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effects of the "swing" hint on the solution of the two-string problem. Second, they showed that problem solving that relied solely on past experience often led to failure; recall the demonstrations of problemsolving set (where a routine method is used) and functional fixedness (when the typical function of an object is assumed).

Gestalt theory was based on a perceptual metaphor carried over from their perceptual theories (and everyday life?). This metaphor makes the theory very attractive and comprehensible but it is also its main weakness. The concepts of "insight" and "restructuring" are attractive because they are easily understood and convey something of the mysterious dynamism of human creativity. However, as theoretical constructs they are radically underspecified (see Chapter 1); the conditions under which insight and restructuring occur were unclear and the theory did not really specify the nature of either concept. However, the Gestalt work is not a Jurassic creature to be buried in the cemetery of psychological theory. In many ways the spirit of Gestalt research, with its emphasis on the productive and non-associationistic nature of thinking, informed the information-processing approach that followed some decades later (Holyoak, 1991; Knoblich & Wartenberg, 1998; Ohlsson, 1984a, 1992). The school also left a large corpus of experimental materials (in the form of problems) and evidence that had to be re-interpreted by later information-processing theory (see later sections). The Gestalt legacy was, therefore, substantial.

NEWELL AND SIMON'S PROBLEM-SPACE THEORY

The problem-solving research of Allen Newell and Herb Simon, of Carnegie-Mellon University, is the very foundation of the information-processing framework. In the late 1950s, they produced the first computational models of psychological phenomena and made milestone discoveries in cognitive psychology and artificial intelligence. Their problem-space theory of problem solving, recounted in their 1972 magnum opus entitled Human Problem Solving, remains at the centre of current problem-solving research. In fact, many of the remaining areas reviewed in this chapter and the next are elaborations of Newell and Simon's basic views.

Problem-space theory

It is very natural to think of problems as being solved through the exploration of different paths to a solution. This is literally the case in finding your way through a labyrinth. You start from a point outside the maze and then progress through it to the centre. On your way, you reach junctions where you have to choose between going straight on, turning to the left or right, or turning back. Each of these alternative paths may branch again and again so that, in the maze as a whole, there are hundreds of alternative paths (only some of which will lead to the centre). Different strategies can be used to find one's way through a labyrinth (e.g., mark your past path, initially always take the left turn). Umberto Eco's (1984) novel The Name of the Rose gives a vivid description of using several strategies to pass through a deadly, monastery labyrinth. These strategies provide you with a systematic method for searching the maze and help you to select one from among the many alternative paths.

Newell and Simon used parallels to these basic ideas to characterise human problem-solving behaviour. They suggested that the objective structure of a problem can be characterised as a set of states, beginning from an initial state (e.g., standing outside the maze), involving many intermediate states (e.g., moving through the maze), and ending with a goal state (e.g., being at the centre of the maze). Just as in the labyrinth, actions can be performed or "operators applied" (e.g., turn left, turn right). The application of these operators results in a move from one state to another. In any given state there may be several different operators that apply (e.g., turn left, turn right, go back) and each of these will generate numerous alternative states. Thus, there is a whole space of possible states and paths through this space (only some of which will lead to the goal state). This problem space describes the abstract structure of a problem.

Newell and Simon take the further step of proposing that when people solve problems they pass

PANEL 14.1:

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