Real World Problem-Solving

5. Proposed Theory

I noted earlier that Ollinger's model for insight problem solving, while serving as a good candidate for RWPS, requires extension. In this section, I propose a candidate model that includes some necessary extensions to Ollinger's framework. I begin by laying out some preliminary notions that underlie the proposed model.

5.1. Dual Attentional Modes

I propose that the attention-switching mechanism described earlier is at the heart of RWPS and enables two modes of operation: focused and defocused mode. In the focused mode, the problem representation is more or less fixed, and problem solving proceeds in a focused and goal directed manner through search, planning, and execution mechanisms. In the defocused mode, problem solving is not necessarily goal directed, but attempts to generate ideas, driven by both internal and external items.

At first glance, these modes might seem similar to convergent and divergent thinking modes postulated by numerous others to account for creative problem solving. Divergent thinking allows for the generation of new ideas and convergent thinking allows for verification and selection of generated ideas. So, it might seem that focused mode and convergent thinking are similar and likewise divergent and defocused mode. They are, however, quite different. The modes relate less to idea generation and verification, and more to the specific mechanisms that are operating with regard to a particular problem at a particular moment in time. Convergent and divergent processes may be occurring during both defocused and focused modes. Some degree of divergent processes may be used to search and identify specific solution strategies in focused mode. Also, there might be some degree of convergent idea verification occuring in defocused mode as candidate items are evaluated for their fit with the problem and goal. Thus, convergent and divergent thinking are one amongst many mechanisms that are utilized in focused and defocused mode. Each of these two modes has to do with degree of attention placed on a particular problem.

There have been numerous dual-process and dual-systems models of cognition proposed over the years. To address criticisms raised against these models and to unify some of the terminology, Evans & Stanovich proposed a dual-process model comprising Type 1 and Type 2 thought. Type 1 processes are those that are believed to be autonomous and do not require working memory. Type 2 processes, on the other hand, are believed to require working memory and are cognitively decoupled to prevent real-world representations from becoming confused with mental simulations. While acknowledging various other attributes that are often used to describe dual process models (e.g., fast/slow, associative/rule-based, automatic/controlled), Evans & Stanovich note that these attributes are merely frequent correlates and not defining characteristics of Type 1 or Type 2 processes. The proposed dual attentional modes share some similarities with the Evans & Stanovich Type 1 and 2 models. Specifically, Type 2 processes might occur in focused attentional mode in the proposed model as they typically involve the working memory and certain amount of analytical thought and planning. Similarly, Type 1 processes are likely engaged in defocused attentional mode as there are notions of associative and generative thinking that might be facilitated when attention has been defocused. The crucial difference between the proposed model and other dual-process models is that the dividing line between focused and defocused attentional modes is the degree of openness to internal and external stimuli (by various networks and functional units in the brain) when problem solving. Many dual process models were designed to classify the "type" of thinking process or a form of cognitive processing. In some sense, the "processes" in dual process theories are characterized by the type of mechanism of operation or the type of output they produced. Here, I instead characterize and differentiate the modes of thinking by the receptivity of different functional units in the brain to input during problem solving.

This, however, raises a different question of the relationship between these attentional modes and conscious vs. unconscious thinking. It is clear that both the conscious and unconscious are involved in problem solving, as well as in RWPS. Here, I claim that a problem being handled is, at any given point in time, in either a focused mode or in a defocused mode. When in the focused mode, problem solving primarily proceeds in a manner that is available for conscious deliberation. More specifically, problem space elements and representations are tightly managed and plans and strategies are available in the working memory and consciously accessible. There are, however, secondary unconscious operations in the focused modes that includes targeted memory retrieval and heuristic-based searches. In the defocused mode, the problem is primarily managed in an unconscious way. The problem space elements are broken apart and loosely managed by various mechanisms that do not allow for conscious deliberation. That said, it is possible that some problem parameters remain accessible. For example, it is possible that certain goal information is still maintained consciously. It is also possible that indexes to all the problems being considered by the solver are maintained and available to conscious awareness.

5.2. RWPS Model

Returning to Ollinger's model for insight problem solving, it now becomes readily apparent how this model can be modified to incorporate environmental effects as well as generalizing the notion of intervening events beyond that of impasses. I propose a theory for RWPS that begins with standard analytical problem-solving process (See Figures 1, 2).

FIGURE 1

FIGURE 2

5.2.1. Focused Problem Solving Mode

Initially, both prior knowledge and perceptual entities help guide the creation of problem representations in working memory. Prior optimal or rewarding solution strategies are obtained from LTM and encoded in the working memory as well. This process is largely analytical and the solver interacts with their environment through focused plan or idea execution, targeted observation of prescribed entities, and estimating prediction error of these known entities. More specifically, when a problem is presented, the problem representations are activated and populated into working memory in the PFC, possibly in structured representations along convergence zones. The PFC along with the Striatum and the MTL together attempt at retrieving an optimal or previously rewarded solution strategy from long term memory. If successfully retrieved, the solution strategy is encoded into the PPC as a mental template, which then guides relevant motor control regions to execute the plan.

5.2.2. Defocusing Event-Triggered Mode Switching
The search and solve strategy then proceeds analytically until a "defocusing event" is encountered. The salience network (AI and ACC) monitor for conflicts and attempt to detect any such events in the problem-solving process. As long as no conflicts are detected, the salience network focuses on recruiting networks to achieve goals and suppresses the DMN. If the plan execution or retrieval of the solution strategy fails, then a defocusing event is detected and the salience network performs mode switching. The salience network dynamically switches from the focused problem-solving mode to a defocused problem-solving mode. Ollinger's current model does not account for other defocusing events beyond an impasse, but it is not inconceivable that there could be other such events triggered by external stimuli (e.g., distraction or an affective event) or by internal stimuli (e.g., mind wandering).

5.2.3. Defocused Problem Solving Mode

In defocused mode, the problem is operated on by mechanisms that allow for the generation and testing of novel ideas. Several large-scale brain networks are recruited to explore and generate new ideas. The search for novel ideas is facilitated by generally defocused attention, which in turn allows for creative idea generation from both internal as well as external sources. The salience network switches operations from defocused event detection to focused event or discovery detection, whereby for example, environmental events or ideas that are deemed interesting can be detected. During this idea exploration phase, internally, the DMN is no longer suppressed and attempts to generate new ideas for problem-solving. It is known that the IPC is involved in the generation of new ideas and together with the PPC in coupling different information together. Beaty et al. have proposed that even this internal idea-generation process can be goal directed, thereby allowing for a closer working relationship between the CEN and the DMN. They point to neuroimaging evidence that support the possibility that the executive control network (comprising the lateral prefrontal and inferior parietal regions) can constrain and direct the DMN in its process of generating ideas to meet task-specific goals via top down monitoring and executive control. The control network is believed to maintain an "internal train of thought" by keeping the task goal activated, thereby allowing for strategic and goal-congruent searches for ideas. Moreover, they suggest that the extent of CEN involvement in the DMN idea-generation may depend on the extent to which the creative task is constrained. In the RWPS setting, I would suspect that the internal search for creative solutions is not entirely unconstrained, even in the defocused mode. Instead, the solver is working on a specified problem and thus, must maintain the problem-thread while searching for solutions. Moreover, self-generated ideas must be evaluated against the problem parameters and thereby might need some top-down processing. This would suggest that in such circumstances, we would expect to see an increased involvement of the CEN in constraining the DMN.

On the external front, several mechanisms are operating in this defocused mode. Of particular note are the dorsal attention network, composed of the visual cortex (V), IPS and the frontal eye field (FEF) along with the precuneus and the caudate nucleus allow for partial cues to be considered. The MTL receives synthesized cue and contextual information and populates the WM in the PFC with a potentially expanded set of information that might be relevant for problem-solving. The precuneus, dlPFC and PPC together trigger the activation and use of a heuristic prototype based on an event in the environment. The caudate nucleus facilitates information routing between the PFC and PPC and is involved in learning and skill acquisition.

5.2.4. Focusing Event-Triggered Mode Switching

The problem's life in this defocused mode continues until a focusing event occurs, which could be triggered by either external (e.g., notification of impending deadline, discovery of a novel property in the environment) or internal items (e.g., goal completion, discovery of novel association or updated relevancy of a previously irrelevant item). As noted earlier, an internal train of thought may be maintained that facilitates top-down evaluation of ideas and tracking of these triggers. The salience network switches various networks back to the focused problem-solving mode, but not without the potential for problem restructuring. As noted earlier, problem space elements are maintained somewhat loosely in the defocused mode. Thus, upon a focusing event, a set or subset of these elements cohere into a tight (restructured) representation suitable for focused mode problem solving. The process then repeats itself until the goal has been achieved.

5.3. Model Predictions

5.3.1. Single-Mode Operation

The proposed RWPS model provides several interesting hypotheses, which I discuss next. First, the model assumes that any given problem being worked on is in one mode or another, but not both. Thus, the model predicts that there cannot be focused plan execution on a problem that is in defocused mode. The corollary prediction is that novel perceptual cues (as those discussed in section 4) cannot help the solver when in focused mode. The corollary prediction, presumably has some support from the inattentional blindness literature. Inattentional blindness is when perceptual cues are not noticed during a task (e.g., counting the number of basketball passes between several people, but not noticing a gorilla in the scene). It is possible that during focused problem solving, that external and internally generated novel ideas are simply not considered for problem solving. I am not claiming that these perceptual cues are always ignored, but that they are not considered within the problem. Sometimes external cues (like distracting occurrences) can serve as defocusing events, but the model predicts that the actual content of these cues are not themselves useful for solving the specific problem at hand.

When comparing dual-process models Sowden et al. discuss shifting from one type of thinking to another and explore how this shift relates to creativity. In this regard, they weigh the pros and cons of serial vs. parallel shifts. In dual-process models that suggest serial shifts, it is necessary to disengage one type of thought prior to engaging the other or to shift along a continuum. Whereas, in models that suggest parallel shifts, each of the thinking types can operate in parallel. Per this construction, the proposed RWPS model is serial, however, not quite in the same sense. As noted earlier, the RWPS model is not a dual-process model in the same sense as other dual process model. Instead, here, the thrust is on when the brain is receptive or not receptive to certain kinds of internal and external stimuli that can influence problem solving. Thus, while the modes may be serial with respect to a certain problem, it does not preclude the possibility of serial and parallel thinking processes that might be involved within these modes.

5.3.2. Event-Driven Transitions

The model requires an event (defocusing or focusing) to transition from one mode to another. After all why else would a problem that is successfully being resolved in the focused mode (toward completion) need to necessarily be transferred to defocused mode? These events are interpreted as conflicts in the brain and therefore the mode-switching is enabled by the saliency network and the ACC. Thus, the model predicts that there can be no transition from one mode to another without an event. This is a bit circular, as an event is really what triggers the transition in the first place. But, here I am suggesting that an external or internal cue triggered event is what drives the transition, and that transitions cannot happen organically without such an event. In some sense, the argument is that the transition is discontinuous, rather than a smooth one. Mind-wandering is good example of when we might drift into defocused mode, which I suggest is an example of an internally driven event caused by an alternative thought that takes attention away from the problem.

A model assumption underlying RWPS is that events such as impasses have a similar effect to other events such as distraction or mind wandering. Thus, it is crucial to be able to establish that there exists of class of such events and they have a shared effect on RWPS, which is to switch attentional modes.

5.3.3. Focused Mode Completion

The model also predicts that problems cannot be solved (i.e., completed) within the defocused mode. A problem can be considered solved when a goal is reached. However, if a goal is reached and a problem is completed in the defocused mode, then there must have not been any converging event or coherence of problem elements. While it is possible that the solver arbitrarily arrived at the goal in a diffused problem space and without conscious awareness of completing the task or even any converging event or problem recompiling, it appears somewhat unlikely. It is true that there are many tasks that we complete without actively thinking about it. We do not think about what foot to place in front of another while walking, but this is not an instance of problem solving. Instead, this is an instance of unconscious task completion.

5.3.4. Restructuring Required

The model predicts that a problem cannot return to a focused mode without some amount of restructuring. That is, once defocused, the problem is essentially never the same again. The problem elements begin interacting with other internally and externally-generated items, which in turn become absorbed into the problem representation. This prediction can potentially be tested by establishing some preliminary knowledge, and then showing one group of subjects the same knowledge as before, while showing the another group of subjects different stimuli. If the model's predictions hold, the problem representation will be restructured in some way for both groups.

There are numerous other such predictions, which are beyond the scope of this paper. One of the biggest challenges then becomes evaluating the model to set up suitable experiments aimed at testing the predictions and falsifying the theory, which I address next.