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1.3 Human memory 27
signal in approximately 150 ms, to a visual signal in 200 ms and to pain in 700 ms. However, a combined signal will result in the quickest response. Factors such as skill or practice can reduce reaction time, and fatigue can increase it. A second measure of motor skill is accuracy. One question that we should ask is whether speed of reaction results in reduced accuracy. This is dependent on the task and the user. In some cases, requiring increased reaction time reduces accuracy. This is the premise behind many arcade and video games where less skilled users fail at levels of play that require faster responses. However, for skilled operators this is not necessarily the case. Studies of keyboard operators have shown that, although the faster operators were up to twice as fast as the others, the slower ones made 10 times the errors. Speed and accuracy of movement are important considerations in the design of interactive systems, primarily in terms of the time taken to move to a particular target on a screen. The target may be a button, a menu item or an icon, for example. The time taken to hit a target is a function of the size of the target and the distance that has to be moved. This is formalized in Fitts’ law [135]. There are many vari- ations of this formula, which have varying constants, but they are all very similar. One common form is
Movement time = a + b log 2 (distance/size + 1)
where a and b are empirically determined constants. This affects the type of target we design. Since users will find it more difficult to manipulate small objects, targets should generally be as large as possible and the distance to be moved as small as possible. This has led to suggestions that pie- chart-shaped menus are preferable to lists since all options are equidistant. However, the trade-off is increased use of screen estate, so the choice may not be so simple. If lists are used, the most frequently used options can be placed closest to the user’s start point (for example, at the top of the menu). The implications of Fitts’ law in design are discussed in more detail in Chapter 12.
HUMAN MEMORY
Have you ever played the memory game? The idea is that each player has to recount a list of objects and add one more to the end. There are many variations but the objects are all loosely related: ‘I went to the market and bought a lemon, some oranges, bacon.. .’ or ‘I went to the zoo and saw monkeys, and lions, and tigers.. .’ and so on. As the list grows objects are missed out or recalled in the wrong order and so people are eliminated from the game. The winner is the person remaining at the end. Such games rely on our ability to store and retrieve information, even seemingly arbitrary items. This is the job of our memory system. Indeed, much of our everyday activity relies on memory. As well as storing all our factual knowledge, our memory contains our knowledge of actions or procedures.
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It allows us to repeat actions, to use language, and to use new information received via our senses. It also gives us our sense of identity, by preserving information from our past experiences. But how does our memory work? How do we remember arbitrary lists such as those generated in the memory game? Why do some people remember more easily than others? And what happens when we forget? In order to answer questions such as these, we need to understand some of the capabilities and limitations of human memory. Memory is the second part of our model of the human as an information-processing system. However, as we noted earlier, such a division is simplistic since, as we shall see, memory is associated with each level of processing. Bearing this in mind, we will consider the way in which memory is structured and the activities that take place within the system. It is generally agreed that there are three types of memory or memory function: sensory buffers , short-term memory or working memory , and long-term memory. There is some disagreement as to whether these are three separate systems or different functions of the same system. We will not concern ourselves here with the details of this debate, which is discussed in detail by Baddeley [21], but will indicate the evidence used by both sides as we go along. For our purposes, it is sufficient to note three separate types of memory. These memories interact, with information being processed and passed between memory stores, as shown in Figure 1.9.
1.3.1 Sensory memory
The sensory memories act as buffers for stimuli received through the senses. A sensory memory exists for each sensory channel: iconic memory for visual stimuli, echoic memory for aural stimuli and haptic memory for touch. These memories are constantly overwritten by new information coming in on these channels. We can demonstrate the existence of iconic memory by moving a finger in front of the eye. Can you see it in more than one place at once? This indicates a persistence of the image after the stimulus has been removed. A similar effect is noticed most vividly at firework displays where moving sparklers leave a persistent image. Information remains in iconic memory very briefly, in the order of 0.5 seconds. Similarly, the existence of echoic memory is evidenced by our ability to ascertain the direction from which a sound originates. This is due to information being received by both ears. However, since this information is received at different times, we must store the stimulus in the meantime. Echoic memory allows brief ‘play-back’
Figure 1.9 A model of the structure of memory
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Did you recall that more easily? Here the digits are grouped or chunked. A general- ization of the 7 ± 2 rule is that we can remember 7 ± 2 chunks of information. Therefore chunking information can increase the short-term memory capacity. The limited capacity of short-term memory produces a subconscious desire to create chunks, and so optimize the use of the memory. The successful formation of a chunk is known as closure. This process can be generalized to account for the desire to com- plete or close tasks held in short-term memory. If a subject fails to do this or is pre- vented from doing so by interference, the subject is liable to lose track of what she is doing and make consequent errors.
