## General Approaches To Creativity

In the past, accounts of creativity have often been descriptive rather than explanatory. The classic example of this descriptive approach is Wallas's (1926) classification of the broad stages of the creative process into:

• Preparation, where the problem under consideration is formulated and preliminary attempts are made to solve it.

• Incubation, where the problem is left aside to work on other tasks.

• Illumination, where the solution comes to the problem solver as a sudden insight.

• Verification, in which the problem solver makes sure that the solution really works.

This classification appears to be supported by the reports of creative scientists. One such famous report is by the French mathematician Henri Poincare (1913), who reported working intensively on the development of Fuchsian functions for 15 days. At the end of this time he reported that:

I wanted to represent these functions by the quotient of two series; this idea was perfectly conscious and deliberate; the analogy with elliptic functions guided me. I asked myself what properties these series must have if they existed, and succeeded without difficulty in forming the series I have called theta-Fuchsian.

Just at that time I left Caen, where I was living, to go on a geologic excursion under the auspices of the school of mines. The changes in travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define Fuchsian functions were identical to those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty.

Poincare's report fits Wallas''s framework perfectly, with illumination following an incubation period after extensive preparation. However, even though Wallas's analysis provides us with a broad framework, it is really too general and descriptive. Fortunately, some attempts have been made to specify these stages; for example, incubation and illumination have been treated in Gestalt research on insight (see Chapter 14).

### Incubation and illumination

Few studies have been carried out on incubation, although on balance they support the existence of the phenomenon (see Ohlsson, 1992, and Kaplan & Simon, 1990). Incubation can be explained within problemspace theory as a special type of forgetting (see Simon, 1966). Simon (1966) makes the distinction between control information about a problem (e.g., a record of the subgoals tried in a problem) and factual information (e.g., some property of an object or substantive aspect of the problem). For example, in Maier's (1931) two-string problem, control knowledge might include the subgoal "try to reach something that is far away" and substantive information would be that "the string is a flexible object" (see Chapter 14 and Keane, 1989). Factual information discovered in the context of one subgoal will not be available to other goals. However, during incubation, control information decays faster than factual information. Therefore, after the problem has been set aside for a time, subgoal information will be lost but the factual information will still be present. This factual information will thus be available to newly generated subgoals of the problem, increasing the likelihood of the problem being solved. Several other recent studies support this sort of account. In cognitive neuroscience studies, Bowden and Beeman (1998) have shown hemispheric differences in the priming of hints to insight problems. Similarly, Yaniv and Meyer (1987) have shown that unsuccessful attempts to retrieve inaccessible stored information can prime the recognition of later information by a process of spreading activation.

Ohlsson (1992) maintains that there is very little empirical support for illumination; the literature on it seems to rely on two anecdotal reports by von Helmholtz and Poincare (see Hadamard, 1945). If we are to relate the phenomenon to any literature, it is that on the use of hints in problem solving. Again, much of this work has been carried out within the Gestalt tradition (see Chapter 14). The current favoured account seems to be that any new information introduced into the problem or met in the environment may activate related concepts in memory and result in the sudden emergence of a solution. For example, in the case of the two-string problem, Maier reported that when the experimenter brushed off the string, setting it swinging in the line of sight of subjects, many of them suddenly produced the solution of swinging the string and catching it on the up-swing, while holding the other string.

### Recent accounts of creativity

Even though Wallas's stages of creativity have been very influential, his formulation is not the final word on creativity. More recently, several cognitive scientists have made a number of proposals about aspects of the phenomenon. None of these proposals is at variance with the theoretical proposals of this and the previous chapter and many of the ideas have been modelled computationally already.

Boden's (1991, 1994) account of creativity makes the distinction between improbabilistic creativity and impossibilistic creativity. Improbabilistic discoveries involve novel combinations of familiar ideas; hence, they are discoveries that have a low probability of occurring. Boden sees this type of creativity as being the product of associationistic or analogical thinking (see later section). Impossibilistic discoveries are more radical, in that ideas are generated that, in some sense, could not have been generated before. Boden argues that ideas are always generated within a conceptual space, like a problem space, which is generated by some set of rules or constraints. People explore these conceptual spaces using various conceptual maps, which characterise typical routes through the space. Some forms of creativity are linked to exploring new parts of the space, or in showing the limits of the space. Other forms of creativity emerge when the fundamental rules of the space are violated or modified. When the space itself changes, ideas that could not have been generated before emerge. For example, James Joyce's Ulysses could be viewed as an exploration and extension of the space of literary styles used in the novel. This conceptual space is explored by writing different sections of Ulysses in widely differing styles (e.g., as a Middle-English, Chaucerian tale or a threepenny-terrible, romantic novel). The space of styles used in the novel is extended by introducing the style of streaming consciousness, which is designed to mimic the flow of an individual's thoughts (see beginning of Chapter 14 for an example). Any computer program that changes its own rules and hence its conceptual space can be said to manifest impossibilistic creativity (Boden, 1991).

Finke, Ward, and Smith (1992) have outlined another general model of creativity, the so-called Geneplore model, which divides creativity into a generative phase and an exploratory phase (Smith, Ward, & Schumacher, 1993; Ward, Smith, & Finke, 1995). In the generative phase, people are said to construct mental representations, called preinventive structures which have certain properties that promote creative discovery. In the exploratory phase, these properties are exploited to make sense of the preinventive structures. If these explorations are successful then a creative product might result, if not then one cycles back to the generative phase to either produce new preinventive structures or to modify the original structure. In this cycling process, various constraints are applied or even discovered on the creative product, gradually refining and improving it. The Geneplore model is very general and can be used to account for everything from conceptual combination (see Chapter 9), to imagination to fixation in insight problems.

One of the Geneplore model's most well known applications has been in the area of structured imagination. The preinventive structures built during the generative processes should be founded on people's prior knowledge; hence, it was predicted that when people were given imagination tasks they would tend to generate products that were structured in various ways. Ward (1992) asked subjects to draw imaginary creatures on a planet somewhere else in the galaxy; subjects were asked to draw their initially imagined animal, another animal of the same species, and a member of a different species (see Figure 15.1). Ward found that the "majority of imagined creatures were structured by properties that are typical of animals on earth: bilateral symmetry, sensory receptors and appendages" (see Figure 15.2). In a similar study, Bredart (1998) found that when a feature was not included (e.g., an eye) a novel structure with the same function was included (e.g., some sensor for extracting sensory information). Ward (1992) has shown that people dealt with the task by first retrieving exemplars of known earth animals (i.e., the preinventive structure) and then modified these representations according to instructions and task constraints (i.e., exploration of the preinventive structure under the guidance of constraints). Furthermore, when some

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