Insight and insight problems: Definition and approaches

Introduction

People spend a significant amount of time solving problems, which thus represents an important area of psychological research. However, the problems can be roughly divided into well-defined (DDP) and ill-defined (ZDP), while most research efforts have been aimed at revealing the regularities related to the solution of DDP. This can be described as a heuristic search of the problem space (PP), i.e. the set of all logical states that can be formed based on the representation of the problem - knowledge of the initial state, the target state, and the operators by which one moves from one state to another (Kaplan & Simon, 1990). It is assumed that the difficulty of DDP depends mainly on the size of the PP. For example, chess is more demanding than checkers because the player has to consider a larger number of states, but in both cases it follows clearly defined rules.

In everyday life, however, people mainly encounter ZDP, which is especially difficult to properly represent, or to determine the starting points on the basis of which the PP should be formed at all. An example is the situation recorded by Max Wertheimer (2020, p. 162), in which two boys were playing badminton: The stronger one kept beating the weaker one, the latter resigned and the stronger one could not persuade him to continue the game. However, the scientific investigation of the solution to such problems is complicated, because it is affected by factors that cannot be measured and isolated well enough in natural conditions. The starting point should be insight problems (VP) - a type of ill-defined tasks, allowing to examine some aspects of the solution of ZDP under controlled conditions. These are mostly emotional riddles, for example: "Elena's earring fell into her coffee cup this morning. Although the cup was full, the earring remained dry. How is this possible?"

Our goal in this article is to approach the issue of VP and, by comparing knowledge from different areas, try to answer whether they can be singled out as a separate category, which theories most meaningfully explain the course of their solution and whether they really help us understand how people face problems in real life.

Delimitation

According to Batchelder and Alexander (2012), it is not productive to attempt a precise definition of VP and instead suggest focusing more on a set of mostly shared characteristics in terms of Wittgenstein's concept of familial kinship. Several authors agree on the most general ones - VPs should be characterized by the fact that: 1. they lead the solver to a non-adaptive initial representation of the problem, which must be overcome, 2. the re-representation of the problem leads to the subsequent finding of a solution quickly and unexpectedly, while it is usually accompanied by the experience of sudden understanding (insight), 3. the solution does not require unique knowledge or computationally demanding operations (Batchelder & Alexander, 2012; Weisberg, 1995, according to: Davidson, 2003; Öllinger & Knoblich, 2009). We will tentatively start from this framework definition, but in the next part we will supplement it with empirical knowledge pointing to possible differences between VP and DDP in terms of phenomenology, individual differences and neurophysiology.

Phenomenology

Janet Metcalfe conducted revolutionary research on the differences between VP and DDP, while they related to the phenomenological level: In the first study, she found that the participant's subjective feeling of knowing the correct answer before the actual solution attempt predicts his performance only in DDP, not VP (Metcalfe, 1986). In another experiment, participants rated the feeling of getting closer to the correct answer every 15 seconds, and in addition to replicating previous findings, it was also shown that in DDP finding the solution is smooth, while in VP it is jumpy (Metcalfe & Wiebe, 1987). However, Weisberg (1992) subsequently pointed out several problematic aspects of these works. He thought, for example, that the detected differences may not be based on current self-monitoring processes, but rather on previous experiences - in short, the participants knew how long it usually takes them to solve DDP but not VP.

Further doubts, but with an interpretation supporting the unique phenomenology of VP, were brought by the introduction of the method of retrospective assessment of the progress of the solution through self-report scales. Laukkonen and Tangen (2018) found that statements obtained by these two methods are practically uncorrelated. They justified the discrepancy by the fact that the continuous evaluation method leads to overlooking some insight experiences, because participants may have the mistaken feeling that they are gradually approaching the solution, then suddenly realize the incorrectness of their thinking and subsequently experience an authentic insight, which cannot be recorded in 15 second intervals. The interpretation was supported by a recent study by Laukkonen et al. (2021), who compared the retrospective assessment with a scale to the ongoing assessment expressed by grip strength on a dynamometer (capable of affecting even quick and small changes). Both types of evaluations were mutually correlated, and the approach to the solution was continuous for DDP and jumpy for VP - as the classical definition assumes.

Individual differences

Only a few works looked for predictors that would be able to discriminate between VP and DDP. However, those available converge to similar results and show that although performance in both types of tasks is correlated (DeYoung et al., 2008; Gilhooly & Murphy, 2005; Schooler & Melcher, 1995), there are also variables that predict only the ability to solve VP: One of them is to overcome the mental setting or to deviate from the framework. Schooler & Melcher (1995) operationalized individual differences in this ability as performance in a test based on Bruner and Potter's experiment with the perception of out-of-focus images, which was statistically significantly correlated only with VP solution. DeYoung et al. (2008) had reservations about the used method and the statistical interpretation – they believe that no strong conclusions can be made based only on the difference in statistical significance, moreover they showed that the test of the difference between the correlations was not statistically significant. For this purpose, they themselves used a task based on Bruner and Postman's experiment with the identification of non-traditional cards and using regression analyzes found that performance in it is uniquely associated with the solution of VP.

