# Cognitive Psychology and the Brain

Imagine the following situation: A young man, let’s call him Knut, is sitting at his desk, reading some papers which he needs to complete a psychology assignment. In his right hand he holds a cup of coffee. With his left one he reaches for a bag of sweets without removing the focus of his eyes from the paper. Suddenly he stares up to the ceiling of his room and asks himself: “What is happening here?”

Probably everybody has had experiences like the one described above. Even though at first sight there is nothing exciting happening in this everyday situation, a lot of what is going on here is highly interesting particularly for researchers and students in the field of Cognitive Psychology. They are involved in the study of lots of incredibly fascinating processes which we are not aware of in this situation. Roughly speaking, an analysis of Knut's situation by Cognitive Psychologists would look like this:

Knut has a problem; he really needs to do his assignment. To solve this problem, he has to perform loads of cognition. The light reaching his eyes is transduced into electrical signals traveling through several stations to his visual cortex. Meanwhile, complex nets of neurons filter the information flow and compute contrast, colour, patterns, positions in space, motion of the objects in Knut's environment. Stains and lines on the screen become words; words get meaning; the meaning is put into context; analyzed on its relevance for Knut's problem and finally maybe stored in some part of his memory. At the same time an appetite for sweets is creeping from Knut's hypothalamus, a region in the brain responsible for controlling the needs of an organism. This appetite finally causes Knut to reach out for his sweets.

Now, let us take a look into the past to see how Cognitive Psychologists developed its terminology and methods to interpret ourselves on the basis of brain, behaviour and theory.

## History of Cognitive Psychology

Early thoughts claimed that knowledge was stored in the brain.

### Renaissance and Beyond

Renaissance philosophers of the 17th century generally agreed with Nativists and even tried to show the structure and functions of the brain graphically. But also empiricist philosophers had very important ideas. According to David Hume, the internal representations of knowledge are formed obeying particular rules. These creations and transformations take effort and time. Actually, this is the basis of much current research in Cognitive Psychology. In the 19th Century Wilhelm Wundt and Franciscus Cornelis Donders made the corresponding experiments measuring the reaction time required for a response, of which further interpretation gave rise to Cognitive Psychology 55 years later.

### 20th Century and the Cognitive Revolution

During the first half of the 20th Century, a radical turn in the investigation of cognition took place. Behaviourists like Burrhus Frederic Skinner claimed that such mental internal operations - such as attention, memory, and thinking – are only hypothetical constructs that cannot be observed or proven. Therefore, Behaviorists asserted, mental constructs are not as important and relevant as the study and experimental analysis of behaviour (directly observable data) in response to some stimulus. According to Watson and Skinner, man could be objectively studied only in this way. The popularity of Behavioralist theory in the psychological world led investigation of mental events and processes to be abandoned for about 50 years.

In the 1950s scientific interest returned again to attention, memory, images, language processing, thinking and consciousness. The “failure” of Behaviourism heralded a new period in the investigation of cognition, called Cognitive Revolution. This was characterized by a revival of already existing theories and the rise of new ideas such as various communication theories. These theories emerged mainly from the previously created information theory, giving rise to experiments in signal detection and attention in order to form a theoretical and practical understanding of communication.

Modern linguists suggested new theories on language and grammar structure, which were correlated with cognitive processes. Chomsky’s Generative Grammar and Universal Grammar theory, proposed language hierarchy, and his critique of Skinner’s “Verbal Behaviour” are all milestones in the history of Cognitive Science. Theories of memory and models of its organization gave rise to models of other cognitive processes. Computer science, especially artificial intelligence, re-examined basic theories of problem solving and the processing and storage of memory, language processing and acquisition.

For clarification: Further discussion on the "behaviorist" history.

Although the above account reflects the most common version of the rise and fall of behaviorism, it is a misrepresentation. In order to better understand the founding of cognitive psychology it must be understood in an accurate historical context. Theoretical disagreements exist in every science. However, these disagreements should be based on an honest interpretation of the opposing view. There is a general tendency to draw a false equivalence between Skinner and Watson. It is true that Watson rejected the role that mental or conscious events played in the behavior of humans. In hindsight this was an error. However, if we examine the historical context of Watson's position we can better understand why he went to such extremes. He, like many young psychologists of the time, was growing frustrated with the lack of practical progress in psychological science. The focus on consciousness was yielding inconsistent, unreliable and conflicting data. Excited by the progress coming from Pavlov's work with elicited responses and looking to the natural sciences for inspiration, Watson rejected the study of observable mental events and also pushed psychology to study stimulus-response relations as a means to better understand human behavior. This new school of psychology, "behaviorism" became very popular. Skinner's school of thought, although inspired by Watson, takes a very different approach to the study of unobservable mental events. Skinner proposed that the distinction between "mind" and "body" brought with it irreconcilable philosophical baggage. He proposed that the events going on "within the skin", previously referred to as mental events, be called private events. This would bring the private experiences of thinking, reasoning, feeling and such, back into the scientific fold of psychology. However, Skinner proposed that these were things we are doing rather than events going on at a theorized mental place. For Skinner, the question was not of a mental world existing or not, it was whether or not we need to appeal to the existence of a mental world in order to explain the things going on inside our heads. Such as the natural sciences ask whether we need to assume the existence of a creator in order to account for phenomena in the natural world. For Skinner, it was an error for psychologists to point to these private events (mental) events as causes of behavior. Instead, he suggested that these too had to be explained through the study of how one evolves as a matter of experience. For example, we could say that a student studies because she "expects" to do better on an exam if she does. To "expect" might sound like an acceptable explanation for the behavior of studying, however, Skinner would ask why she "expects". The answer to this question would yield the true explanation of why the student is studying. To "expect" is to do something, to behave "in our head", and thus must also be explained.