DESIGN FOCUS
Cashing in
Closure gives you a nice ‘done it’ when we complete some part of a task. At this point our minds have a tendency to flush short-term memory in order to get on with the next job. Early automatic teller machines (ATMs) gave the customer money before returning their bank card. On receiving the money the customer would reach closure and hence often forget to take the card. Modern ATMs return the card first!
The sequence of chunks given above also makes use of pattern abstraction: it is written in the form of a UK telephone number which makes it easier to remember. We may even recognize the first sets of digits as the international code for the UK and the dialing code for Leeds – chunks of information. Patterns can be useful as aids
1.3 Human memory 31
to memory. For example, most people would have difficulty remembering the fol- lowing sequence of chunks:
HEC ATR ANU PTH ETR EET
However, if you notice that by moving the last character to the first position, you get the statement ‘the cat ran up the tree’, the sequence is easy to recall. In experiments where subjects were able to recall words freely, evidence shows that recall of the last words presented is better than recall of those in the middle [296]. This is known as the recency effect. However, if the subject is asked to perform another task between presentation and recall (for example, counting backwards) the recency effect is eliminated. The recall of the other words is unaffected. This suggests that short-term memory recall is damaged by interference of other information. However, the fact that this interference does not affect recall of earlier items provides some evidence for the existence of separate long-term and short-term memories. The early items are held in a long-term store which is unaffected by the recency effect. Interference does not necessarily impair recall in short-term memory. Baddeley asked subjects to remember six-digit numbers and attend to sentence processing at the same time [21]. They were asked to answer questions on sentences, such as ‘A precedes B: AB is true or false?’. Surprisingly, this did not result in interference, suggesting that in fact short-term memory is not a unitary system but is made up of a number of components, including a visual channel and an articulatory channel. The task of sen- tence processing used the visual channel, while the task of remembering digits used the articulatory channel, so interference only occurs if tasks utilize the same channel. These findings led Baddeley to propose a model of working memory that incorp- orated a number of elements together with a central processing executive. This is illustrated in Figure 1.10.
Figure 1.10 A more detailed model of short-term memory
1.3 Human memory 33
associated to each other in classes, and may inherit attributes from parent classes. This model is known as a semantic network. As an example, our knowledge about dogs may be stored in a network such as that shown in Figure 1.11. Specific breed attributes may be stored with each given breed, yet general dog information is stored at a higher level. This allows us to generalize about specific cases. For instance, we may not have been told that the sheepdog Shadow has four legs and a tail, but we can infer this information from our general knowledge about sheepdogs and dogs in general. Note also that there are connections within the net- work which link into other domains of knowledge, for example cartoon characters. This illustrates how our knowledge is organized by association. The viability of semantic networks as a model of memory organization has been demonstrated by Collins and Quillian [74]. Subjects were asked questions about different properties of related objects and their reaction times were measured. The types of question asked (taking examples from our own network) were ‘Can a collie breathe?’, ‘Is a beagle a hound?’ and ‘Does a hound track?’ In spite of the fact that the answers to such questions may seem obvious, subjects took longer to answer ques- tions such as ‘Can a collie breathe?’ than ones such as ‘Does a hound track?’ The reason for this, it is suggested, is that in the former case subjects had to search fur- ther through the memory hierarchy to find the answer, since information is stored at its most abstract level. A number of other memory structures have been proposed to explain how we represent and store different types of knowledge. Each of these represents a different
Figure 1.11 Long-term memory may store information in a semantic network
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aspect of knowledge and, as such, the models can be viewed as complementary rather than mutually exclusive. Semantic networks represent the associations and relation- ships between single items in memory. However, they do not allow us to model the representation of more complex objects or events, which are perhaps composed of a number of items or activities. Structured representations such as frames and scripts organize information into data structures. Slots in these structures allow attribute values to be added. Frame slots may contain default, fixed or variable information. A frame is instantiated when the slots are filled with appropriate values. Frames and scripts can be linked together in networks to represent hierarchical structured knowledge. Returning to the ‘dog’ domain, a frame-based representation of the knowledge may look something like Figure 1.12. The fixed slots are those for which the attribute value is set, default slots represent the usual attribute value, although this may be overridden in particular instantiations (for example, the Basenji does not bark), and variable slots can be filled with particular values in a given instance. Slots can also contain procedural knowledge. Actions or operations can be associated with a slot and performed, for example, whenever the value of the slot is changed. Frames extend semantic nets to include structured, hierarchical information. They represent knowledge items in a way which makes explicit the relative importance of each piece of information. Scripts attempt to model the representation of stereotypical knowledge about situ- ations. Consider the following sentence:
John took his dog to the surgery. After seeing the vet, he left.
