessary. In an ecology-conscious world, the importance of these findings is enormous. Kempton estimates that if people had an appropriate and accurate model of home heating then the saving for all US households in a single year could be around $5 billion.

Home heating models illustrate some of the main properties of mental models. First, mental models are predictive; they suggest different ways in which physical mechanisms operate. Second, they simulate physical mechanisms and phenomena, and are often accompanied by visual imagery. For example, someone using the valve model could easily imagine a signal going from the dial on the wall to the furnace causing the valve to open, stoking the flames of the boiler. Third, people can have multiple models to deal with different aspects of the same system; Kempton identified two different models but admitted that many people may have a mixture of both. Fourth, mental models can be volatile; they can undergo sudden changes depending on the knowledge used to construct them and an individual's conception of the task situation. Finally, it is also possible that people's protocols, which appear to reflect model use, include ad-hoc rationalisations to account for actions that have been taken. So, some of the information that people report may not be part of the model at all.

Naive models of motion

Similar evidence for the use of mental models has been found in studies of people's naive theories of object motion (see Caramazza, McCloskey, & Green, 1981; McCloskey, 1983). These models are fairly consistent across individuals and can be applied to many different situations; however, they differ markedly from the fundamental principles of classical physics (interestingly enough, they parallel early pre-Newtonian physics). McCloskey and his colleagues examined these naive theories by looking at subjects' answers to problems like the following one (see Figure 15.3):

In the diagram, an airplane is flying along at a constant speed. The plane is also flying at a constant altitude, so that the flight path is parallel to the ground. The arrow shows the direction in which the plane is flying. When the plane is in the position shown in the diagram a large metal ball is dropped from the plane. The plane continues flying at the same speed in the same direction and at the same altitude. Draw the path the ball will follow from the time it is dropped until it hits the ground. Ignore wind or air resistance. Also show as well as you can the position of the plane at the moment that the ball hits the ground.

Only one of the diagrams in Figure 15.3 is correct (the first). When the ball is dropped it will describe a parabolic arc and the plane will be above the ball when it hits the ground. The total velocity of the ball is made up of two independent velocities; a horizontal and a vertical velocity. Before the ball is dropped, it has a horizontal velocity equal to that of the plane and a vertical velocity of zero. After the ball is released, it undergoes a constant vertical acceleration due to gravity, and thus acquires a constantly increasing vertical velocity. The ball's horizontal velocity, however, does not change; it continues to move horizontally at the same speed as the plane. It is the combination of the constant horizontal velocity and the continually increasing vertical velocity that produces a parabolic arc. Because the horizontal velocity of the ball equals that of the plane, it hits the ground directly beneath the plane.

The correct response (a) and incorrect responses (b-d) for the aeroplane problem. Reproduced from Mental models (edited by D.Gentner & A. Stevens) published by Lawrence Erlbaum Associates Inc., © 1983 Lawrence Erlbaum Associates Inc.

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