Incubation in Problem Solving and Creativity

Unconscious Processes

Kenneth J. Gilhooly

• Publisher: Routledge
• Year: 2019
• ISBN:
  9781351375962
• Edition: 1
• Topic: Psicología
• Subtopic: Historia y teoría en psicología

Can problems be solved by setting them aside or by sleeping on them? Incubation, the process of stopping conscious work on problems for a set period of time, is an integral part of the creative problem solving process.

Providing an overview of the main issues, findings and implications of cognitive research on incubation effects in problem solving and creativity, this book argues that incubation is an effective strategy for tackling problems that do not yield to initial solution attempts. Gilhooly reasons that unconscious work is automatic and explores the underlying processes involved in incubation, providing evidence to showcase the major role of unconscious processing in problem solving. Incubation in Problem Solving and Creativity concludes with a discussion of the implications of unconscious work theory for enhanced problem solving, positioning incubation as an effective and important stage in creative problem solving.

This book is an invaluable resource for students and researchers of problem solving, creativity and thinking and reasoning as well as for students from all disciplines taking problem solving modules.

1

PROBLEMS, PROBLEM SOLVING AND CREATIVITY

Introduction: problems, problems, problems

Since our focus is on the possible effects of setting problems aside, generally known as “incubation”, let us start by defining “problems” and outlining the main features of problems. Over 70 years ago, Karl Duncker (1945) gave a useful definition of a problem as a situation in which an organism has a goal but does not know how to reach that goal. So, if a person with no knowledge of car mechanics has the goal of starting a car and finds turning the ignition key yields only a “clunk” sound without the engine firing, then that person will have a problem. A skilled car mechanic who has the required knowledge would not have a problem.

Of course, problems come in many shapes and sizes, but it seems that all problems have three main components. These are (1) a goal, (2) a starting state of affairs in which the goal is not met and (3) a set of possible actions that if applied in the right order could change the situation to achieve the goal. Although we can say that all problems share this common abstract structure, it is also true that problems can be classified in various ways. One classification is into those problems in which all the elements of the problem, the starting state, the goal and the actions available for moving from the starting state to the goal, are well-defined or completely specified as against problems where some or all elements are ill-defined or not completely specified (Reitman, 1964; Simon, 1973; Lynch et al., 2006; Reed, 2016). A chess problem is a prototypical example of a well-defined problem, in which the starting state is given by the layout of standard pieces on the standard board, the goal is well-defined (say, “Checkmate for White in three moves”) and the means available are specified by the legal moves of the pieces in the game. On the other hand, a problem may be very ill-defined, such as that of “Improving the quality of life in this country”, in which the starting state, the goal state and the means available are not at all well-defined. In ill-defined problems, it does seem likely that an initial step will be to try to convert the problem into a better defined one by trying out possible specifications of the ill-defined components (Weisberg, 2006, p. 139). In the problem of “Improving the quality of life”, some of the missing details could be filled in by deciding on a particular way of measuring quality of life. One could try using a well-established questionnaire measure, such as the World Health Organisation Quality of Life (WHO-QOL) questionnaire (WHO-QOL group, 1995), and that would help specify the starting state (e.g. as the mean score on the WHO-QOL for a large representative sample of people living in the country), and the questionnaire could be used to assess any effects of interventions as bringing about progress to the goal or not (e.g. has an intervention led to a significant change in WHO-QOL scores in the desired direction?).

A second way in which problems can vary is in requiring extensive expert knowledge (i.e. “knowledge rich” problems) or being within the scope of any normally educated literate adult (i.e. “knowledge lean” problems). The typical laboratory puzzle, such as an anagram (e.g. what word has been scrambled to make the string “rpolbme”?), is a knowledge lean problem. This means that it can be tackled within a reasonable time by anyone of a large population of participants. Knowledge rich problems, such as problems arising in running a nuclear power station, diagnosing car problems, flying a passenger plane or treating a rare disease, can only be tackled by very small numbers of highly trained individuals (“experts”). Knowledge rich problem solving is less easily open to laboratory research than knowledge lean problem solving. Nevertheless, there is a large and growing literature on expertise effects in problem solving where experts’ approaches and strategies are contrasted with those of beginners (novices) and people with intermediate levels of knowledge between novices and experts (Ericsson et al., 2006).

Another way of dividing problems is into those that can be solved by straightforward search processes without any need to re-interpret the problem statement and those which require re-interpretation or “re-structuring” of the problem. An example of a problem that could be solved by routine search is an anagram; for example, by trying out systematically possible re-arrangements of the letters “ccpteno”, one could sooner or later find the scrambled word “concept”. Some problems, however, do typically induce a misleading representation which then needs a re-interpretation or re-structuring. For example, “How could a man marry 30 women in one month and break no laws against bigamy?” Here the typical interpretation of the word “marry” as “becoming married to another person” is misleading. “Marry” here must be re-interpreted as “causing others to become married”. Thus, the man is authorised to conduct marriages. Another example is “How could a man walk over the surface of a deep, mile wide lake without any floatation devices or aids?” This problem requires the solver to move from a default representation (at least in non-Arctic regions) of the water in the lake as being in a liquid state and to represent the water instead in a solidly frozen state. Such problems, which typically require re-structuring or re-interpretation, are often labelled “insight” problems. Once the appropriate re-structuring occurs the solution is immediately understood. Problems that are typically solved without re-structuring are often labelled as “non-insight” problems.

