Problem solving stages in the five square problem

The lack of Aha! experience can be dependent on the problem difficulty

Previous research on how problem-difficulty affects solution-types of insight-problems has yielded contradictory findings. Thus, we aimed to examine the impact of problem-difficulty on solution-types in both inter- and intra-problem-difficulty contexts. For this, we employed the original 8-coin, and 9-dot problems and four hinted-versions of those that were manipulated by using hints-to-remove-sources-of-difficulty to alter their difficulty level. Those manipulations were executed based on the assumptions of constraint-relaxation and chunk-decomposition as posited by representational change theory. The study involved a total of 165 participants who were tested in five groups (33 per se), with each group receiving an original or hinted problem. Following their correct solutions, problem-solvers classified their solution-types (insight or non-insight solutions) by whether they had an Aha!-experience during the solution. Across all groups, 56.1% of correctly solved insight problems were solved with Aha!-experience, based on participants' self-reports, implying that correct solutions should not be equated with insight. Subsequently, the solution-type rates were compared for both original problems (inter-problem-difficulty) and hinted versions of those at each difficulty level (intra-problem-difficulty). Inter-problem-difficulty comparisons demonstrated that the easier 8-coin problem was more likely to be solved with insight than the harder 9-dot problem. In contrast, intra-problem-difficulty comparisons revealed that harder problems were more likely to be solved with insight. These findings suggest that problem-difficulty should be considered in future studies of insight. Finally, separate analyses on the predictive values of the cognitive-affective-dimensions on solution-types revealed that, after adjusting for problem-difficulty, problem-solvers with higher suddenness scores in both problems exhibited a significantly higher probability of generating insight solutions.

Insight and non-insight problem solving: A heart rate variability study

Occasionally, problems are solved with a sudden Aha! moment (insight), while the mundane approach to solving problems is analytical (non-insight). At first glance, non-insight appears to depend on the availability and taxation of cognitive resources to execute the step-by-step approach, whereas insight does not, or to a lesser extent. However, this remains debated. To investigate the reliance of both solution types on cognitive resources, we assessed the involvement of the prefrontal cortex using vagally mediated heart rate variability (vmHRV) as an index. Participants (N = 68) solved 70 compound remote associates word puzzles solvable with insight and non-insight. Before, during, and after solving the word puzzles, we measured the vmHRV. Our results showed that resting-state vmHRV (trait) showed a negative association with behavioural performance for both solution types. This might reflect inter-individual differences in inhibitory control. As the solution search requires one to think of remote associations, inhibitory control might hamper rather than aid this process. Furthermore, we observed, for both solution types, a vmHRV increase from resting-state to solution search (state), lingering on in the post-task recovery period. This could mark the increase of prefrontal resources to promote an open-minded stance, essential for divergent thinking, which arguably is crucial for this task. Our findings suggest that, at a general level, both solution types share common aspects. However, a closer analysis of early and late solutions and puzzle difficulty suggested that metacognitive differentiation between insight and non-insight improved with higher trait vmHRV, and that a unique association between trait vmHRV and puzzle difficulty was present for each solution type.

Impasse-Driven problem solving: The multidimensional nature of feeling stuck

This study reports findings across four preregistered experiments (total N = 856) that establish the multidimensional nature of impasse and resolve two paradoxes implicit in the problem-solving literature: how a state of impasse can be at once necessary to solve a problem with insight yet also have appear to have a catastrophic effect on solution rates, and why individuals such as problem-solving and gaming enthusiasts seem to seek out this apparently aversive state. We introduce a new way of measuring impasse based on qualitative reports and subsequently confirmed through quantitative analysis that exploits two aspects of impasse: its dynamic and unstable nature (it can be resolved or unresolved) and its multidimensionality in terms of feelings of cognitive speediness, motivation, and affect. The feeling of being stuck varies between resolved and unresolved impasse in terms of feelings of speediness and positive affect, but not motivation, which remains constant. We demonstrate that the feeling of insight can be reliably elicited by experiencing and resolving impasse but also in the absence of impasse, which suggests that there is more than one path to an insight experience. This adds depths to current proposals of the cognitive mechanisms underlying both insight problem-solving and impasse. Our findings are robust across a range of problem types. The novel conception of impasse in this paper as dynamic and multidimensional has implications for theories of insight problem solving, and also wider implications for understanding how impasse can be resolved across different domains such as education and design.

Tracing executive functions in insight

Usually the central executive is considered as a single capacity in the insight studies which leads to inconsistent results on the link between the central executive of working memory and insight. We suppose a more detailed view on the process of insight solution in which various executive functions could be important at different solution stages: updating is necessary to build a problem's representation, inhibition-to overcome the impasse, shifting-to restructure the problem's representation. These assumptions were not confirmed in an experiment via dual-task paradigm and cognitive load. We did not find the relation between executive functions and solution stages, but we demonstrated that the more complexity of dual-task, the more cognitive load in problem solving. Moreover, the highest load of executive functions is observed at the end of insight solution. We speculate that the loading occurs either due to decrease of the free space in working memory storage systems, or due to a resource-intensive event (for example, representational change).