Using the same method, the authors found that the flexibility of divergent thinking is uniquely associated with the VP solution (DeYoung et al. 2008). The results are also supported by the study of Gilhooly and Murpy (2005), who compared the average correlations of figurative fluency and the ability to find alternative uses of objects with VP and DDP, while they discovered a statistically significant difference between them. For completeness, let us add that while Schooler and Melcher (1995) used only 8 tasks and DeYoung et al. (2008) 9 (only verbal), Gilhooly and Murphy (2005) to 24 (of different kinds) while also performing a cluster analysis, which showed the tendency of VP and DDP to cluster into separable categories.

Neurophysiology

A lot of work has been done using fMRI or EEG to reveal the neuronal substrate of the experience of insight or the processes involved in solving VP, and some authors even talk about identifiable networks forming the "insightful brain" (Shen et al., 2013). However, these works are necessarily correlative and, especially in the case of insight research, it can be difficult to distinguish with imaging methods whether the given results really reflect the investigated variables or undesirable effects associated with the specific nature of the task or environmental factors - a critical review of older works with conceptual parallels for current research is also given by Batchelder and Alexander (2012). So we will focus on data obtained through other methods: Reverberi et al. (2005) compared the performance in solving match puzzles (see section 4.4 below) in the general population and patients with damage to the dorsolateral prefrontal cortex (DLPFK, which plays an important role in executive processes important for solving DDP) and found that while only 42% of the healthy participants solved the more difficult of them, the proportion of the group with a DLPFK lesion was as high as 82%. The authors interpret the results so that damage to the DLPFK resulted in a reduction of the so-called top-down control (responsible for limiting solution options resulting from past experiences), which can have an adaptive nature when solving VP even at the cost of a cognitive deficit in DDP. Luft et al. (2017) repeated these results with a smaller effect in an experiment where they temporarily inhibited DLPFK functions in healthy people using transcranial magnetic stimulation (TMS).

Lateralization is also a stimulating area. Chi and Snyder (2011) showed that success in solving match puzzles can be dramatically increased by inhibiting the anterior temporal lobes in the left and stimulating them in the right hemisphere (success rate 20% in the control vs. 60% in the experimental group). One year later, they increased participants' performance in the same way in the "unsolvable" 9-point problem (Fig. 1 in section 4.2) (0% vs. > 40%) (Chi & Snyder, 2012). Although the authors did not deal with the possible effect of the procedure on the ability to solve DDP, their interpretation is similar to that of Reverberi et al. (2005) - believe that the left hemisphere contains top-down organized abstract concepts that prevent a person from perceiving "raw" sensory data and being flexible in their categorization (a more detailed explanation is offered by Snyder et al. (2004)). Given this, we see no reason why people should benefit significantly from it even when dealing with DDP.

Ecological validity

An important feature of the construct is its usability outside of "laboratory" conditions. However, the ecological validity of VP has received almost no attention - so far only two studies are available, which reached contradictory results: Lubart and Sternberg (1995) found that performance in VP is moderately to strongly correlated with the ability to create creative (artistic, scientific...) works under experimental conditions. However, the authors did not investigate whether the established relationships are independent of other factors (intelligence, interests) and although the research design allowed them to operationalize creativity on a behavioral level, it may be distant from spontaneous and long-term creative activity in everyday life. Beaty et al. (2014) compensated for this deficiency by using self-reported, but valid and reliable methods. However, they did not discover the relationship between performance in the VP solution and real achievements in various creative fields.

Approaches

The course of the VP solution describes several models based on different backgrounds. In the following part, we briefly describe the most important ones and we also try to confront them with each other in view of the knowledge presented in the previous part.

Shape psychology

Shape psychology arose in response to associationism and behaviorism (Ash, 1995; Davidson, 2003; Ohlsson, 1984a; Öllinger & Knoblich, 2009), in which problem solving was reduced to the result of learning by trial and error (Thorndike, 1922, according to: Wertheimer, 2020, p. 44). The representatives of Form Psychology considered thinking in this way to be ethically and aesthetically repulsive and tried to prove that it must include something more, on the basis of which they distinguished between bad (reproductive) and good (productive) thinking (Ohlsson, 1984a).