The classifications into “insight” and “ill-defined” tend to overlap in that ill-defined problems need initial structuring and often re-structuring, and so tend to be classifiable as “insight” problems. However, some insight problems are well-defined in terms of starting state, goal and means available, such as the nine-dot problem, where the starting state is given (a square 3 × 3 array of dots), the goal state is specified (connect dots by four straight lines without lifting pen from paper) and the means available are specified (draw four straight lines without lifting pen from paper to connect dots).

Solving non-insight problems: forward search and hill-climbing

How are problems typically solved? Let us start with non-insight tasks as a simpler case than insight problems. For well-defined problems, in which the starting state, the goal state and the available actions are all completely specified, a complete systematic search is, in principle, an algorithmic way to be sure of solving, without changing the initial problem representation. The conceptually simplest approach to actually performing a complete search is to systematically generate all the possible states that could be reached from the starting state by applying all possible actions or moves from the starting state and keep generating new states from each new state generated until the goal state is reached – whereupon the problem is solved. If the problem is insoluble, the whole problem space would be generated. This complete search approach is known as breadth-first search and in theory is a “magic key” to solve all well-defined problems! Why then are so many well-defined problems unsolved, such as “Is chess a game that White should always win, or is it a game that should always be drawn, if both players play perfectly?” Unfortunately, problems of any real scale, such as the chess problem, quickly involve astronomically vast problem spaces with more states than atoms in the universe and cannot realistically be searched completely. Even the humble noughts-and-crosses or tic-tac-toe game has a problem space of some 255,000 states. Part of the space of noughts-and-crosses (tic-tac-toe) is shown in Figure 1.1. In this game, players alternately place Xs or Os in the 3 × 3 grid until one player has an unbroken line of their symbols, or the grid is full (a draw). If both adversaries play perfectly, a draw will always result … but this is not immediately obvious.

People have very limited working memories to use in exploring problem spaces without memory aids such as paper and pencil, and we tend to use shortcut methods known as heuristics to narrow and focus our searches. (Heuristics aid problem solving but do not guarantee solutions.) A typical heuristic is that known as hill-climbing. With this approach the solver assesses all possible moves a limited depth ahead, say going just one step ahead, choosing the move which is evaluated as looking to be nearer to the goal (getting warmer!). The process repeats until the goal is reached or until a state is reached from which no further progress is possible. Should such an impasse be reached the person can back up and try alternative routes, avoiding the impasse state. The hill-climbing method derives from the real world problem of finding a peak when climbing a hill in a thick fog; in this situation, trying out one step in each of the four main directions, North, South, East and West, and picking the step that reaches the highest next point and repeating the process will lead to a peak. It may be a false peak if you have started up a foot-hill as against the main hill and so is not guaranteed to solve, but it will often be useful.

FIGURE 1.1 Partial problem space for the game of noughts-and-crosses (or tic-tac-toe) after two moves.

Using a hill-climbing heuristic seems to underlie the difficulties that participants have with a frequently studied laboratory problem known as the Hobbits and Orcs problem (Thomas, 1974). The task is to get three Hobbits and three Orcs across a river. The only way to cross is by a small boat that can carry only one or two passengers at most. However, there must be at least one passenger in the boat for it to cross, and most importantly, you have to avoid Orcs outnumbering Hobbits on same side of river – the Orcs will eat the Hobbits if they outnumber them (based on Tolkien, 1966).

The complete problem space for the Hobbits and Orcs problem is shown in Figure 1.2. The space of possible states in this problem is quite small, comprising just 15 states, and the minimum path from starting state to goal state is 11 moves long. However, typically participants take around 22 moves rather than just 11. There is a strong tendency to get involved in unnecessary loops and backtracks – going round in circles! Some of the looping probably arises as a result of hill-climbing. For instance, in State 5 of the problem space, going to State 4 looks attractive as that has more creatures on the target side, but it puts the solver into a loop. A further difficulty is often experienced at State 8, where the solver has four out of six creatures on the target side. Difficulty here most likely arises because people feel they are making good progress (the problem seems to be 67% solved!) and are reluctant to make a detour, moving away from the goal, which is the best move. Moving to State 9, where only two creatures are on target side as against four on the target side, looks very unattractive. That is, people typically are using a hill-climbing heuristic, which causes difficulties at State 8 because at that state, they have to detour and go further from the goal (from only two more to move, to four more to move) in order to progress, and that goes against a pure hill-climbing strategy.

FIGURE 1.2 Problem space for Hobbits and Orcs.

Problem reduction and means-ends analysis

In addition to forward search of a problem space, from the starting state onwards, using limited look-ahead and hill-climbing, well-defined problems can often be tackled by problem reduction, also known as means-ends analysis or sub-goaling. This approach involves breaking the overall problem into smaller independent sub-problems and if need be dividing the sub-problems into sub-sub-problems, and so on, until a sub-sub-…-sub-problem is reached that can be solved in a single step. A real life example would be making travel plans, say to travel from London to New York. The overall goal is to reduce a long distance. That can be tackled by means of a plane or a boat. Say Plane is chosen; there is now a sub-problem of “getting on board a plane to use it”. This requires solving a “ticket getting sub-sub-problem” and a “getting to the airport sub-sub-problem”. The airport sub-sub-problem could be solved by catching a train to the airport. That, in turn, raises the sub-sub-sub-problem of getting to the train station, which may be solved by walking, in which case that action can be carried out. Once at the station, the train can be caught, and then at the airport, the plane can be accessed.

This problem reduction approach is widely used in real life and has been shown in laboratory studies of artificial tasks such as the Towe...