Real World Problem-Solving

2.1. What is Real World Problem-Solving?

Archimedes was embodied in the real world when he found his solution. In fact, the real world helped him solve the problem. Whether or not these sorts of historic accounts of creative inspiration are accurate, they do correlate with some of our own key intuitions about how problem solving occurs "in the wild". Real world problem solving (RWPS) is different from those that occur in a classroom or in a laboratory during an experiment. They are often dynamic and discontinuous, accompanied by many starts and stops. Solvers are never working on just one problem. Instead, they are simultaneously juggling several problems of varying difficulties and alternating their attention between them. Real world problems are typically ill-defined, and even when they are well-defined, often have open-ended solutions. Coupled with that is the added aspect of uncertainty associated with the solver's problem solving strategies. As introduced earlier, an important dimension of RWPS is the continuous interaction between the solver and their environment. During these interactions, the solver might be inspired or arrive at an "aha!" moment. However, more often than not, the solver experiences dozens of minor discovery events - "hmmm, interesting…" or "wait, what?…" moments. Like discovery events, there's typically never one singular impasse or distraction event. The solver must iterate through the problem solving process experiencing and managing these sorts of intervening events (including impasses and discoveries). In summary, RWPS is quite messy and involves a tight interplay between problem solving, creativity, and insight. Next, I explore each of these processes in more detail and explicate a possible role of memory, attention, conflict management and perception.

2.2. Analytical Problem-Solving

In psychology and neuroscience, problem-solving broadly refers to the inferential steps taken by an agent that leads from a given state of affairs to a desired goal state. The agent does not immediately know how this goal can be reached and must perform some mental operations (i.e., thinking) to determine a solution.

The problem solving literature divides problems based on clarity (well-defined vs. ill-defined) or on the underlying cognitive processes (analytical, memory retrieval, and insight). While memory retrieval is an important process, I consider it as a sub-process to problem solving more generally. I first focus on analytical problem-solving process, which typically involves problem-representation and encoding, and the process of forming and executing a solution plan.

2.2.1. Problem Definition and Representation

An important initial phase of problem-solving involves defining the problem and forming a representation in the working memory. During this phase, components of the prefrontal cortex (PFC), default mode network (DMN), and the dorsal anterior cingulate cortex (dACC) have been found to be activated. If the problem is familiar and well-structured, top-down executive control mechanisms are engaged and the left prefrontal cortex including the frontopolar, dorso-lateral (dlPFC), and ventro-lateral (vlPFC) are activated. The DMN along with the various structures in the medial temporal lobe (MTL) including the hippocampus (HF), parahippocampal cortex, perirhinal and entorhinal cortices are also believed to have limited involvement, especially in episodic memory retrieval activities during this phase. The problem representation requires encoding problem information for which certain visual and parietal areas are also involved, although the extent of their involvement is less clear.

2.2.1.1. Working memory

An important aspect of problem representation is the engagement and use of working memory (WM). The WM allows for the maintenance of relevant problem information and description in the mind. Research has shown that WM tasks consistently recruit the dlPFC and left inferior frontal cortex (IC) for encoding an manipulating information; dACC for error detection and performance adjustment; and vlPFC and the anterior insula (AI) for retrieving, selecting information and inhibitory control.

2.2.1.2. Representation

While we generally have a sense for the brain regions that are functionally influential in problem definition, less is known about how exactly events are represented within these regions. One theory for how events are represented in the PFC is the structured event complex theory (SEC), in which components of the event knowledge are represented by increasingly higher-order convergence zones localized within the PFC, akin to the convergence zones (from posterior to anterior) that integrate sensory information in the brain. Under this theory, different zones in the PFC (left vs. right, anterior vs. posterior, lateral vs. medial, and dorsal vs. ventral) represent different aspects of the information contained in the events (e.g., number of events to be integrated together, the complexity of the event, whether planning, and action is needed). Other studies have also suggested the CEN's role in tasks requiring cognitive flexibility, and functions to switch thinking modes, levels of abstraction of thought and consider multiple concepts simultaneously.

Thus, when the problem is well-structured, problem representation is largely an executive control activity coordinated by the PFC in which problem information from memory populates WM in a potentially structured representation. Once the problem is defined and encoded, planning and execution of a solution can begin.

2.2.2. Planning

The central executive network (CEN), particularly the PFC, is largely involved in plan formation and in plan execution. Planning is the process of generating a strategy to advance from the current state to a goal state. This in turn involves retrieving a suitable solution strategy from memory and then coordinating its execution.