The cognitive psychologist Henry Roediger pointed out that many psychologists erroneously subscribe to the version of psychology presented in the first paragraph. He also pointed to the successful rebuttal against Chomsky's review of Verbal behavior. The evidence for the utility in Skinner's book can be seen in the abundance of actionable data it has generated, therapies unmatched by any modern linguistic account of language. Roediger reminded his readers that in fact, we all measure behavior, some simply choose to make more assumptions about its origins than others. He recalls how, even as a cognitive psychologist, he has been the focus of criticism for not making more assumptions about his data. The law of parsimony tells us that when choosing an explanation for a set of data about observable behavior (the data all psychologists collect), we must be careful not to make assumptions beyond those necessary to explain the data. This is where the main division lies between modern day behavior analysts and cognitive psychologists. It is not in the rejection of our private experiences, it is in how these experiences are studied. Behavior analysts study them in relation to our learning history and the brain correlates of that history. They use this information to design environments that change our private experience by changing our interaction with the world. After all, it is through our interaction with our relative world that our private experiences evolve. It is a far cry from the mechanical stimulus-response psychology of John Watson. Academic honesty requires that we make a good faith effort to understand what we wish to criticize. Henry Roediger pointed out that many psychologists understand a very stereotyped, erroneous version of psychology's history. In doing so they miss the many successful real world applications that Skinner's analysis has generated.

Neuroinformatics, which is based on the natural structure of the human nervous system, tries to build neuronal structures by the idea of artificial neurons. In addition to that, Neuroinformatics is used as a field of evidence for psychological models, for example models for memory. The artificial neuron network “learns” words and behaves like “real” neurons in the brain. If the results of the artificial neuron network are quite similar to the results of real memory experiments, it would support the model. In this way psychological models can be “tested”. Furthermore it would help to build artificial neuron networks, which posses similar skills like the human such as face recognition.

If more about the ways humans process information was understood, it would be much simpler to build artificial structures, which have the same or similar abilities. The area of cognitive development investigation tried to describe how children develop their cognitive abilities from infancy to adolescence. The theories of knowledge representation were first strongly concerned with sensory inputs. Current scientists claim to have evidence that our internal representation of reality is not a one-to-one reproduction of the physical world. It is rather stored in some abstract or neurochemical code. Tolman, Bartlett, Norman and Rumelhart made some experiments on cognitive mapping. Here, the inner knowledge seemed not only to be related to sensory input, but also to be modified by some kind of knowledge network modeled by past experience.

Newer methods, like Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) have given researchers the possibility to measure brain activity and possibly correlate it to mental states and processes. All these new approaches in the study of human cognition and psychology have defined the field of Cognitive Psychology, a very fascinating field which tries to answer what is quite possibly the most interesting question posed since the dawn of reason. There is still a lot to discover and to answer and to ask again, but first we want to make you more familiar with the concept of Cognitive Psychology.

## What is Cognitive Psychology?

The easiest answer to this question is: “Cognitive Psychology is the study of thinking and the processes underlying mental events.” Of course this creates the new problem of what a mental event actually is. There are many possible answers for this:

Let us look at Knut again to give you some more examples and make the things clearer. He needs to focus on reading his paper. So all his attention is directed at the words and sentences which he perceives through his visual pathways. Other stimuli and information that enter his cognitive apparatus - maybe some street noise or the fly crawling along a window - are not that relevant in this moment and are therefore attended much less. Many higher cognitive abilities are also subject to investigation. Knut’s situation could be explained as a classical example of problem solving: He needs to get from his present state – an unfinished assignment – to a goal state - a completed assignment - and has certain operators to achieve that goal. Both Knut’s short and long term memory are active. He needs his short term memory to integrate what he is reading with the information from earlier passages of the paper. His long term memory helps him remember what he learned in the lectures he took and what he read in other books. And of course Knut’s ability to comprehend language enables him to make sense of the letters printed on the paper and to relate the sentences in a proper way.

This situation can be considered to reflect mental events like perception, comprehension and memory storage. Some scientists think that our emotions cannot be considered separate from cognition, so that hate, love, fear or joy are also sometimes looked at as part of our individual minds. Cognitive psychologists study questions like: How do we receive information about the outside world? How do we store it and process it? How do we solve problems? How is language represented?

Cognitive Psychology is a field of psychology that learns and researches about mental processes, including perception, thinking, memory, and judgment. The mainstay of cognitive psychology is the idea where sensation and perception are both different issues.

## Relations to Neuroscience

### Cognitive Neuropsychology

Of course it would be very convenient if we could understand the nature of cognition without the nature of the brain itself. But unfortunately it is very difficult if not impossible to build and prove theories about our thinking in absence of neurobiological constraints. Neuroscience comprises the study of neuroanatomy, neurophysiology, brain functions and related psychological and computer based models. For years, investigations on a neuronal level were completely separated from those on a cognitive or psychological level. The thinking process is so vast and complex that there are too many conceivable solutions to the problem of how cognitive operation could be accomplished.