From our knowledge of the activities of dog owners and vets, we may fill in a substantial amount of detail. The animal was ill. The vet examined and treated the animal. John paid for the treatment before leaving. We are less likely to assume the alternative reading of the sentence, that John took an instant dislike to the vet on sight and did not stay long enough to talk to him!
Figure 1.12 A frame-based representation of knowledge
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Long-term memory processes
So much for the structure of memory, but what about the processes which it uses? There are three main activities related to long-term memory: storage or remember- ing of information, forgetting and information retrieval. We shall consider each of these in turn. First, how does information get into long-term memory and how can we improve this process? Information from short-term memory is stored in long-term memory by rehearsal. The repeated exposure to a stimulus or the rehearsal of a piece of informa- tion transfers it into long-term memory. This process can be optimized in a number of ways. Ebbinghaus performed numerous experiments on memory, using himself as a subject [117]. In these experi- ments he tested his ability to learn and repeat nonsense syllables, comparing his recall minutes, hours and days after the learning process. He discovered that the amount learned was directly proportional to the amount of time spent learning. This is known as the total time hypothesis. However, experiments by Baddeley and others suggest that learning time is most effective if it is distributed over time [22]. For example, in an experiment in which Post Office workers were taught to type, those whose training period was divided into weekly sessions of one hour performed better than those who spent two or four hours a week learning (although the former obviously took more weeks to complete their training). This is known as the distribu- tion of practice effect. However, repetition is not enough to learn information well. If information is not meaningful it is more difficult to remember. This is illustrated by the fact that it is more difficult to remember a set of words representing concepts than a set of words representing objects. Try it. First try to remember the words in list A and test yourself. List A: Faith Age Cold Tenet Quiet Logic Idea Value Past Large
Now try list B.
List B: Boat Tree Cat Child Rug Plate Church Gun Flame Head
The second list was probably easier to remember than the first since you could visualize the objects in the second list. Sentences are easier still to memorize. Bartlett performed experiments on remem- bering meaningful information (as opposed to meaningless such as Ebbinghaus used) [28]. In one such experiment he got subjects to learn a story about an un- familiar culture and then retell it. He found that subjects would retell the story replacing unfamiliar words and concepts with words which were meaningful to them. Stories were effectively translated into the subject’s own culture. This is related to the semantic structuring of long-term memory: if information is meaningful and familiar, it can be related to existing structures and more easily incorporated into memory.
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So if structure, familiarity and concreteness help us in learning information, what causes us to lose this information, to forget? There are two main theories of forget- ting: decay and interference. The first theory suggests that the information held in long-term memory may eventually be forgotten. Ebbinghaus concluded from his experiments with nonsense syllables that information in memory decayed logarith- mically, that is that it was lost rapidly to begin with, and then more slowly. Jost’s law , which follows from this, states that if two memory traces are equally strong at a given time the older one will be more durable. The second theory is that information is lost from memory through interference. If we acquire new information it causes the loss of old information. This is termed retroactive interference. A common example of this is the fact that if you change tele- phone numbers, learning your new number makes it more difficult to remember your old number. This is because the new association masks the old. However, some- times the old memory trace breaks through and interferes with new information. This is called proactive inhibition. An example of this is when you find yourself driv- ing to your old house rather than your new one. Forgetting is also affected by emotional factors. In experiments, subjects given emotive words and non-emotive words found the former harder to remember in the short term but easier in the long term. Indeed, this observation tallies with our experience of selective memory. We tend to remember positive information rather than negative (hence nostalgia for the ‘good old days’), and highly emotive events rather than mundane.
Memorable or secure?