2.2.2.1. Plan formation

The dlPFC supports sequential planning and plan formation, which includes the generation of hypothesis and construction of plan steps. Interestingly, the vlPFC and the angular gyrus (AG), implicated in a variety of functions including memory retrieval, are also involved in plan formation. Indeed, the AG together with the regions in the MTL (including the HF) and several other regions form a what is known as the "core" network. The core network is believed to be activated when recalling past experiences, imagining fictitious, and future events and navigating large-scale spaces, all key functions for generating plan hypotheses. A recent study suggests that the AG is critical to both episodic simulation, representation, and episodic memory. One possibility for how plans are formulated could involve a dynamic process of retrieving an optimal strategy from memory. Research has shown significant interaction between striatal and frontal regions. The striatum is believed to play a key role in declarative memory retrieval, and specifically helping retrieve optimal (or previously rewarded) memories. Relevant to planning and plan formation, Scimeca & Badre have suggested that the striatum plays two important roles: (1) in mapping acquired value/utility to action selection, and thereby helping plan formation, and (2) modulation and re-encoding of actions and other plan parameters. Different types of problems require different sets of specialized knowledge. For example, the knowledge needed to solve mathematical problems might be quite different (albeit overlapping) from the knowledge needed to select appropriate tools in the environment.

Thus far, I have discussed planning and problem representation as being domain-independent, which has allowed me to outline key areas of the PFC, MTL, and other regions relevant to all problem-solving. However, some types of problems require domain-specific knowledge for which other regions might need to be recruited. For example, when planning for tool-use, the superior parietal lobe (SPL), supramarginal gyrus (SMG), anterior inferior parietal lobe (AIPL), and certain portions of the temporal and occipital lobe involved in visual and spatial integration have been found to be recruited. It is believed that domain-specific information stored in these regions is recovered and used for planning.

2.2.2.2. Plan execution

Once a solution plan has been recruited from memory and suitably tuned for the problem on hand, the left-rostral PFC, caudate nucleus (CN), and bilateral posterior parietal cortices (PPC) are responsible for translating the plan into executable form. The PPC stores and maintains "mental template" of the executable form. Hemispherical division of labor is particularly relevant in planning where it was shown that when planning to solve a Tower of Hanoi (block moving) problem, the right PFC is involved in plan construction whereas the left PFC is involved in controlling processes necessary to supervise the execution of the plan. On a separate note and not the focus of this paper, plan execution and problem-solving can require the recruitment of affective and motivational processing in order to supply the agent with the resolve to solve problems, and the vmPFC has been found to be involved in coordinating this process.

2.3. Creativity

During the gestalt movement in the 1930s, Maier noted that "most instances of "real" problem solving involves creative thinking". Maier performed several experiments to study mental fixation and insight problem solving. This close tie between insight and creativity continues to be a recurring theme, one that will be central to the current discussion. If creativity and insight are linked to RWPS as noted by Maier, then it is reasonable to turn to the creativity and insight literature for understanding the role played by the environment. A large portion of the creativity literature has focused on viewing creativity as an internal process, one in which the solvers attention is directed inwards, and toward internal stimuli, to facilitate the generation of novel ideas and associations in memory. Focusing on imagination, a number of researchers have looked at blinking, eye fixation, closing eyes, and looking nowhere behavior and suggested that there is a shift of attention from external to internal stimuli during creative problem solving. The idea is that shutting down external stimuli reduces cognitive load and focuses attention internally. Other experiments studying sleep behavior have also noted the beneficial role of internal stimuli in problem solving. The notion of ideas popping into ones consciousness, suddenly, during a shower is highly intuitive for many and researchers have attempted to study this phenomena through the lens of incubation, and unconscious thought that is internally-driven. There have been several theories and counter-theories proposed to account specifically for the cognitive processes underlying incubation, but none of these theories specifically address the role of the external environment.

The neuroscience of creativity has also been extensively studied and I do not focus on an exhaustive literature review in this paper. From a problem-solving perspective, it has been found that unlike well-structured problems, ill-structured problems activate the right dlPFC. Most of the past work on creativity and creative problem-solving has focused on exploring memory structures and performing internally-directed searches. Creative idea generation has primarily been viewed as internally directed attention and a primary mechanism involved is divergent thinking, which is the ability to produce a variety of responses in a given situation. Divergent thinking is generally thought to involve interactions between the DMN, CEN, and the salience network. One psychological model of creative cognition is the Geneplore model that considers two major phases of generation (memory retrieval and mental synthesis) and exploration (conceptual interpretation and functional inference). It has been suggested that the associative mode of processing to generate new creative association is supported by the DMN, which includes the medial PFC, posterior cingulate cortex (PCC), tempororparietal juntion (TPJ), MTL, and IPC.

That said, the creativity literature is not completely devoid of acknowledging the role of the environment. In fact, it is quite the opposite. Researchers have looked closely at the role played by externally provided hints from the time of the early gestalt psychologists and through to present day studies. In addition to studying how hints can help problem solving, researchers have also looked at how directed action can influence subsequent problem solving - e.g., swinging arms prior to solving the two-string puzzle, which requires swinging the string. There have also been numerous studies looking at how certain external perceptual cues are correlated with creativity measures. Vohs et al. suggested that untidiness in the environment and the increased number of potential distractions helps with creativity. Certain colors such as blue have been shown to help with creativity and attention to detail. Even environmental illumination, or lack thereof, have been shown to promote creativity. However, it is important to note that while these and the substantial body of similar literature show the relationship of the environment to creative problem solving, they do not specifically account for the cognitive processes underlying the RWPS when external stimuli are received.

2.4. Insight Problem Solving

Analytical problem solving is believed to involve deliberate and conscious processing that advances step by step, allowing solvers to be able to explain exactly how they solved it. Inability to solve these problems is often associated with lack of required prior knowledge, which if provided, immediately makes the solution tractable. Insight, on the other hand, is believed to involve a sudden and unexpected emergence of an obvious solution or strategy sometimes accompanied by an affective aha! experience. Solvers find it difficult to consciously explain how they generated a solution in a sequential manner. That said, research has shown that having an aha! moment is neither necessary nor sufficient to insight and vice versa. Generally, it is believed that insight solvers acquire a full and deep understanding of the problem when they have solved it. There has been an active debate in the problem solving community about whether insight is something special. Some have argued that it is not, and that there are no special or spontaneous processes, but simply a good old-fashioned search of a large problem space. Others have argued that insight is special and suggested that it is likely a different process. This debate lead to two theories for insight problem solving. MacGregor et al. proposed the Criterion for Satisfactory Progress Theory (CSPT), which is based on Newell and Simons original notion of problem solving as being a heuristic search through the problem space. The key aspect of CSPT is that the solver is continually monitoring their progress with some set of criteria. Impasses arise when there is a criterion failure, at which point the solver tries non-maximal but promising states. The representational change theory (RCT) proposed by Ohlsson et al., on the other hand, suggests that impasses occur when the goal state is not reachable from an initial problem representation (which may have been generated through unconscious spreading activation). In order to overcome an impasse, the solver needs to restructure the problem representation, which they can do by (1) elaboration (noticing new features of a problem), (2) re-encoding fixing mistaken or incomplete representations of the problem, and by (3) changing constraints. Changing constraints is believed to involve two sub-processes of constraint relaxation and chunk-decomposition.

The current position is that these two theories do not compete with each other, but instead complement each other by addressing different stages of problem solving: pre- and post-impasse. Along these lines, Ollinger et al. proposed an extended RCT (eRCT) in which revising the search space and using heuristics was suggested as being a dynamic and iterative and recursive process that involves repeated instances of search, impasse and representational change. Under this theory, a solver first forms a problem representation and begins searching for solutions, presumably using analytical problem solving processes as described earlier. When a solution cannot be found, the solver encounters an impasse, at which point the solver must restructure or change the problem representation and once again search for a solution. The model combines both analytical problem solving (through heuristic searches, hill climbing and progress monitoring), and creative mechanisms of constraint relaxation and chunk decomposition to enable restructuring.

Ollingers model appears to comprehensively account for both analytical and insight problem solving and, therefore, could be a strong candidate to model RWPS. However, while compelling, it is nevertheless an insufficient model of RWPS for many reasons, of which two are particularly significant for the current paper. First, the model does explicitly address mechanisms by which external stimuli might be assimilated. Second, the model is not sufficiently flexible to account for other events (beyond impasse) occurring during problem solving, such as distraction, mind-wandering and the like.

So, where does this leave us? I have shown the interplay between problem solving, creativity and insight. In particular, using Ollinger's proposal, I have suggested (maybe not quite explicitly up until now) that RWPS involves some degree of analytical problem solving as well as the post-impasse more creative modes of problem restructuring. I have also suggested that this model might need to be extended for RWPS along two dimensions. First, events such as impasses might just be an instance of a larger class of events that intervene during problem solving. Thus, there needs to be an accounting of the cognitive mechanisms that are potentially influenced by impasses and these other intervening events. It is possible that these sorts of events are crucial and trigger a switch in attentional focus, which in turn facilitates switching between different problem solving modes. Second, we need to consider when and how externally-triggered stimuli from the solver's environment can influence the problem solving process. I detail three different mechanisms by which external knowledge might influence problem solving. I address each of these ideas in more detail in the next two sections.