Neurobiological data provide physical evidence for a theoretical approach to the investigation of cognition. Therefore it narrows the research area and makes it much more exact. The correlation between brain pathology and behaviour supports scientists in their research. It has been known for a long time that different types of brain damage, traumas, lesions, and tumours affect behaviour and cause changes in some mental functions. The rise of new technologies allows us to see and investigate brain structures and processes never seen before. This provides us with a lot of information and material to build simulation models which help us to understand processes in our mind. As neuroscience is not always able to explain all the observations made in laboratories, neurobiologists turn towards Cognitive Psychology in order to find models of brain and behaviour on an interdisciplinary level – Cognitive Neuropsychology. This “inter-science” as a bridge connects and integrates the two most important domains and their methods of research of the human mind. Research at one level provides constraints, correlations and inspirations for research at another level.

### Neuroanatomy Basics

The basic building blocks of the brain are a special sort of cells called neurons. There are approximately 100 billion neurons involved in information processing in the brain. When we look at the brain superficially, we can't see these neurons, but rather look at two halves called the hemispheres. The hemispheres themselves may differ in size and function, as we will see later in the book, but principally each of them can be subdivided into four parts called the lobes: the temporal, parietal, occipital and frontal lobe. This division of modern neuroscience is supported by the up- and down-bulging structure of the brain's surface. The bulges are called gyri (singular gyrus), the creases sulci (singular sulcus). They are also involved in information processing. The different tasks performed by different subdivisions of the brain as attention, memory and language cannot be viewed as separated from each other, nevertheless some parts play a key role in a specific task. For example the parietal lobe has been shown to be responsible for orientation in space and the relation you have to it, the occipital lobe is mainly responsible for visual perception and imagination etc. Summed up, brain anatomy poses some basic constraints to what is possible for us and a better understanding will help us to find better therapies for cognitive deficits as well as guide research for cognitive psychologists. It is one goal of our book to present the complex interactions between the different levels on which the brain that can be described, and their implications for Cognitive Neuropsychology.

### Methods

Newer methods, like EEG and fMRI etc. allow researchers to correlate the behaviour of a participant in an experiment with the brain activity which is measured simultaneously. It is possible to record neurophysiological responses to certain stimuli or to find out which brain areas are involved in the execution of certain mental tasks. EEG measures the electric potentials along the skull through electrodes that are attached to a cap. While its spatial resolution is not very precise, the temporal resolution lies within the range of milliseconds. The use of fMRI benefits from the fact the increased brain activity goes along with increased blood flow in the active region. The haemoglobin in the blood has magnetic properties that are registered by the fMRI scanner. The spatial resolution of fMRI is very precise in comparison to EEG. On the other hand, the temporal resolution is in the range of just 1–2 seconds.

## Conclusion

Remember the scenario described at the beginning of the chapter. Knut was asking himself “What is happening here?” It should have become clear that this question cannot be simply answered with one or two sentences. We have seen that the field of Cognitive Psychology comprises a lot of processes and phenomena of which every single one is subject to extensive research to understand how cognitive abilities are produced by our brain. In the following chapters of this WikiBook you will see how the different areas of research in Cognitive Psychology are trying to solve the initial question raised by Knut.

# Problem Solving from an Evolutionary Perspective

## Introduction

Same place, different day. Knut is sitting at his desk again, staring at a blank paper in front of him, while nervously playing with a pen in his right hand. Just a few hours left to hand in his essay and he has not written a word. All of a sudden he smashes his fist on the table and cries out: "I need a plan!"

That thing Knut is confronted with is something everyone of us encounters in his daily life. He has got a problem – and he does not really know how to solve it. But what exactly is a problem? Are there strategies to solve problems? These are just a few of the questions we want to answer in this chapter.

We begin our chapter by giving a short description of what psychologists regard as a problem. Afterwards we are going to present different approaches towards problem solving, starting with gestalt psychologists and ending with modern search strategies connected to artificial intelligence. In addition we will also consider how experts do solve problems and finally we will have a closer look at two topics: The neurophysiological background on the one hand and the question what kind of role can be assigned to evolution regarding problem solving on the other.

The most basic definition is “A problem is any given situation that differs from a desired goal”. This definition is very useful for discussing problem solving in terms of evolutionary adaptation, as it allows to understand every aspect of (human or animal) life as a problem. This includes issues like finding food in harsh winters, remembering where you left your provisions, making decisions about which way to go, learning, repeating and varying all kinds of complex movements, and so on. Though all these problems were of crucial importance during the evolutionary process that created us the way we are, they are by no means solved exclusively by humans. We find a most amazing variety of different solutions for these problems in nature (just consider, e.g., by which means a bat hunts its prey, compared to a spider). For this essay we will mainly focus on those problems that are not solved by animals or evolution, that is, all kinds of abstract problems (e.g. playing chess). Furthermore, we will not consider those situations as problems that have an obvious solution: Imagine Knut decides to take a sip of coffee from the mug next to his right hand. He does not even have to think about how to do this. This is not because the situation itself is trivial (a robot capable of recognising the mug, deciding whether it is full, then grabbing it and moving it to Knut’s mouth would be a highly complex machine) but because in the context of all possible situations it is so trivial that it no longer is a problem our consciousness needs to be bothered with. The problems we will discuss in the following all need some conscious effort, though some seem to be solved without us being able to say how exactly we got to the solution. Still we will find that often the strategies we use to solve these problems are applicable to more basic problems, too.

