Constraint relaxation and chunk decomposition as means to insight

Constraint relaxation and chunk decomposition as means to insight


Insight is usually described as a phenomenon accompanied by an Aha moment which occurs when there’s a conscious change in a person’s representation of a situation, event or a problem. A common component of insight problem solving is an impasse which precedes the Aha moment, although it may not always be present.

This is important because we can see some connections between the practice of writing evergreen notes ad the processes that facilitate insights:

Theories on insights

In the Gestalt view, insight is described as a spontaneous restructuring of the problem’s mental representation. An insight occurs not due to making incremental associations between information, but due to overcoming a fixation as a result of past experience. In this gestalt view, the restructuring often occurs suddenly, so individuals tend to not be aware of how the solution is reached.

The Progress Monitoring Theory of insight explains insight as a strategic switch made in an incremental problem solving process. It is based on The Problem Space Theory which models problem solving as applying operators to transform initial state to goal state. This theory interprets insight problem solving as just another instance of problem solving and in which incremental progress can be made.

The Representational Change Theory of insight suggests that insight is a re-organization of the problem’s representations. This bears some similarity to the Gestalt theory, however it does not state that the restructuring is sudden. This theory also doesn’t exclude incremental problem solving process from the list of process that can lead to the restructuring of problems.

How these theories explain impasse

In insight problem solving, an impasse is often experienced by problem solvers. Theories on insight aim to explain how these impasse is reached, and how insight is possible as a result of overcoming such impasse.

One explanation that stays close to The Progress Monitoring Theory of insight is that impasse is a state where problem solvers realize the current heuristic is inappropriate in solving the problem. Heuristics are used to select a set of moves that reduce the distance from the current state to the goal state. In this view, an impasse is reached when the distance to the goal state is large and the number of remaining moves is small. As a result, overcoming the impasse is amount to switching to another heuristic or strategy.

An explanation for impasse consistent with the Gestalt interpretation of insight is that impasse is a counterproductive use or undesirable effect of prior knowledge. When making wrong moves, the unsuccessful approaches and irrelevant information keep getting activated in the working memory. In this view, the main way to escape from the impasse is to set the problem aside for a while (entering an incubation period) for the activation of unsuccessful paths to decay to the point where alternative paths can compete fairly during problem solving process.

The Representational Change Theory of insight posits that problem solvers fail to generate an adequate representation of the problem in order to arrive at a solution. For example, the initial representation over-constraints the search space and thus a valid solution cannot be found. In the famous nine-dots problem, the usual representation over-constraints that the lines must be within the grid. An impasse is reached when the solvers have exhausted the implications from the inappropriate problem representation. Overcoming an impasse thus necessitates restructuring the problem’s representation.

Insight is a reorganization of the problem’s representation that enables a valid solution

Research indicates that representational change influences solution rates stronger than inappropriate heuristics, which means applying heuristics on an inappropriate initial problem state will not produce insights. In other words, restructuring is necessary to solve insight problems. This is consistent with The Representational Change Theory of insight. Unlike what the Gestalt theory suggests, the process of restructuring is not sudden, but gradual – a problem solver gets warmer and warmer as he approaches the point where restructuring takes place. Put it all together, we can describe an insight problem as that which necessitates reorganization of the problem’s representation. As a consequence, insight is a reorganization of the problem’s representation that enables a solution to be found. Note that this definition doesn’t downplay the importance of applying appropriate heuristics to solve problems. A reorganization must be followed by appropriate problem solving strategies in order to enable a valid solution.

Reorganize problem’s representation with constraint relaxation and chunk decomposition

Under The Representational Change Theory of insight, insight problem solving must involve realizing the insufficiency of problem’s mental representation and then changing them. Research has been done on how problems are represented and how they affect solutions. A problem can be represented by a set of constraints on the solution. It can also be represented by the perceptual chunks that we use to interpret the world.

As mentioned earlier, an insufficient set of constraints may over-constrain and exclude the correct solution. An insufficient set of chunks cannot be used to produce a correct parse of the situation. Correspondingly, reorganizing a problem’s representation can be done through relaxing unnecessary constraints and decomposing inappropriate chunks into more appropriate chunks.

Research shows that constraint relaxation and chunk decomposition predicts difficulties of insight problems. Specifically, Constraints of smaller scopes are more likely to be relaxed, and Loose chunks are more likely to be decomposed. The difficulty of a problem is then based on the number of constraints that need to be relaxed, and the tightness of chunks that need to be decomposed.

This also explains why sometimes people do not experience Aha moments when solving classical insight problems (nine-dots, matchstick, etc): the likelihood of experiencing Aha would decrease with the number of constraints need to be relaxed. The same also is also likely for chunks. In other words, the more difficult an (insight) problem is in terms of constraints and chunks, the less sudden it feels to a problem solver.

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