Since they devoted a considerable part of attention to the research of perception, good thinking was not only closely connected with it, but also characterized by similar principles: According to them, perception was characterized by the fact that the visual field is organized into meaningful structures with different properties than those belonging to the simple sum of elementary sensations, which was demonstrated by the so-called reversible figures (Ash, 1995). Similarly, good thinking depended on the correct breakdown of the problem situation (Wertheimer, 2020). The key was restructuring, during which the original structure is melted and a new, more meaningful whole is formed, thanks to which a person: "...goes beyond the boundaries of old associations and sees the problem in a completely different light." (Davidson, 2003, p. 150).

An example is Köhler's (1925, according to: M.G. Ash (1995)) experiment, in which the chimpanzee Sultan wanted to reach bananas and had 2 sticks at his disposal that could be inserted into each other: He tried unsuccessfully to get the fruit for about an hour and did not come up with a solution even when Köhler indicated it by inserting a finger into one of the sticks. But later in the game, he accidentally caught the poles in such a way that they formed a straight line. Thanks to this, the information in the visual field was reorganized, and the originally indifferent object was given the meaning of a tool, because it was integrated into a new overall structure. The chimpanzee then connected the bars, ran to the bars of the cage and pulled the bananas.

The restructuring itself was considered an unconscious process, but this does not mean that, according to form psychologists, a person could not influence it - they claimed that it is the result of the tension of forces that arises from the contradiction between the current and desired state, while it is dependent, for example, on from the depth of knowledge of the situation, the number of repeated failures (Ohlsson, 1984a), or to a larger whole oriented attitude (Wertheimer, 2020)... The identification of factors that can prevent restructuring was beneficial for practice: E.g. Wertheimer (2020) criticized the teaching method based on the memorization of mathematical sentences and showed how easily it can confuse the student if he is confronted with the changed wording of the example. His own experiments showed that knowledge based on understanding the structure of a problem has greater transferability.

Shape psychology thus started the research of VP. But critics point out that even though she asked important questions and pointed out the inadequacy of the "mainstream" directions at the time, she brought few answers and her explanations did not result in easily falsifiable theories (Davidson, 2003; Weisberg & Alba, 1981). Moreover, it did not remain the only alternative to behaviorism: The cognitive revolution (based on the mind-as-computer metaphor) later enabled thinking to be operationalized precisely, while preserving the distinction between bad and good thinking (Ohlsson, 1984a). But is it possible to apply the approaches derived from it to VP as well?

Non-specific approach

In direct opposition to the approach of Shape Psychology is the so-called a non-specific approach that tests the null hypothesis – that ordinary processes of memory search and application of domain-specific knowledge are actually behind the solution of VP (Davidson, 2003).

Authors based on this tradition point out that the behavior of people when solving VP does not show the signs that we would expect based on the principles of Shape Psychology. For example, in the 9-dot problem (Fig. 1), the participant's task is to connect all the dots using 4 lines without lifting the pen from the paper. Weisberg and Alba (1981) claim to have disproved the classic explanation that people have difficulty restructuring—that is, overcoming fixation on the imaginary boundaries of a square as a "good shape": They found that explicitly instructing probands to do so led to little improvement and did not result in an experience of sudden understanding. However, participants performed better if they received training involving similar tasks. Similar inconsistencies were found in other tasks, leading the authors to hypothesize that people simply: "...apply knowledge to a new problem and, if it's not useful, try to come up with something new that solves the problem through a straightforward extension of what they already know. No exotic processes like sudden insight are needed." (Weisberg & Alba, 1981, p. 189)

Fig. 1 – 9 point problem

It is questionable to what extent these observations can be generalized to the course of solving other problems (Ohlsson, 1984a), but in favor of a non-specific approach are the findings that the success of solving VP is also related to fluid (g factor, possibly working memory) and crystalline intelligence (level of knowledge) (DeYoung et al., 2008).

However, a non-specific approach does not sufficiently take into account the fact that knowledge can also represent an obstacle. An example is the basic computational bias, as Keith Stanovich (2003) refers to the tendency to automatically bring past experience into judgment. The following syllogism e.g. up to 70% of students wrongly marked as correct: P1: All living things need water. P2: Roses need water. Z: Roses are living things.

Problem space theory and heuristics

While the initial conception of PP was oriented only to the explanation of the DDP solution, Herbert Simon and Craig Kaplan (1990) later applied the same theoretical framework to the explanation of the processes that should be part of the VP solution.