Non-trivial, abstract problems can be divided into two groups:

### Well-defined Problems

For many abstract problems it is possible to find an algorithmic solution. We call all those problems well-defined that can be properly formalised, which comes along with the following properties:

• The problem has a clearly defined given state. This might be the line-up of a chess game, a given formula you have to solve, or the set-up of the towers of Hanoi game (which we will discuss later).
• There is a finite set of operators, that is, of rules you may apply to the given state. For the chess game, e.g., these would be the rules that tell you which piece you may move to which position.
• Finally, the problem has a clear goal state: The equations is resolved to x, all discs are moved to the right stack, or the other player is in checkmate.

Not surprisingly, a problem that fulfils these requirements can be implemented algorithmically (also see convergent thinking). Therefore many well-defined problems can be very effectively solved by computers, like playing chess.

### Ill-defined Problems

Though many problems can be properly formalised (sometimes only if we accept an enormous complexity) there are still others where this is not the case. Good examples for this are all kinds of tasks that involve creativity, and, generally speaking, all problems for which it is not possible to clearly define a given state and a goal state: Formalising a problem of the kind “Please paint a beautiful picture” may be impossible. Still this is a problem most people would be able to access in one way or the other, even if the result may be totally different from person to person. And while Knut might judge that picture X is gorgeous, you might completely disagree.

Nevertheless ill-defined problems often involve sub-problems that can be totally well-defined. On the other hand, many every-day problems that seem to be completely well-defined involve- when examined in detail- a big deal of creativity and ambiguities.

If we think of Knut's fairly ill-defined task of writing an essay, he will not be able to complete this task without first understanding the text he has to write about. This step is the first subgoal Knut has to solve. Interestingly, ill-defined problems often involve subproblems that are well-defined.

## Restructuring – The Gestalt Approach

One dominant approach to Problem Solving originated from Gestalt psychologists in the 1920s. Their understanding of problem solving emphasises behaviour in situations requiring relatively novel means of attaining goals and suggests that problem solving involves a process called restructuring. Since this indicates a perceptual approach, two main questions have to be considered:

• How is a problem represented in a person's mind?
• How does solving this problem involve a reorganisation or restructuring of this representation?

This is what we are going to do in the following part of this section.

### How is a problem represented in the mind?

In current research internal and external representations are distinguished: The first kind is regarded as the knowledge and structure of memory, while the latter type is defined as the knowledge and structure of the environment, such like physical objects or symbols whose information can be picked up and processed by the perceptual system autonomously. On the contrary the information in internal representations has to be retrieved by cognitive processes.

Generally speaking, problem representations are models of the situation as experienced by the agent. Representing a problem means to analyse it and split it into separate components:

• objects, predicates
• state space
• operators
• selection criteria

Therefore the efficiency of Problem Solving depends on the underlying representations in a person’s mind, which usually also involves personal aspects. Analysing the problem domain according to different dimensions, i.e., changing from one representation to another, results in arriving at a new understanding of a problem. This is basically what is described as restructuring. The following example illustrates this:

Two boys of different age are playing badminton. The older one is a more skilled player, and therefore it is predictable for the outcome of usual matches who will be the winner. After some time and several defeats the younger boy finally loses interest in playing, and the older boy faces a problem, namely that he has no one to play with anymore.
The usual options, according to M. Wertheimer (1945/82), at this point of the story range from 'offering candy' and 'playing another game' to 'not playing to full ability' and 'shaming the younger boy into playing'. All those strategies aim at making the younger stay.
And this is what the older boy comes up with: He proposes that they should try to keep the bird in play as long as possible. Thus they change from a game of competition to one of cooperation. They'd start with easy shots and make them harder as their success increases, counting the number of consecutive hits. The proposal is happily accepted and the game is on again.

The key in this story is that the older boy restructured the problem and found out that he used an attitude towards the younger which made it difficult to keep him playing. With the new type of game the problem is solved: the older is not bored, the younger not frustrated.

Possibly, new representations can make a problem more difficult or much easier to solve. To the latter case insight– the sudden realisation of a problem’s solution – seems to be related.

### Insight

There are two very different ways of approaching a goal-oriented situation. In one case an organism readily reproduces the response to the given problem from past experience. This is called reproductive thinking.

The second way requires something new and different to achieve the goal, prior learning is of little help here. Such productive thinking is (sometimes) argued to involve insight. Gestalt psychologists even state that insight problems are a separate category of problems in their own right.

Tasks that might involve insight usually have certain features – they require something new and non-obvious to be done and in most cases they are difficult enough to predict that the initial solution attempt will be unsuccessful. When you solve a problem of this kind you often have a so called "AHA-experience" – the solution pops up all of a sudden. At one time you do not have any ideas of the answer to the problem, you do not even feel to make any progress trying out different ideas, but in the next second the problem is solved.

For all those readers who would like to experience such an effect, here is an example for an Insight Problem: Knut is given four pieces of a chain; each made up of three links. The task is to link it all up to a closed loop and he has only 15 cents. To open a link costs 2, to close a link costs 3 cents. What should Knut do?

If you want to know the correct solution, click to enlarge the image.

To show that solving insight problems involves restructuring, psychologists created a number of problems that were more difficult to solve for participants provided with previous experiences, since it was harder for them to change the representation of the given situation (see Fixation). Sometimes given hints may lead to the insight required to solve the problem. And this is also true for involuntarily given ones. For instance it might help you to solve a memory game if someone accidentally drops a card on the floor and you look at the other side. Although such help is not obviously a hint, the effect does not differ from that of intended help.