Tracing Cognitive Processes in Insight Problem Solving: Using GAMs and Change Point Analysis to Uncover Restructuring

Insight problems are likely to trigger an initial, incorrect mental representation, which needs to be restructured in order to find the solution. Despite the widespread theoretical assumption that this restructuring process happens suddenly, leading to the typical "Aha!" experience, the evidence is inconclusive. Among the reasons for this lack of clarity is that many measures of insight rely solely on the solvers' subjective experience of the solution process. In our previous paper, we used matchstick arithmetic problems to demonstrate that it is possible to objectively trace problem-solving processes by combining eye movements with new analytical and statistical approaches. Specifically, we divided the problem-solving process into ten (relative) temporal phases to better capture possible small changes in problem representation. Here, we go a step further to demonstrate that classical statistical procedures, such as ANOVA, cannot capture sudden representational change processes, which are typical for insight problems. Only nonlinear statistical models, such as generalized additive (mixed) models (GAMs) and change points analysis, correctly identified the abrupt representational change. Additionally, we demonstrate that explicit hints reorient participants' focus in a qualitatively different manner, changing the dynamics of restructuring in insight problem solving. While insight problems may indeed require a sudden restructuring of the initial mental representation, more sophisticated analytical and statistical approaches are necessary to uncover their true nature.

Opposites in Reasoning Processes: Do We Use Them More Than We Think, but Less Than We Could?

Our aim in this paper is to contribute toward acknowledging the general role of opposites as an organizing principle in the human mind. We support this claim in relation to human reasoning by collecting evidence from various studies which shows that "thinking in opposites" is not only involved in formal logical thinking, but can also be applied in both deductive and inductive reasoning, as well as in problem solving. We also describe the results of a series of studies which, although they have been developed within a number of different theoretical frameworks based on various methodologies, all demonstrate that giving hints or training reasoners to think in terms of opposites improves their performance in tasks in which spontaneous thinking may lead to classic biases and impasses. Since we all possess an intuitive idea of what opposites are, prompting people to "think in opposites" is something which is undoubtedly within everyone's reach and in the final section, we discuss the potential of this strategy and suggest possible future research directions of systematic testing the benefits that might arise from the use of this technique in contexts beyond those tested thus far. Ascertaining the conditions in which reasoners might benefit will also help in terms of clarifying the underlying mechanisms from the point of view, for instance, of analytical, conscious processing vs. automatic, unconscious processing.

Pleasures of the Mind: What Makes Jokes and Insight Problems Enjoyable

In this paper, a parallel analysis of the enjoyment derived from humor and insight problem solving is presented with reference to a “general” Theory of the Pleasures of the Mind (TPM) (Kubovy, 1999) rather than to “local” theories regarding what makes humor and insight problem solving enjoyable. The similarity of these two cognitive activities has already been discussed in previous literature in terms of the cognitive mechanisms which underpin getting a joke or having an insight experience in a problem solving task. The paper explores whether we can learn something new about the similarities and differences between humor and problem solving by means of an investigation of what makes them pleasurable. In the first part of the paper, the framework for this joint analysis is set. Two descriptive studies are then presented in which the participants were asked to report on their experiences relating to solving visuo-spatial insight problems (Study 1) or understanding cartoons (Study 2) in terms of whether they were enjoyable or otherwise. In both studies, the responses were analyzed with reference to a set of categories inspired by the TPM. The results of Study 1 demonstrate that finding the solution to a problem is associated with a positive evaluation, and the most frequent explanations for this were reported as being Curiosity, Virtuosity and Violation of expectations. The results of Study 2 suggest that understanding a joke (Joy of verification) and being surprised by it (Feeling of surprise) were two essential conditions: when they were not present, the cartoons were perceived as not enjoyable. However, this was not enough to explain the motivations for the choice of the most enjoyable cartoons. Recognizing a Violation of expectations and experiencing a Diminishment in the cleverness or awareness initially attributed to the characters in the cartoon were the aspects which were most frequently indicated by the participants to explain why they enjoyed the joke. These findings are evaluated in the final discussion, together with their limitations and potential future developments.

Expectation Violation in Political Decision Making: A Psychological Case Study

Since the early Gestaltists there has been a strong interest in the question of how problem solvers get stuck in a mental impasse. A key idea is that the repeated activation of a successful strategy from the past results in a mental set (‘Einstellung’) which determines and constrains the option space to solve a problem. We propose that this phenomenon, which mostly was tested by fairly restricted experiments in the lab, could also be applied to more complex problem constellations and naturalistic decision making. We aim at scrutinizing and reconstructing how a mental set determines the misinterpretation of facts in the field of political decision making and leads in consequence to wrong expectations and an ill-defined problem representation. We will exemplify this psychological mechanism considering a historical example, namely the unexpected stabilization of the Franco regime at the end of World War II and its survival thereafter. A specific focus will be drawn to the significant observation that erroneous expectations were taken as the basis for decisions. This is congruent with the notion that in case of discrepancy between preconceived notions and new information, the former prevails over the new findings. Based on these findings, we suggest a theoretical model for expectation violation in political decision making and develop novel approaches for cognitive empirical research on the mechanisms of expectation violation and its maintenance in political decision making processes.

Insight into the ten-penny problem: guiding search by constraints and maximization

For a long time, insight problem solving has been either understood as nothing special or as a particular class of problem solving. The first view implicates the necessity to find efficient heuristics that restrict the search space, the second, the necessity to overcome self-imposed constraints. Recently, promising hybrid cognitive models attempt to merge both approaches. In this vein, we were interested in the interplay of constraints and heuristic search, when problem solvers were asked to solve a difficult multi-step problem, the ten-penny problem. In three experimental groups and one control group (N = 4 × 30) we aimed at revealing, what constraints drive problem difficulty in this problem, and how relaxing constraints, and providing an efficient search criterion facilitates the solution. We also investigated how the search behavior of successful problem solvers and non-solvers differ. We found that relaxing constraints was necessary but not sufficient to solve the problem. Without efficient heuristics that facilitate the restriction of the search space, and testing the progress of the problem solving process, the relaxation of constraints was not effective. Relaxing constraints and applying the search criterion are both necessary to effectively increase solution rates. We also found that successful solvers showed promising moves earlier and had a higher maximization and variation rate across solution attempts. We propose that this finding sheds light on how different strategies contribute to solving difficult problems. Finally, we speculate about the implications of our findings for insight problem solving.

Cognitive Architecture with Evolutionary Dynamics Solves Insight Problem

In this paper, we show that a neurally implemented a cognitive architecture with evolutionary dynamics can solve the four-tree problem. Our model, called Darwinian Neurodynamics, assumes that the unconscious mechanism of problem solving during insight tasks is a Darwinian process. It is based on the evolution of patterns that represent candidate solutions to a problem, and are stored and reproduced by a population of attractor networks. In our first experiment, we used human data as a benchmark and showed that the model behaves comparably to humans: it shows an improvement in performance if it is pretrained and primed appropriately, just like human participants in Kershaw et al. (2013)'s experiment. In the second experiment, we further investigated the effects of pretraining and priming in a two-by-two design and found a beginner's luck type of effect: solution rate was highest in the condition that was primed, but not pretrained with patterns relevant for the task. In the third experiment, we showed that deficits in computational capacity and learning abilities decreased the performance of the model, as expected. We conclude that Darwinian Neurodynamics is a promising model of human problem solving that deserves further investigation.

Can Contraries Prompt Intuition in Insight Problem Solving?

This paper aims to test whether the use of contraries can facilitate spatial problem solving. Specifically, we examined whether a training session which included explicit guidance on thinking in contraries would improve problem solving abilities. In our study, the participants in the experimental condition were exposed to a brief training session before being presented with seven visuo-spatial problems to solve. During training it was suggested that it would help them to find the solution to the problems if they systematically transformed the spatial features of each problem into their contraries. Their performance was compared to that of a control group (who had no training). Two participation conditions were considered: small groups and individuals. Higher success rates were found in the groups exposed to training as compared to the individuals (in both the training and no training conditions), even though the time required to find a solution was longer. In general, participants made more attempts (i.e., drawings) when participating in groups than individually. The number of drawings done while the participants were trying to solve the problems did not increase after training. In order to explore if the quality (if not the number) of drawings was modified, we sampled one problem out of the seven we had used in the experiment (the “pigs in a pen” problem) and examined the drawings in detail. Differences between the training and no training conditions emerged in terms of properties focused on and transformed in the drawings. Based on these results, in the final discussion possible explanations are suggested as to why training had positive effects specifically in the group condition.

Intuition and Insight: Two Processes That Build on Each Other or Fundamentally Differ?

Intuition and insight are intriguing phenomena of non-analytical mental functioning: whereas intuition denotes ideas that have been reached by sensing the solution without any explicit representation of it, insight has been understood as the sudden and unexpected apprehension of the solution by recombining the single elements of a problem. By face validity, the two processes appear similar; according to a lay perspective, it is assumed that intuition precedes insight. Yet, predominant scientific conceptualizations of intuition and insight consider the two processes to differ with regard to their (dis-)continuous unfolding. That is, intuition has been understood as an experience-based and gradual process, whereas insight is regarded as a genuinely discontinuous phenomenon. Unfortunately, both processes have been investigated differently and without much reference to each other. In this contribution, we therefore set out to fill this lacuna by examining the conceptualizations of the assumed underlying cognitive processes of both phenomena, and by also referring to the research traditions and paradigms of the respective field. Based on early work put forward by Bowers et al. (1990, 1995), we referred to semantic coherence tasks consisting of convergent word triads (i.e., the solution has the same meaning to all three clue words) and/or divergent word triads (i.e., the solution means something different with respect to each clue word) as an excellent kind of paradigm that may be used in the future to disentangle intuition and insight experimentally. By scrutinizing the underlying mechanisms of intuition and insight, with this theoretical contribution, we hope to launch lacking but needed experimental studies and to initiate scientific cooperation between the research fields of intuition and insight that are currently still separated from each other.