They proposed that if people fail to heuristically search the original PP, they use the switching heuristic and begin to consciously search the meta-space of potential PPs (Kaplan & Simon, 1990). Since there can be unbearably many of them, the key question has become: How do people limit the browsing of the meta-space? The authors quantitatively and qualitatively analyzed the behavior of the participants during the solution of the cut-off chessboard problem (Fig. 2), in which the task is to answer whether the entire chessboard with two cut-off squares can be covered using dominoes (with dimensions 2x1 square) and justify their answer (The solution requires representing the chessboard as consisting of 32 pairs of squares, not 64 separate ones.).

Fig. 2 – The cut-off checkerboard problem

The results showed that the resources for the search come from external stimuli, knowledge and heuristics. The authors consider the most generalizable strategy to be the heuristic of searching for invariants, i.e. aspects of the problem that remain unchanged during different attempts at solving them - in the case of a chessboard, this is the observation that uncovered places are always of the same color (Kaplan & Simon, 1990).

The theory of process monitoring also draws from the concept of problem space and heuristics. McGregor et al. (2001) developed Weisberg and Albau's (1981) observations regarding the 9-dot problem (Fig. 1): They found that it is helpful for participants to indicate the first line - provided that it reduces the number of dots that can be connected by subsequent lines. Therefore, they believe that the participants use the classic heuristic of approaching the goal: With each movement, they try to connect as many dots as possible, while comparing the current state of the solution with the partial goal. Those who, thanks to their skills or specific aspects of the problem situation, can foresee the result of a larger number of moves (look ahead), will realize sooner that they do not meet the established criteria and start looking for other procedures.

An indisputable advantage of the approach is the possibility of proposing very specific predictions and testing them using simulations (Kaplan, 1988, according to: Kaplan & Simon, 1990). Kaplan & Simon's (1990) approach is also consistent with knowledge about the importance of divergent thinking (successful solvers showed more flexibility in finding invariants). In both cases, however, the role of detachment from past experiences remains unconsidered.

Theory of representational change

The theory of representational change also has its roots in the concept of problem space, but in this case the explicit goal of its author, Stellan Ohlsson (1984a, 1984b), was to integrate into it the fundamental concept of Shape Psychology: Restructuring. He postulates that VPs lead the solver to a representation from which it is not possible to derive the correct operators for searching PPs and only its change leads to finding them (Ohlsson, 1984b). The approach also explains the phenomenology of insight: If the subsequent PP is small, the solution appears "in sight" after restructuring.

Ohlsson (1984b) initially explained restructuring in terms of processes of elaboration, abstraction, and the propagation of interpretation in semantic networks, while being cautious about whether the way to reach a new representation differs from the formation of the original one. But later, with Günther Knoblich, he developed an approach according to which the processes leading to restructuring are special, unconscious and preceded by a phase of helplessness, resulting from the exhaustion of the possibilities offered by the primary PP (Knoblich et al., 1999, 2001). The authors consider the release of restrictions (deactivation of unsuitable concepts in memory) and the distribution of chunks (separation of the perceptual whole into its components) to be the most important. The theory finds support in studies using match puzzles: P1: IV = III + III P2: III = III + III P2: XI = III + III

According to the starting points, P1 should be simple and solvable without a bewilderment phase, because the participants decompose the free chunk (IV into meaningful I and V) (Knoblich et al., 2001). But P2 and P3 challenging, and accompanied by helplessness: In P2 the solution is hindered by experience with equations at school (where + is not decomposed into – and –). In P3, it is necessary to decompose a fixed chunk (X into meaningless \ and /). The authors' predictions were confirmed in terms of performance and by observing the eye movements of the participants, who initially fixed their gaze on its irrelevant elements due to the incorrect representation of the equation. Only after the phase of helplessness and subsequent restructuring, the successful ones began to pay attention to really important objects.

The theory of representational change is consistent with the difference between VP and DDP on the experiential, behavioral and neurophysiological levels. But it was tested on a narrow spectrum of tasks, and the course of solving other problems does not correspond to it, or is better predicted by an approach based on heuristics. It therefore seems promising to integrate both approaches, based on the assumption that both describe different phases of the VP solution – e.g. Öllinger et al. (2014) found that in a 9-dot problem, probands are dramatically more likely to restructure (necessary for the solution) (moves outside the square) if they are led to do so by an experimental manipulation. But while only 50% of those who cross the border come to a solution, manipulation reducing the size of PP (before and after restructuring) increases their share to over 90%.

Conclusion

Researches from various fields support the relevance of understanding VPs as special. Their advantage lies in the fact that they allow the investigation of processes that are typically not involved in a DDP solution. Different problems can be difficult due to factors that one theory explains better than another, but attempts to synthesize them are currently emerging. However, it is questionable whether the study of VP really contributes to the understanding of coping with the problems of real life, and this area has been neglected for a long time.

Authors: Mgr. Filip Jendrol Department of Psychology, FF TU in Trnava

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