For non-insight problems the opposite is the case. Solving arithmetical problems, for instance, requires schemas, through which one can get to the solution step by step.

### Fixation

Sometimes, previous experience or familiarity can even make problem solving more difficult. This is the case whenever habitual directions get in the way of finding new directions – an effect called fixation.

#### Functional fixedness

Functional fixedness concerns the solution of object-use problems. The basic idea is that when the usual way of using an object is emphasised, it will be far more difficult for a person to use that object in a novel manner. An example for this effect is the candle problem: Imagine you are given a box of matches, some candles and tacks. On the wall of the room there is a cork-board. Your task is to fix the candle to the cork-board in such a way that no wax will drop on the floor when the candle is lit. – Got an idea?

Explanation: The clue is just the following: when people are confronted with a problem and given certain objects to solve it, it is difficult for them to figure out that they could use them in a different (not so familiar or obvious) way. In this example the box has to be recognised as a support rather than as a container.

A further example is the two-string problem: Knut is left in a room with a chair and a pair of pliers given the task to bind two strings together that are hanging from the ceiling. The problem he faces is that he can never reach both strings at a time because they are just too far away from each other. What can Knut do?

Solution: Knut has to recognise he can use the pliers in a novel function – as weight for a pendulum. He can bind them to one of the :strings, push it away, hold the other string and just wait for the first one moving towards him. If necessary, Knut can even climb on the chair, but he is not that small, we suppose . . .

#### Mental fixedness

Functional fixedness as involved in the examples above illustrates a mental set – a person’s tendency to respond to a given task in a manner based on past experience. Because Knut maps an object to a particular function he has difficulties to vary the way of use (pliers as pendulum's weight).

One approach to studying fixation was to study wrong-answer verbal insight problems. It was shown that people tend to give rather an incorrect answer when failing to solve a problem than to give no answer at all.

A typical example: People are told that on a lake the area covered by water lilies doubles every 24 hours and that it takes 60 days to cover the whole lake. Then they are asked how many days it takes to cover half the lake. The typical response is '30 days' (whereas 59 days is correct).

These wrong solutions are due to an inaccurate interpretation, hence representation, of the problem. This can happen because of sloppiness (a quick shallow reading of the problem and/or weak monitoring of their efforts made to come to a solution). In this case error feedback should help people to reconsider the problem features, note the inadequacy of their first answer, and find the correct solution. If, however, people are truly fixated on their incorrect representation, being told the answer is wrong does not help. In a study made by P.I. Dallop and R.L. Dominowski in 1992 these two possibilities were contrasted. In approximately one third of the cases error feedback led to right answers, so only approximately one third of the wrong answers were due to inadequate monitoring.[1]

Another approach is the study of examples with and without a preceding analogous task. In cases such like the water-jug task analogous thinking indeed leads to a correct solution, but to take a different way might make the case much simpler:

Imagine Knut again, this time he is given three jugs with different capacities and is asked to measure the required amount of water. :Of course he is not allowed to use anything despite the jugs and as much water as he likes. In the first case the sizes are: 127 litres, 21 litres and 3 litres while 100 litres are desired.
In the second case Knut is asked to measure 18 litres from jugs of 39, 15 and three litres size.

In fact participants faced with the 100 litre task first choose a complicate way in order to solve the second one. Others on the contrary who did not know about that complex task solved the 18 litre case by just adding three litres to 15.

## Problem Solving as a Search Problem

The idea of regarding problem solving as a search problem originated from Alan Newell and Herbert Simon while trying to design computer programs which could solve certain problems. This led them to develop a program called General Problem Solver which was able to solve any well-defined problem by creating heuristics on the basis of the user's input. This input consisted of objects and operations that could be done on them.

As we already know, every problem is composed of an initial state, intermediate states and a goal state (also: desired or final state), while the initial and goal states characterise the situations before and after solving the problem. The intermediate states describe any possible situation between initial and goal state. The set of operators builds up the transitions between the states. A solution is defined as the sequence of operators which leads from the initial state across intermediate states to the goal state.

The simplest method to solve a problem, defined in these terms, is to search for a solution by just trying one possibility after another (also called trial and error).

As already mentioned above, an organised search, following a specific strategy, might not be helpful for finding a solution to some ill-defined problem, since it is impossible to formalise such problems in a way that a search algorithm can find a solution.

As an example we could just take Knut and his essay: he has to find out about his own opinion and formulate it and he has to make sure he understands the sources texts. But there are no predefined operators he can use, there is no panacea how to get to an opinion and even not how to write it down.

### Means-End Analysis

In Means-End Analysis you try to reduce the difference between initial state and goal state by creating subgoals until a subgoal can be reached directly (probably you know several examples of recursion which works on the basis of this).

An example for a problem that can be solved by Means-End Analysis are the „Towers of Hanoi“:

Towers of Hanoi – A well defined problem

The initial state of this problem is described by the different sized discs being stacked in order of size on the first of three pegs (the “start-peg“). The goal state is described by these discs being stacked on the third pegs (the “end-peg“) in exactly the same order.

There are three operators:

• You are allowed to move one single disc from one peg to another one
• You are only able to move a disc if it is on top of one stack
• A disc cannot be put onto a smaller one.