As online activities become more widespread, people are having to remember more and more access information, such as passwords and security checks. The average active internet user may have separate passwords and user names for several email accounts, mailing lists, e-shopping sites, e-banking, online auctions and more! Remembering these passwords is not easy.
From a security perspective it is important that passwords are random. Words and names are very easy to crack, hence the recommendation that passwords are frequently changed and constructed from random strings of letters and numbers. But in reality these are the hardest things for people to commit to memory. Hence many people will use the same password for all their online activities (rarely if ever changing it) and will choose a word or a name that is easy for them to remember, in spite of the obviously increased security risks. Security here is in conflict with memorability!
A solution to this is to construct a nonsense password out of letters or numbers that will have meaning to you but will not make up a word in a dictionary (e.g. initials of names, numbers from significant dates or postcodes, and so on). Then what is remembered is the meaningful rule for constructing the password, and not a meaningless string of alphanumeric characters.
1.4 Thinking: reasoning and problem solving 39
THINKING: REASONING AND PROBLEM SOLVING
We have considered how information finds its way into and out of the human system and how it is stored. Finally, we come to look at how it is processed and manipulated. This is perhaps the area which is most complex and which separates
Improve your memory
Many people can perform astonishing feats of memory: recalling the sequence of cards in a pack (or multiple packs – up to six have been reported), or recounting π to 1000 decimal places, for example. There are also adverts to ‘Improve Your Memory’ (usually leading to success, or wealth, or other such inducement), and so the question arises: can you improve your memory abilities? The answer is yes; this exercise shows you one technique.
Look at the list below of numbers and associated words:
1 bun 6 sticks 2 shoe 7 heaven 3 tree 8 gate 4 door 9 wine 5 hive 10 hen
Notice that the words sound similar to the numbers. Now think about the words one at a time and visualize them, in as much detail as possible. For example, for ‘1’, think of a large, sticky iced bun, the base spiralling round and round, with raisins in it, covered in sweet, white, gooey icing. Now do the rest, using as much visualization as you can muster: imagine how things would look, smell, taste, sound, and so on.
This is your reference list, and you need to know it off by heart.
Having learnt it, look at a pile of at least a dozen odd items collected together by a colleague. The task is to look at the collection of objects for only 30 seconds, and then list as many as possible without making a mistake or viewing the collection again. Most people can manage between five and eight items, if they do not know any memory-enhancing techniques like the following.
Mentally pick one (say, for example, a paper clip), and call it number one. Now visualize it inter- acting with the bun. It can get stuck into the icing on the top of the bun, and make your fingers all gooey and sticky when you try to remove it. If you ate the bun without noticing, you’d get a crunched tooth when you bit into it – imagine how that would feel. When you’ve really got a graphic scenario developed, move on to the next item, call it number two, and again visualize it interacting with the reference item, shoe. Continue down your list, until you have done 10 things.
This should take you about the 30 seconds allowed. Then hide the collection and try and recall the numbers in order, the associated reference word, and then the image associated with that word. You should find that you can recall the 10 associated items practically every time. The technique can be easily extended by extending your reference list.
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humans from other information-processing systems, both artificial and natural. Although it is clear that animals receive and store information, there is little evid- ence to suggest that they can use it in quite the same way as humans. Similarly, artificial intelligence has produced machines which can see (albeit in a limited way) and store information. But their ability to use that information is limited to small domains. Humans, on the other hand, are able to use information to reason and solve problems, and indeed do these activities when the information is partial or unavail- able. Human thought is conscious and self-aware: while we may not always be able to identify the processes we use, we can identify the products of these processes, our thoughts. In addition, we are able to think about things of which we have no experience, and solve problems which we have never seen before. How is this done? Thinking can require different amounts of knowledge. Some thinking activities are very directed and the knowledge required is constrained. Others require vast amounts of knowledge from different domains. For example, performing a subtrac- tion calculation requires a relatively small amount of knowledge, from a constrained domain, whereas understanding newspaper headlines demands knowledge of pol- itics, social structures, public figures and world events. In this section we will consider two categories of thinking: reasoning and problem solving. In practice these are not distinct since the activity of solving a problem may well involve reasoning and vice versa. However, the distinction is a common one and is helpful in clarifying the processes involved.
1.4.1 Reasoning
Reasoning is the process by which we use the knowledge we have to draw conclusions or infer something new about the domain of interest. There are a number of differ- ent types of reasoning: deductive , inductive and abductive. We use each of these types of reasoning in everyday life, but they differ in significant ways.
Deductive reasoning
Deductive reasoning derives the logically necessary conclusion from the given pre- mises. For example,
If it is Friday then she will go to work It is Friday Therefore she will go to work.
It is important to note that this is the logical conclusion from the premises; it does not necessarily have to correspond to our notion of truth. So, for example,
If it is raining then the ground is dry It is raining Therefore the ground is dry.
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Abductive reasoning
The third type of reasoning is abduction. Abduction reasons from a fact to the action or state that caused it. This is the method we use to derive explanations for the events we observe. For example, suppose we know that Sam always drives too fast when she has been drinking. If we see Sam driving too fast we may infer that she has been drinking. Of course, this too is unreliable since there may be another reason why she is driving fast: she may have been called to an emergency, for example. In spite of its unreliability, it is clear that people do infer explanations in this way, and hold onto them until they have evidence to support an alternative theory or explanation. This can lead to problems in using interactive systems. If an event always follows an action, the user will infer that the event is caused by the action unless evidence to the contrary is made available. If, in fact, the event and the action are unrelated, confusion and even error often result.
Figure 1.14 Wason’s cards
Filling the gaps
Look again at Wason’s cards in Figure 1.14. In the text we say that you only need to check the E and the 7. This is correct, but only because we very carefully stated in the text that ‘each card has a number on one side and a letter on the other’. If the problem were stated without that condition then the K would also need to be examined in case it has a vowel on the other side. In fact, when the problem is so stated, even the most careful subjects ignore this possibility. Why? Because the nature of the problem implicitly suggests that each card has a number on one side and a letter on the other. This is similar to the embellishment of the story at the end of Section 1.3.3. In fact, we constantly fill in gaps in the evidence that reaches us through our senses. Although this can lead to errors in our reasoning it is also essential for us to function. In the real world we rarely have all the evid- ence necessary for logical deductions and at all levels of perception and reasoning we fill in details in order to allow higher levels of reasoning to work.
1.4 Thinking: reasoning and problem solving 43
1.4.2 Problem solving
If reasoning is a means of inferring new information from what is already known, problem solving is the process of finding a solution to an unfamiliar task, using the knowledge we have. Human problem solving is characterized by the ability to adapt the information we have to deal with new situations. However, often solutions seem to be original and creative. There are a number of different views of how people solve problems. The earliest, dating back to the first half of the twentieth century, is the Gestalt view that problem solving involves both reuse of knowledge and insight. This has been largely superseded but the questions it was trying to address remain and its influence can be seen in later research. A second major theory, proposed in the 1970s by Newell and Simon, was the problem space theory , which takes the view that the mind is a limited information processor. Later variations on this drew on the earlier theory and attempted to reinterpret Gestalt theory in terms of information- processing theories. We will look briefly at each of these views.
Gestalt theory
Gestalt psychologists were answering the claim, made by behaviorists, that prob- lem solving is a matter of reproducing known responses or trial and error. This explanation was considered by the Gestalt school to be insufficient to account for human problem-solving behavior. Instead, they claimed, problem solving is both pro- ductive and reproductive. Reproductive problem solving draws on previous experi- ence as the behaviorists claimed, but productive problem solving involves insight and restructuring of the problem. Indeed, reproductive problem solving could be a hind- rance to finding a solution, since a person may ‘fixate’ on the known aspects of the problem and so be unable to see novel interpretations that might lead to a solution. Gestalt psychologists backed up their claims with experimental evidence. Kohler provided evidence of apparent insight being demonstrated by apes, which he observed joining sticks together in order to reach food outside their cages [202]. However, this was difficult to verify since the apes had once been wild and so could have been using previous knowledge. Other experiments observed human problem-solving behavior. One well-known example of this is Maier’s pendulum problem [224]. The problem was this: the subjects were in a room with two pieces of string hanging from the ceiling. Also in the room were other objects including pliers, poles and extensions. The task set was to tie the pieces of string together. However, they were too far apart to catch hold of both at once. Although various solutions were proposed by subjects, few chose to use the weight of the pliers as a pendulum to ‘swing’ the strings together. How- ever, when the experimenter brushed against the string, setting it in motion, this solution presented itself to subjects. Maier interpreted this as an example of produc- tive restructuring. The movement of the string had given insight and allowed the subjects to see the problem in a new way. The experiment also illustrates fixation: subjects were initially unable to see beyond their view of the role or use of a pair of pliers.
1.4 Thinking: reasoning and problem solving 45
Worked exercise Identify the goals and operators involved in the problem ‘delete the second paragraph of the
document’ on a word processor. Now use a word processor to delete a paragraph and note your actions, goals and subgoals. How well did they match your earlier description?
Answer Assume you have a document open and you are at some arbitrary position within it.
You also need to decide which operators are available and what their preconditions and results are. Based on an imaginary word processor we assume the following operators (you may wish to use your own WP package):
Operator Precondition Result
delete_paragraph Cursor at start of paragraph Paragraph deleted move_to_paragraph Cursor anywhere in document Cursor moves to start of next paragraph (except where there is no next paragraph when no effect) move_to_start Cursor anywhere in document Cursor at start of document
Goal : delete second paragraph in document Looking at the operators an obvious one to resolve this goal is delete_paragraph which has the precondition ‘cursor at start of paragraph’. We therefore have a new subgoal: move_to_paragraph. The precondition is ‘cursor anywhere in document’ (which we can meet) but we want the second paragraph so we must initially be in the first. We set up a new subgoal, move_to_start, with precondition ‘cursor anywhere in docu- ment’ and result ‘cursor at start of document’. We can then apply move_to_paragraph and finally delete_paragraph. We assume some knowledge here (that the second paragraph is the paragraph after the first one).
Analogy in problem solving
A third element of problem solving is the use of analogy. Here we are interested in how people solve novel problems. One suggestion is that this is done by mapping knowledge relating to a similar known domain to the new problem – called analo- gical mapping. Similarities between the known domain and the new one are noted and operators from the known domain are transferred to the new one. This process has been investigated using analogous stories. Gick and Holyoak [149] gave subjects the following problem: A doctor is treating a malignant tumor. In order to destroy it he needs to blast it with high-intensity rays. However, these will also destroy the healthy tissue sur- rounding the tumor. If he lessens the rays’ intensity the tumor will remain. How does he destroy the tumor?
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The solution to this problem is to fire low-intensity rays from different directions converging on the tumor. That way, the healthy tissue receives harmless low- intensity rays while the tumor receives the rays combined, making a high-intensity dose. The investigators found that only 10% of subjects reached this solution with- out help. However, this rose to 80% when they were given this analogous story and told that it may help them: A general is attacking a fortress. He can’t send all his men in together as the roads are mined to explode if large numbers of men cross them. He therefore splits his men into small groups and sends them in on separate roads. In spite of this, it seems that people often miss analogous information, unless it is semantically close to the problem domain. When subjects were not told to use the story, many failed to see the analogy. However, the number spotting the analogy rose when the story was made semantically close to the problem, for example a general using rays to destroy a castle. The use of analogy is reminiscent of the Gestalt view of productive restructuring and insight. Old knowledge is used to solve a new problem.
1.4.3 Skill acquisition
All of the problem solving that we have considered so far has concentrated on handling unfamiliar problems. However, for much of the time, the problems that we face are not completely new. Instead, we gradually acquire skill in a particular domain area. But how is such skill acquired and what difference does it make to our problem-solving performance? We can gain insight into how skilled behavior works, and how skills are acquired, by considering the difference between novice and expert behavior in given domains.
Chess: of human and artificial intelligence
A few years ago, Deep Blue, a chess-playing computer, beat Gary Kasparov, the world’s top Grand Master, in a full tournament. This was the long-awaited breakthrough for the artificial intelligence (AI) community, who have traditionally seen chess as the ultimate test of their art. However, despite the fact that computer chess programs can play at Grand Master level against human players, this does not mean they play in the same way. For each move played, Deep Blue investigated many millions of alternative moves and counter-moves. In contrast, a human chess player will only consider a few dozen. But, if the human player is good, these will usually be the right few dozen. The ability to spot patterns allows a human to address a problem with far less effort than a brute force approach. In chess, the number of moves is such that finally brute force, applied fast enough, has overcome human pattern-matching skill. In Go, which has far more pos- sible moves, computer programs do not even reach a good club level of play. Many models of the mental processes have been heavily influenced by computation. It is worth remembering that although there are similarities, computer ‘intelligence’ is very different from that of humans.