In order to use Means-End Analysis we have to create subgoals. One possible way of doing this is described in the picture:

1. Moving the discs lying on the biggest one onto the second peg.

2. Shifting the biggest disc to the third peg.

3. Moving the other ones onto the third peg, too

You can apply this strategy again and again in order to reduce the problem to the case where you only have to move a single disc – which is then something you are allowed to do.

Strategies of this kind can easily be formulated for a computer; the respective algorithm for the Towers of Hanoi would look like this:

1. move n-1 discs from A to B

2. move disc #n from A to C

3. move n-1 discs from B to C

where n is the total number of discs, A is the first peg, B the second, C the third one. Now the problem is reduced by one with each recursive loop.

Means-end analysis is important to solve everyday-problems – like getting the right train connection: You have to figure out where you catch the first train and where you want to arrive, first of all. Then you have to look for possible changes just in case you do not get a direct connection. Third, you have to figure out what are the best times of departure and arrival, on which platforms you leave and arrive and make it all fit together.

### Analogies

Analogies describe similar structures and interconnect them to clarify and explain certain relations. In a recent study, for example, a song that got stuck in your head is compared to an itching of the brain that can only be scratched by repeating the song over and over again.

### Restructuring by Using Analogies

One special kind of restructuring, the way already mentioned during the discussion of the Gestalt approach, is analogical problem solving. Here, to find a solution to one problem – the so called target problem, an analogous solution to another problem – the source problem, is presented.

An example for this kind of strategy is the radiation problem posed by K. Duncker in 1945:

As a doctor you have to treat a patient with a malignant, inoperable tumour, buried deep inside the body. There exists a special kind of ray, which is perfectly harmless at a low intensity, but at the sufficient high intensity is able to destroy the tumour – as well as the healthy tissue on his way to it. What can be done to avoid the latter?

When this question was asked to participants in an experiment, most of them couldn't come up with the appropriate answer to the problem. Then they were told a story that went something like this:

A General wanted to capture his enemy's fortress. He gathered a large army to launch a full-scale direct attack, but then learned, that all the roads leading directly towards the fortress were blocked by mines. These roadblocks were designed in such a way, that it was possible for small groups of the fortress-owner's men to pass them safely, but every large group of men would initially set them off. Now the General figured out the following plan: He divided his troops into several smaller groups and made each of them march down a different road, timed in such a way, that the entire army would reunite exactly when reaching the fortress and could hit with full strength.

Here, the story about the General is the source problem, and the radiation problem is the target problem. The fortress is analogous to the tumour and the big army corresponds to the highly intensive ray. Consequently a small group of soldiers represents a ray at low intensity. The solution to the problem is to split the ray up, as the general did with his army, and send the now harmless rays towards the tumour from different angles in such a way that they all meet when reaching it. No healthy tissue is damaged but the tumour itself gets destroyed by the ray at its full intensity.

M. Gick and K. Holyoak presented Duncker's radiation problem to a group of participants in 1980 and 1983. Only 10 percent of them were able to solve the problem right away, 30 percent could solve it when they read the story of the general before. After given an additional hint – to use the story as help – 75 percent of them solved the problem.

With this results, Gick and Holyoak concluded, that analogical problem solving depends on three steps:

1. Noticing that an analogical connection exists between the source and the target problem.
2. Mapping corresponding parts of the two problems onto each other (fortress → tumour, army → ray, etc.)
3. Applying the mapping to generate a parallel solution to the target problem (using little groups of soldiers approaching from different directions → sending several weaker rays from different directions)

Next, Gick and Holyoak started looking for factors that could be helpful for the noticing and the mapping parts, for example:

Discovering the basic linking concept behind the source and the target problem.

-->picture coming soon<--

#### Schema

The concept that links the target problem with the analogy (the “source problem“) is called problem schema. Gick and Holyoak obtained the activation of a schema on their participants by giving them two stories and asking them to compare and summarise them. This activation of problem schemata is called “schema induction“.

The two presented texts were picked out of six stories which describe analogical problems and their solution. One of these stories was "The General" (remember example in Chapter 4.1).

After solving the task the participants were asked to solve the radiation problem (see chapter 4.2). The experiment showed that in order to solve the target problem reading of two stories with analogical problems is more helpful than reading only one story: After reading two stories 52% of the participants were able to solve the radiation problem (As told in chapter 4.2 only 30% were able to solve it after reading only one story, namely: “The General“).

Gick and Holyoak found out that the quality of the schema a participant developed differs. They classified them into three groups:

• Good schemata: In good schemata it was recognised that the same concept was used in order to solve the problem (21% of the participants created a good schema and 91% of them were able to solve the radiation problem).
• Intermediate schemata: The creator of an intermediate schema has figured out that the root of the matter equals (here: many small forces solved the problem). (20% created one, 40% of them had the right solution).
• Poor schemata: The poor schemata were hardly related to the target problem. In many poor schemata the participant only detected that the hero of the story was rewarded for his efforts (59% created one, 30% of them had the right solution).

The process of using a schema or analogy, i.e. applying it to a novel situation is called transduction. One can use a common strategy to solve problems of a new kind.

To create a good schema and finally get to a solution is a problem-solving skill that requires practise and some background knowledge.

## How do Experts Solve Problems?

With the term expert we describe someone who devotes large amounts of his or her time and energy to one specific field of interest in which he, subsequently, reaches a certain level of mastery. It should not be of surprise that experts tend to be better in solving problems in their field than novices (people who are beginners or not as well trained in a field as experts) are. They are faster in coming up with solutions and have a higher success rate of right solutions. But what is the difference between the way experts and non-experts solve problems? Research on the nature of expertise has come up with the following conclusions:

Experts know more about their field,
their knowledge is organised differently, and
they spend more time analysing the problem.

When it comes to problems that are situated outside the experts' field, their performance often does not differ from that of novices.

Knowledge: An experiment by Chase and Simon (1973a, b) dealt with the question how well experts and novices are able to reproduce positions of chess pieces on chessboards when these are presented to them only briefly. The results showed that experts were far better in reproducing actual game positions, but that their performance was comparable with that of novices when the chess pieces were arranged randomly on the board. Chase and Simon concluded that the superior performance on actual game positions was due to the ability to recognise familiar patterns: A chess expert has up to 50,000 patterns stored in his memory. In comparison, a good player might know about 1,000 patterns by heart and a novice only few to none at all. This very detailed knowledge is of crucial help when an expert is confronted with a new problem in his field. Still, it is not pure size of knowledge that makes an expert more successful. Experts also organise their knowledge quite differently from novices.

Organisation: In 1982 M. Chi and her co-workers took a set of 24 physics problems and presented them to a group of physics professors as well as to a group of students with only one semester of physics. The task was to group the problems based on their similarities. As it turned out the students tended to group the problems based on their surface structure (similarities of objects used in the problem, e.g. on sketches illustrating the problem), whereas the professors used their deep structure (the general physical principles that underlay the problems) as criteria. By recognising the actual structure of a problem experts are able to connect the given task to the relevant knowledge they already have (e.g. another problem they solved earlier which required the same strategy).

Analysis: Experts often spend more time analysing a problem before actually trying to solve it. This way of approaching a problem may often result in what appears to be a slow start, but in the long run this strategy is much more effective. A novice, on the other hand, might start working on the problem right away, but often has to realise that he reaches dead ends as he chose a wrong path in the very beginning.

## Creative Cognition

We already introduced a lot of ways to solve a problem, mainly strategies that can be used to find the “correct” answer. But there are also problems which do not require a “right answer” to be given – It is time for creative productiveness!

Imagine you are given three objects – your task is to invent a completely new object that is related to nothing you know. Then try to describe its function and how it could additionally be used. Difficult? Well, you are free to think creatively and will not be at risk to give an incorrect answer. For example think of what can be constructed from a half-sphere, wire and a handle. The result is amazing: a lawn lounger, global earrings, a sled, a water weigher, a portable agitator, ... [2]

### Divergent Thinking

The term divergent thinking describes a way of thinking that does not lead to one goal, but is open-ended. Problems that are solved this way can have a large number of potential 'solutions' of which none is exactly 'right' or 'wrong', though some might be more suitable than others.

Solving a problem like this involves indirect and productive thinking and is mostly very helpful when somebody faces an ill-definedproblem, i.e. when either initial state or goal state cannot be stated clearly and operators or either insufficient or not given at all.

The process of divergent thinking is often associated with creativity, and it undoubtedly leads to many creative ideas. Nevertheless, researches have shown that there is only modest correlation between performance on divergent thinking tasks and other measures of creativity. Additionally it was found that in processes resulting in original and practical inventions things like searching for solutions, being aware of structures and looking for analogies are heavily involved, too.

Thus, divergent thinking alone is not an appropriate tool for making an invention. You also need to analyse the problem in order to make the suggested, i.e. invention, solution appropriate.

#### right or wrong

The ability of children to imitate the people and the surrounding environment also influential in recognizing the concepts of right and wrong To introduce the concepts of right and wrong must be seen from the age of the child. When children are a year old, their brains are not fully developed so their understanding is still limited. But keep in mind, too, from an early age the average child is able to imitate parents, see their surroundings and do imitation or called modeling. Therefore, the introduction of the concept of right and wrong also depends on how the parents or other adults live with the child. "If a mother often sits on the couch while raising both legs, children tend to sit with more or less the same style and think this is true. As we get older, modeling is the most natural thing that children can get about right and wrong," said this psychologist called Kiki. The method of giving understanding about the concepts of right and wrong is also adjusted to the age of the child. If children are still toddlers, they can go through activities such as telling stories that are rich in social values. Slip conclusions at the end of a fairy tale. "For example, the Kancil tale, after storytelling parents can say, 'So, stealing is not good', to emphasize the moral message in the fairy tale," said the psychologist from the Indonesian Psychological Practice Foundation, Bintaro, South Jakarta. For children who are older, for example in primary school age and still under 12 years of age, understanding can be given by giving an explanation of their eyes. Because the nature of them still tends to be egocentric. However, when entering adolescence, giving an explanation can be through a general perspective, especially cause and effect. "When giving to tell children about the concepts of right and wrong, parents need to pay attention to whether the child really understands the message that was delivered as a whole or only part of the contents of the message," Kiki added. For example, when parents want to teach the concept of stealing is not good through the story of Kancil, parents must make sure the child understands that anyone should not steal, no matter what the circumstances. Do not let the child who understands that is not allowed to steal a mouse deer or that should not be stolen is cucumber. Therefore, ask the child to explain his understanding once more so that the child is sure to understand. Responsible Learning If you have been taught the concept of right and wrong, but the child still violates it, parents must act and the child needs to know the consequences of the wrong actions. "For example, it was explained that you should not pick rambutan from a neighboring tree, but the child still did it, immediately reprimanded firmly and words that were not ambiguous or ambiguous, but still polite. "However, the child must be responsible for his attitude," Kiki reminded. Of course, continued Kiki, all this depends on the age of the child. In a small age for certain things, it is better for parents to stay with children, but when they are older, children need to know that parents will not risk their mistakes. Children who from childhood have understood between right and wrong will grow into individuals who are independent, responsible and well-mannered. This will also make it easier for them to socialize in their environment, have healthy friendships and make it easier for them to get good jobs because employers and coworkers certainly want to work with people who are polite, honest and responsible. Important to remember The following basic things can be done by parents to instill in children the right behavior - To say thanks - Say a word please if you want to ask for help - apologize if wrong, even to the child if the parents are wrong - Say greetings

### Convergent Thinking

Convergent thinking patterns are problem solving techniques that unite different ideas or fields to find a solution. The focus of this mindset is speed, logic and accuracy, also identification of facts, reapplying existing techniques, gathering information. The most important factor of this mindset is: there is only one correct answer. You only think of two answers, namely right or wrong. This type of thinking is associated with certain science or standard procedures. People with this type of thinking have logical thinking, are able to memorize patterns, solve problems and work on scientific tests. Most school subjects sharpen this type of thinking ability.

Research shows that the creative process involves both types of thought processes. But experts recommend not joining the two processes in one session. For example, in the next 30 minutes, you invite everyone on your team to brainstorm creating new ideas (which involve divergent thinking patterns). Within 30 minutes, all ideas should only be recorded, not judged, for example by saying that an idea is irrelevant because of a limited budget. After all the ideas are contained, go to the next session, namely analysis and decision making (which involves convergent thinking patterns). Based on research too, doing creative jobs causes mood swings (mood swings), and it turns out that both types of thinking create two different moods. Convergent thinking patterns create negative moods, while divergent thinking patterns create a positive mood. J.A. Research Horne in 1988 revealed that lack of sleep will greatly affect the performance of people with divergent thought patterns, whereas people with convergent mindsets will be more likely to be fine. Including which mindset do you have? Use wisely your talents, and practice both types of thinking to be able to use them in balance at the right times.

## Neurophysiological Background

Presenting Neurophysiology in its entirety would be enough to fill several books. Fortunately we do not have to concern ourselves with most of these facts. Instead, let's just focus on the aspects that are really relevant to problem solving. Nevertheless this topic is quite complex and problem solving cannot be attributed to one single brain area. Rather there are systems of several brain areas working together to perform a specific task. This is best shown by an example:

In 1994 Paolo Nichelli and coworkers used the method of PET (Positron Emission Tomography), to localise certain brain areas, which are involved in solving various chess problems. In the following table you can see which brain area was active during a specific task:
• Identifying chess pieces
• determining location of pieces

• Thinking about making a move
• Remembering a pieces move

• Planning and executing strategies
• Pathway from Occipital to Temporal Lobe

(also called the "what"-pathway of visual processing)

• Pathway from Occipital to parietal Lobe

(also called the "where"-pathway of visual processing)

• Premotor area
• Hippocampus

(forming new memories)

• Prefrontal cortex
Lobes of the Brain

One of the key tasks, namely planning and executing strategies, is performed by a brain area which also plays an important role for several other tasks correlated with problem solving – the prefrontal cortex (PFC). This can be made clear if you take a look at several examples of damages to the PFC and their effects on the ability to solve problems.
Patients with a lesion in this brain area have difficulty switching from one behaviouristic pattern to another. A well known example is the wisconsin card-sorting task. A patient with a PFC lesion who is told to separate all blue cards from a deck, would continue sorting out the blue ones, even if the experimenter told him to sort out all brown cards. Transferred to a more complex problem, this person would most likely fail, because he is not flexible enough to change his strategy after running into a dead end.
Another example is the one of a young homemaker, who had a tumour in the frontal lobe. Even though she was able to cook individual dishes, preparing a whole family meal was an infeasible task for her.

As the examples above illustrate, the structure of our brain seems to be of great importance regarding problem solving, i.e. cognitive life. But how was our cognitive apparatus designed? How did perception-action integration as a central species specific property come about?

## The Evolutionary Perspective

Charles Darwin developed the evolutionary theory which was primarily meant to explain why there are so many different kinds of species. This theory is also important for psychology because it explains how species were designed by evolutionary forces and what their goals are. By knowing the goals of species it is possible to explain and predict their behaviour.

The process of evolution involves several components, for instance natural selection – which is a feedback process that 'chooses' among 'alternative designs' on the basis of deciding how good the respective modulation is. As a result of this natural selection we find adaption. This is a process that constantly tests the variations among individuals in relation to the environment. If adaptions are useful they get passed on; if not they’ll just be an unimportant variation.

Another component of the evolutionary process is sexual selection, i.e. increasing of certain sex characteristics, which give individuals the ability to rival with other individuals of the same sex or an increased ability to attract individuals of the opposite sex.

Altruism is a further component of the evolutionary process, which will be explained in more detail in the following chapter Evolutionary Perspective on Social Cognitions.

## Summary and Conclusion

After Knut read this WikiChapter he was relieved that he did not waste his time for the essay – quite the opposite! He now has a new view on problem solving – and recognises his problem as a well-defined one:

His initial state was the clear blank paper without any philosophical sentences on it. The goal state was just in front of his mind's eye: Him – grinning broadly – handing in the essay with some carefully developed arguments.

He decides to use the technique of Means-End Analysis and creates several subgoals: