Mental Imagery and Cognitive Maps Chapter 7 PDF

7 Mental Imagery and Cognitive Maps Chapter Introduction Classical Research on Visual Imagery Overview of Mental Imagery Mental Rotation The Imagery Debate Visual Imagery and Ambiguous Figures Factors That...

7 Mental Imagery and Cognitive Maps Chapter Introduction Classical Research on Visual Imagery Overview of Mental Imagery Mental Rotation The Imagery Debate Visual Imagery and Ambiguous Figures Factors That Influence Visual Imagery Distance and Shape Effects on Visual Imagery Visual Imagery and Interference Visual Imagery and Other Vision-Like Processes Gender Comparisons in Spatial Ability Auditory Imagery Auditory Imagery and Pitch Auditory Imagery and Timbre Cognitive Maps Distance and Shape Effects on Cognitive Maps Relative Position Effects on Cognitive Maps Creating a Cognitive Map Chapter Introduction During perception, you rely on knowledge stored in memory to interpret the environmental stimuli regis- tered by your senses. In other words, perception requires both bottom-up and top-down processing (Koss- lyn et al., 2001). But, it is possible to have sensory-related experiences without bottom-up input being registered by your sensory receptors. For example, take a moment to close your eyes and create a clear mental image of the cover of this textbook. Be sure to include details such as its size, shape, and color, as well as the photo of the nautilus shell. Now try to create an auditory image. Can you hear the voice of a close friend saying your name? Finally, close your eyes again and create a “mental map” of the most direct route between your current location and the nearest store where you can buy a quart of milk. In each of these example exercises, you were able to create a mental image of something without seeing or hearing it. Thus, the processes that give rise to your ability to create mental images are exclusively top-down in nature (Kosslyn & Thompson, 2000). In other words, mental imagery is knowledge-driven—it involves utilizing the information stored in long-term memory to create internal images of sounds and objects that you have previously experienced. 134  Classical Research on Visual Imagery 135 This chapter explores three important aspects of imagery that have intrigued contemporary researchers. First, we examine the nature of visual images, with an emphasis on the way that we can transform these images. We then consider the nature of auditory images, a relatively new topic in cognitive psychology. Our third topic focuses on cognitive maps, which are mental representations of geographic information, including the environment that surrounds us. Classical Research on Visual Imagery Mental imagery (also called imagery) refers to the mental representation of stimuli when those stimuli are not physically present in the environment (Kosslyn et al., 2010). You can have a mental image for any sensory experience. Most of the psychological research on mental images, however, has focused on visual imagery, or the mental representation of visual stimuli. Fortunately, during the past decade, the research has increased for auditory imagery, which is the mental representation of auditory stimuli. In this section, we first examine some key topics and questions related to research on mental imagery before discussing mental rotation, a form of visual imagery. We then consider a controversial debate in the field of mental imagery—namely, a debate about the format of the stored knowledge that we access when creating mental images. Overview of Mental Imagery We use mental imagery for a wide variety of everyday cognitive activities (Denis et al., 2004; Tversky, 2005a). For example, consider a situation in which you can’t find your car keys, although you know that they must be somewhere on your messy desk. You must create and maintain a mental image of your keys while you visually inspect your messy desk to find your keys. If you didn’t maintain some type of mental image while you were searching, then how would you know that the coffee mug sitting on your desk isn’t the thing you’re looking for? Additionally, some professions emphasize mental imagery as a crucial component of performance on the job (Reed, 2010). Would you want to fly on an airplane if your pilot had weak spatial imagery? Imagery is also important in clinical psychology. Therapists often work with clients who have psychologi- cal problems such as post-traumatic stress disorder, depression, or eating disorders. With each of these disorders, individuals sometimes report that they experience intrusive, distressing mental images (Dargan et al., 2015; Mazhari et al., 2015; Moran et al., 2015). Therapists have successfully worked with clients by encouraging them to create alternative, more positive images (Bisby et al., 2010; Brewin et al., 2010; Liu & Chan, 2015). Spatial ability is extremely important in the STEM disciplines, that is, science, technology, engineer- ing, and mathematics (Ganis et al., 2009). For instance, Albert Einstein is well known as one of the geni- uses of the last 100 years. Einstein reported that his own thinking processes typically used spatial images, instead of verbal descriptions (Newcombe, 2010). Unfortunately, elementary school teachers in the United States rarely teach children about spatial skills. In fact, the curriculum may not emphasize spatial skills until students enroll in a geometry class. Psychologist Nora Newcombe (2010) describes some interesting methods for enhancing young children’s spatial skills. A typical task might require students to mentally rotate a picture until it resembles one of five options. Many high school and college students believe that they cannot possibly improve their spatial skills. However, training in spatial skills improves spatial per- formance for students of any age (Ganis et al., 2009; Reed, 2010; Twyman & Newcombe, 2010). Although imagery and perception share many characteristics, they are not identical. During the act of perceiving an object in the visual world, for example, sensory information is registered by your sensory systems. Early after information has been registered by your senses, features of the sensory stimulus are detected (edges, lines, color, and so forth). This bottom-up information about the properties of an envi- ronmental stimulus is then processed in progressively more complex ways until an internal representation of the stimulus arises. As this representation is constructed, it is matched to information stored in your long-term memory. An object is recognized once bottom-up information has been processed enough for this matching process to occur. Just about every topic in this book relies on both bottom-up and top-down processes, working together in concert to provide you with the ability to successfully perform some type of cognitive task. Mental imagery, however, is a rare exception. Indeed, by definition, mental imagery is knowledge-driven. You rely 136 MENTAL IMAGERY AND COGNITIVE MAPS on what you know—and thus, information stored in your long-term memory—to create internal mental images. For example, when you create a mental image of the shape of Colorado, no one would suggest that the rods and cones in your retina are registering a Colorado-shaped pattern of stimulation. The subjective experiences for visual imagery and visual perception are obviously different, and it takes about one-tenth of a second longer to create a visual image (Reddy et al., 2010). Sometimes, these internal mental images are created while you are laying in bed trying to fall asleep, or when you’re daydreaming. In these cases, mental images arise as a result of general thought processes. In fact, the ability to create and manipulate mental images has often been considered a hallmark of creativity and imagination (Brann, 1991; Thomas, 1999). Note, however, that internal mental images are often necessary to perform some cognitive task. In the visual search example above, in which someone must find their keys on a messy desk, a mental image of the keys is necessary in order to successfully search. In this sense, mental imagery is not a form of per- ception, per se, but is a close relative of perception. Chapter 1 of this textbook provided an overview of the history of psychology. You may recall that Wilhelm Wundt is often described as the founder of psychology. Wundt and other early psychologists con- sidered imagery to be an important part of the discipline (Palmer, 1999). In contrast, behaviorists such as John Watson strongly opposed research on mental imagery because it could not be connected to observable behavior. In fact, Watson even argued that imagery did not exist (Kosslyn et al., 2010). As a result, North American psychologists seldom studied imagery during the behaviorist period between 1920 and 1960 (Ganis et al., 2009; Kosslyn et al., 2010). For example, I used PsycINFO to search for the term “mental imagery” in any part of every journal article published during the decade from 1950 through 1959. The search identified only 34 articles. As cognitive psychology gained popularity, however, researchers redis- covered imagery. The topic continues to be important in contemporary cognitive psychology, especially with the development of more sophisticated techniques in cognitive neuroscience (Ganis et al., 2009; Reed, 2010). Mental imagery is a challenging topic to study. Compared with a topic such as verbal memory, the topic of mental imagery is elusive and inaccessible. Researchers have attacked this problem by using the following logic: Suppose that a mental image really does resemble a physical object. Then people should be able to make judgments about this mental image in the same way that they make judgments about the corresponding physical object (Hubbard, 2010). For example, we should be able to rotate a mental image in the same way that we can rotate a physical object. Judgments about distance in a mental image should also be similar, as well as judgments about shape. In addition, a mental image should create interference when we try to perceive a physical object. Furthermore, we should be able to discover two interpretations of a mental image of an ambiguous figure, and we should be able to produce other vision-like effects when we construct a mental image. Mental Rotation As you might expect, research on mental imagery is difficult to conduct, especially because researchers cannot directly observe mental images and because they fade so quickly (Kosslyn et al., 2006). However, psychologists have modified some research techniques that were originally developed for studying visual perception so that they can now be applied to the study of mental images (Allen, 2004). As a result, the investigation of imagery has made impressive advances. Try Demonstration 7.1, which illustrates an important research technique that we’ll examine shortly. Suppose that you are a researcher who wants to study whether people rotate a mental image in the same way that they rotate a physical object. It’s tempting to think that you could simply ask people to analyze their mental images and use these reports as a basis for describing mental imagery. However, consider why these introspective reports could be inaccurate and biased. We may not always have conscious access to the processes associated with our mental imagery (Anderson, 1998; Pylyshyn, 2006). Demonstration 7.1 illustrates a classic experiment by Roger Shepard and his coauthor Jacqueline Metzler (1971). Researchers have explored the mental-rotation issue more than any other topic connected with imagery. Here was their reasoning. Suppose that you are holding a physical, geometric object in your hands, and you decide to rotate it. It will take you longer to rotate this physical object by 180 degrees than to rotate it only 90 degrees. Now suppose that our mental images operate the same way that physical objects operate. It will take you longer to rotate this mental image 180 degrees, instead of 90 degrees. Again, remember that this entire  Classical Research on Visual Imagery 137 Demonstration 7.1 Mental Rotation For the top pair of objects, labeled A, look at the object on the left. objects are the same, and which are different? Record your answers; Try rotating it in any direction you wish. Can you rotate it so that we’ll discuss this study shortly. it matches the object on the right? Which of these three pairs of Source: Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701–703. Copyright 1971 American Association for the Advancement of Science. question was quite daring during this era. No genuine behaviorist would ever consider research about mental images! In Demonstration 7.1, notice that, in the top pair of designs (Part A), the left-hand figure can be changed into the right-hand figure by keeping it flat on the page and rotating it clockwise. Suddenly, the two figures match up, and you conclude “same.” You can match these two figures by using a two-dimensional rotation. In contrast, the middle pair (Part B) requires a rotation in a third dimension. You may, for example, take the two-block “arm” that is jutting out toward you and push it over to the left and away from you. Suddenly, the figures match up, and you conclude “same.” However, in the case of the bottom pair (Part C), you cannot rotate the figure on the left so that it matches the figure on the right. Therefore, you must conclude “different.” Shepard and Metzler (1971) asked eight extremely dedicated participants to judge 1,600 pairs of line drawings like these. They were instructed to pull a lever with their right hand if they judged the figures to be the same, and to pull a different lever with their left hand if they judged the figures to be different. In 138 MENTAL IMAGERY AND COGNITIVE MAPS FIGURE 7.1 Reaction time for 5 5 Reaction time (in seconds) Reaction time (in seconds) deciding that pairs of figures are the same, as a function of the angle 4 4 of rotation and the nature of rotation. Note: The centers of the 3 3 circles indicate the means, and the bars on either side provide an index of the 2 2 variability of those means. Source: Shepard, R. N., & Metzler, J. (1971). Mental rotation of three- 1 1 dimensional objects. Science, 171, 701–703. Copyright © 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 1971. American Association Angle of rotation (degrees) Angle of rotation (degrees) for the Advancement of Science. A. Picture-plane pairs B. Depth pairs each case, the experimenters measured the amount of time required for a decision. Notice, then, that the dependent variable is reaction time, in contrast to the dependent variable of accuracy used in most of the research we have examined in previous chapters. Now look at Figure 7.1A, which shows the results for figures like Pair A from Demonstration 7.1. These figures require only a two-dimensional rotation, similar to rotating a flat picture. In contrast, Figure 7.1B shows the results for figures like Pair B in Demonstration 7.1. These figures require a three-dimensional rotation, similar to rotating an object in depth. As both graphs show, people’s decision time was strongly influenced by the amount of mental rotation required to match a figure with its mate. For example, rotating a figure 160 degrees requires much more time than rotating it a mere 20 degrees. Furthermore, notice the similarity between Figures 7.1A and 7.1B. In other words, the participants in this study performed a three-dimensional rotation almost as quickly as a two-dimensional rotation. (Pairs of figures like the two in Pair C in Demonstration 7.1 are based on dif- ferent shapes, so these data are not included in either Figure 7.1A or 7.1B.) As you can see, both figures show that the relationship between rotation and reaction time is a straight line. Subsequent Research on Mental Rotation The basic findings about mental rotation have been replicated many times. Using a variety of other stimuli, such as letters of the alphabet, researchers have found a clear relationship between angle of rotation and reaction time (e.g., Bauer & Jolicoeur, 1996; Cooper & Lang, 1996; Dahlstrom-Hakki et al., 2008; Koss- lyn et al., 2006; Newcombe, 2002). That is, people make judgments more quickly if they need to rotate a mental image just a short distance. If you are left-handed, you may wonder if handedness can influence the mental-rotation process. Kotaro Takeda and his coauthors (2010) asked the participants in their study to look at pictures of a human hand and to identify whether they were viewing a left hand or a right hand. Right-handers recognized a right hand faster than a left hand. In contrast, left-handers recognized right and left hands equally quickly. How- ever, both groups recognized upright pictures faster—and more accurately—than upside-down pictures. This particular finding is consistent with the earlier research. After all, people take less time to rotate an image 0 degrees, rather than 180 degrees. We also know that elderly people perform more slowly than younger people on a mental-rotation task. In contrast, age is not consistently correlated with other imagery skills, such as sense of direction or the ability to scan mental images (Beni et al., 2006; Dror & Kosslyn, 1994). Other research shows that deaf individuals who are fluent in American Sign Language (ASL) are espe- cially skilled in looking at an arrangement of objects in a scene and mentally rotating that scene by 180 degrees (Emmorey et al., 1998). Why should deaf people perform so well on these mental rotation tasks? They have an advantage because they have had extensive experience in watching a narrator produce a sign. Then, they must mentally rotate this sign 180 degrees. They need to perform this rotation frequently, so  Classical Research on Visual Imagery 139 that they can match the perspective that they would use when producing this sign. (If you are not fluent in ASL, stand in front of a mirror and notice how you and a viewer would have very different perspectives for your hand movements.) Cognitive Neuroscience Research on Mental Rotation Tasks In one of the early neuroscience studies on mental rotation, Kosslyn et al. (2001) examined whether people use their motor cortex when they imagine themselves rotating one of the geometric figures in Demonstration 7.1. These researchers instructed one group of participants to rotate—with their own hands—one of the geometric figures that had been used in Shepard and Metzler’s (1971) study. They instructed a second group of participants to simply watch as an electric motor rotated this same figure. Next, the people in both groups performed the matching task that you tried in Demonstration 7.1, by rotating the figures mentally. Meanwhile, the researchers conducted PET scans to see which areas of the brain the participants were using during the mental-rotation task. Participants who had originally rotated the original geometric figure with their hands now showed activity in their primary motor cortex—the same part of the brain that had been active when they had rotated the figure with their hands. In contrast, consider the participants who had originally watched the electric motor as it rotated the figure. On the mental-rotation task, these people now showed no activity in the primary motor cortex. Without the “hands on” experience, their primary motor cortex was not active. The nature of the instructions during the actual mental rotation can also influence the pattern of activa- tion in the cortex. Specifically, when people received the standard instructions to rotate the figure, their right frontal lobes and their parietal lobes were strongly activated (Wraga et al., 2005; Zacks et al., 2003). However, this pattern of activation was different when researchers modified the instructions. In a second condition, the participants were instructed to imagine rotating themselves so that they could “see” the figure from a different perspective (Kosslyn et al., 2001). These instructions produced increased activity in the left temporal lobe, as well as in a part of the motor cortex (Wraga et al., 2005; Zacks et al., 2003). Notice, then, that a relatively subtle change in wording can make a dramatic change in the way that the brain responds to a mental-imagery task. The research on mental rotation has practical implications for people who are recovering from a stroke. By watching the rotation of virtual-reality figures, these individuals can provide stimulation to their motor cortex. This form of “exercise” can shorten the time required before they make actual motor movements by themselves (Dijkerman et al., 2010; Ganis et al., 2009). The Imagery Debate Now that you have read about the research on visual imagery, let’s consider the famous imagery debate. For several decades, cognitive psychologists have debated the potential explanations for mental imagery. Stephen Kosslyn and his colleagues (2006) use the term imagery debate to refer to an important con- troversy: Do our mental images resemble perception (using an analog code), or do they resemble language (using a propositional code)? The majority of theorists believe that information about a mental image is stored in an analog code (Howes, 2007; Kosslyn et al., 2006; Reisberg et al., 2003). An analog code is a representation that closely resembles the physical object. Notice that the word analog suggests the word analogy, such as the analogy between the real object and the mental image. According to the analog-code approach, mental imagery is a close relative of perception (Tversky, 2005a). When you look at a sketch of a triangle, the physical features of that triangle are registered in your brain in a form that preserves the physical relationship among the three lines. Those who support analog coding propose that your mental image of a triangle is registered in a somewhat similar fashion, preserving the same relationship among the lines. Under this framework, when you are engaged in mental imagery, you create a mental image of an object that closely resembles the actual perceptual image on your retina (Ganis et al., 2009; Kosslyn et al., 2006). Note that supporters of the analog approach do not suggest that people literally have a picture in their head (Ganis et al., 2009; Kosslyn et al., 2006). They also point out that people often fail to notice precise visual details when they look at an object. These details will also be missing from their mental image of this object (Howes, 2007; Kosslyn et al., 2006). In contrast to the analog-code position, other theorists argue that we store images in terms of a propo- sitional code (Pylyshyn, 2003, 2006). A propositional code is an abstract, language-like representation; 140 MENTAL IMAGERY AND COGNITIVE MAPS storage is neither visual nor spatial, and it does not physically resemble the original stimulus (Ganis et al., 2009; Reed, 2010). According to the propositional-code approach, mental imagery is a close relative of language, not perception. For example, when you store a mental image of a triangle, your brain will reg- ister a language-like description of the lines and angles. Theorists have not specified the precise nature of the verbal description. However, it is abstract, and it does not resemble English or any other natural language. Your brain can then use this verbal description to generate a visual image (Kosslyn et al., 2006; Reed, 2010). According to the propositional perspective, mental images are stored in an abstract, language-like form that does not physically resemble the original stimulus. Zenon Pylyshyn (2003, 2004, 2006) has been the strongest supporter of this perspective. Pylyshyn agrees that people do experience mental images. Pyly- shyn notes, however, that these images are not a necessary, central component of imagery. He argues that it would be awkward—and perhaps even unworkable—to store information in terms of mental images. For instance, people would need a huge space to store all the images that they claim to have. Pylyshyn (2004, 2006) also emphasizes the differences between perceptual experiences and mental images. For example, you can re-examine and reinterpret a real photograph. Mental images are less likely to be so stable and easy to re-reference over time. Teasing apart these two perspectives on the representational format of mental imagery is quite difficult. Shepard and Metzler’s ground-breaking work on mental rotation, discussed above, supports an analog perspective. In general, the research on rotating geometric figures provides some of the strongest support for the analog-coding approach. We seem to treat mental images the same way we treat physical objects when we rotate them through space. In both cases, it takes longer to perform a large mental rotation than a small one, suggesting that you were considering, and thus activating, visual properties of the objects. In contrast, a propositional code would predict similar reaction times for these two conditions; the language- like description for the figure would not vary with the amount of rotation (Howes, 2007). Neuroimaging research also provides a great deal of evidence in favor of the analog perspective. For example, the primary visual cortex is activated when people work on tasks that require detailed visual imagery (Ganis et al., 2009). This is the same part of the cortex that is active when we perceive actual visual objects. Furthermore, researchers have studied people who have prosopagnosia. People with prosopagnosia cannot recognize human faces visually, though they perceive other objects relatively nor- mally (Farah, 2004). These individuals also have comparable problems in creating visual imagery for faces (Ganis et al., 2009). Surveying a large number of studies, Kosslyn and his colleagues (2010) conclude that visual imagery activates between about 70% and 90% of the same brain regions that are activated during visual percep- tion. For instance, when people have brain damage in the most basic region of the visual cortex, they have parallel problems in both their visual perception and their visual imagery. Furthermore, some individu- als with brain damage cannot distinguish between (1) the colors registered during visual perception and (2) the visual imagery created in a mental image. Additionally, as previously noted, people who have prosopagnosia cannot recognize human faces visu- ally, though they perceive other objects relatively normally. The research shows that these individuals also cannot use mental imagery to distinguish between faces (Kosslyn et al., 2010). Thus, behavioral and cognitive neuroscientific data support the notion that mental imagery is repre- sented in an analog format. There is at least one phenomenon, however, that is difficult for the analog account to accommodate—the effect of ambiguous visual images. We discuss this effect below, and pro- vide an explanation for why a propositional account may be more applicable under certain circumstances. Visual Imagery and Ambiguous Figures Before you read further, try Demonstration 7.2, and note whether you were able to reinterpret the figure. Most people have difficulty with tasks like this. In the 1970s, Stephen Reed was concerned that mental imagery might have some limitations (Reed, 1974, 2010). Perhaps language helps us to store visual stimuli on some occasions. Reed’s 1974 study tested people’s ability to decide whether a specific visual pattern was a portion of a design that they had seen earlier. Specifically, Reed presented a series of paired figures. For example, people might first see a pattern like the Star of David in Demonstration 7.2, and then this figure disappeared. Next, after a brief delay, people saw a second pattern, such as a parallelogram with slanted right and left sides. In half of the  Classical Research on Visual Imagery 141 Demonstration 7.2 Imagery and an Ambiguous Figure Look at the figure below, and form a clear mental image of the figure. Then turn to the paragraph labeled “Further instructions for Demonstration 7.2” at the bottom of Demonstration 7.3. trials, the second pattern was truly part of the first one (for example, a parallelogram). In the other half, it was not (for example, a rectangle). Suppose that people actually do store mental images in their head that correspond to the physical objects they have seen. Then they should be able to draw forth that mental image of the star and quickly discover the parallelogram shape hidden within it. However, the participants in Reed’s (1974) study were correct only 14% of the time on the star/parallelogram example. Across all stimuli, they were correct only 55% of the time, hardly better than chance. Reed (1974) argued that people could not have stored a visual image for figures like the Star of David, given the high error rate on items like this one. Instead, Reed proposed that people sometimes store pic- tures as descriptions, using the kind of propositional code discussed above. For example, suppose that you stored the description in Demonstration 7.2 as a verbal code, “two triangles, one pointing up and the other pointing down, placed on top of each other.” When the instructions asked you whether the figure contained a parallelogram, you may have searched through your verbal description. Your search would locate only triangles, not parallelograms. Notice that Reed’s (1974) research supports the verbal propositional-code approach, rather than the analog-code approach. Similar research explored whether people could provide reinterpretations for a mental image of an ambiguous figure. For example, you can interpret the ambiguous stimulus in Figure 7.2 in two ways: a rabbit facing to the right or a duck facing to the left. Chambers and Reisberg (1985) asked participants to create a clear mental image of this figure. Next, the researchers removed the figure. The participants were then asked to give a second, different interpretation of that particular figure. None of the 15 people could do so. In other words, they apparently could not consult a stored mental image. Next, the participants were asked to draw the figure from memory. Could they reinterpret this physical stimulus? All of them looked at the figure they had just drawn, and all 15 were able to supply a second interpretation. Chambers and Reisberg’s research suggests that a strong verbal propositional code—such as “a duck that is facing left”—can overshadow a relatively weak analog code. Other similar research has replicated these findings. It’s often easy to reverse a visual stimulus while you are looking at a physical picture that is ambiguous. In contrast, it’s usually more difficult to reverse a mental image (Reisberg & Heuer, 2005). Now try Demonstration 7.3 before you read further. FIGURE 7.2 An example of an ambiguous figure from chambers and reisberg’s study. 142 MENTAL IMAGERY AND COGNITIVE MAPS Demonstration 7.3 Reinterpreting Ambiguous Stimuli Imagine the capital letter H. Now imagine the capital letter X super- (Further instructions for Demonstration 7.2: Without glancing back imposed directly on top of the H, so that the four corners of each at the figure in Demonstration 7.2, consult your mental image. Does letter match up exactly. From this mental image, what new shapes that mental image contain a parallelogram?) and objects do you see in your mind’s eye? It seems likely that people often use an analog code when they are thinking about fairly simple figures (like the two hands of a clock). In contrast, people may use a propositional code when the figures are more complex, as in the case of the research by Reed (1974) and Chambers and Reisberg (1985). As Kosslyn and his coauthors (2006) point out, our memory has a limited capacity for visual imagery. We may therefore have difficulty storing complex visual information in an analog code and then making accurate judgments about these mental images. Verbal labels (and a propositional code) may be especially helpful if the visual stimulus is complex. For example, when I work on a jigsaw puzzle, I often find that I’ve attached a verbal label—such as “angel with outstretched wings”—to aid my search for a missing piece. In the case of these complex shapes, stor- age may be mostly propositional. In other research, Finke and his colleagues (1989) asked people to combine two mental images, as in Demonstration 7.3. The participants in this study could indeed create new interpretations for these ambigu- ous stimuli. In addition to a combined X and H figure, they reported some new geometric shapes (such as a right triangle), some new letters (such as M), and some objects (such as a bow tie). Other research confirms that observers can locate similar, unanticipated shapes in their mental images (Brandimonte & Gerbino, 1996; Kosslyn et al., 2006; Rouw et al., 1997). Individual differences in mental imagery There has long existed a recognition that individuals may differ in the degree to which they rely on mental imagery or verbal descriptions during cognitive processing. Individuals who report the experience of constructing strong mental images are referred to as visualizers. Other individuals, often referred to as verbalizers, rely less on mental images and more on verbal descriptions (Paivio & Harshman, 1983; Riding & Douglas, 1993). These different cognitive styles do not represent discrete categories of individuals who only process information one way or the other. Instead, they represent biases that individuals have regarding the types of representations that tend to be activated during cognitive processing. Individuals can self-report the experience of mental imagery, although self-report measures do not provide reliable insight into the types of processes that are engaged as the individual thinks. Cognitive neuroscientific techniques, on the other hand, may be able to shed light on whether individuals that self- report larger amounts of mental imagery are indeed more likely to activate portions of visual cortex than their verbalizing counterparts. Nishimura and colleagues (2016) utilized the magnetoencephalography (MEG) technique in order to investigate this question. As discussed in Chapter 1, MEG is a cognitive neuroscientific testing method in which stimulus-evoked neuronal activity is recorded via sensors placed on the scalp. The sensors pick up on fluctuations in the magnetic fields produced by neural activity. Moreover, the robust nature of the magnetic field signal allows researchers to make reasonable inferences about where in the brain a sensor- detected signal was generated. In their experiment, Nishimura and colleagues administered a scale designed to determine whether an individual has a more visualizer or verbalizer cognitive style. Neural responses were recorded as partici- pants were asked to visualize objects, such as a famous landmark in the Japanese city of Kyoto, where this experiment was conducted. As hypothesized, visualizers produced more activity in occipital regions of cortex, regions that are strongly implicated in processing visual information. Verbalizers, on the other hand, produced more activation in areas often associated with linguistic processing, such as frontal cortical areas. This observation is consistent with the notion that different types of representations can be engaged by different individuals during imagery tasks.  Factors That Influence Visual Imagery 143 Summary In summary, the controversy about analog versus propositional coding is difficult to resolve. As with any big debate in cognitive psychology, there are currently no clear-cut winners (if there were, there wouldn’t be any debate in the first place). The analog code apparently explains most stimuli and most tasks. And, generally speaking, the majority of people who conduct research on visual imagery support the analog position, perhaps partly because they personally experience vivid, picture-like images (Reisberg et al., 2003). Like most controversies in psychology, both the analog and the propositional approaches are prob- ably at least partially correct, depending on the specific task. The research on ambiguous figures shows that people can create mental images using both propositional and analog codes. That is, we often use analog codes to provide picture-like representations that capture our mental images. However, when the stimuli or situations make it difficult to use analog codes, we may create a verbal representation, using a propositional code. Furthermore, some evidence exists that individual differences in cognitive style may partially determine the types of representations active during imagery. People who report greater degrees of visual imagery appear to activate visual cortex more so than do individuals who report reliance on ver- bal descriptions while thinking. Factors That Influence Visual Imagery As we have seen, the first systematic research on imagery demonstrated the similarity between rotating mental images and rotating physical objects. Researchers soon began to examine other attributes of mental images, such as the distance between two points and the shape of the mental image. In this section, we focus on a number of factors that have been shown to influence speed and accuracy on mental rotation and other visual imagery tasks. We conclude this section by addressing a controversial topic in cognitive psychology—namely, whether or not males and females differ in their spatial reasoning and other cogni- tive abilities. Distance and Shape Effects on Visual Imagery A classic study by Kosslyn and his colleagues (1978) showed that people took a long time to scan the distance between two widely separated points on a mental image of a map that they had created. In con- trast, they quickly scanned the distance between two nearby points on a mental image of that map. Later research confirms that there is a linear relationship between the distance to be scanned in a mental image and the amount of time required to scan this distance (Borst & Kosslyn, 2008; Denis & Kosslyn, 1999; Kosslyn et al., 2006). Consider, for example, another classic study on visual imagery. Allan Paivio (1978) asked participants to make judgments about the angle formed by the two hands on an imaginary clock. For instance, try to visualize the two hands on a standard, nondigital clock. Next, create a visual image of the angle formed by the two hands if the time were 3:20. Now create a visual image of the angle between the two hands if the time were 7:25. Which of these two “mental clocks” has the smaller angle between the two hands? Paivio also gave the participants several standardized tests to assess their visual-imagery ability (simi- lar to the one discussed above in relation to individual differences in cognitive style). As you can see in Figure 7.3, the high-imagery participants made decisions much more quickly than the low-imagery participants. As Figure 7.3 also shows, participants in both groups made decisions very slowly when they compared the angle formed by the hands at 3:20 with the angle of the hands at 7:25. After all, these two angles are quite similar. In contrast, their decisions were relatively fast if the two angles were very different in size, perhaps 3:20 and 7:05. Think about the implications of this study. With real objects, people take a long time to make decisions when two angles are very similar to each other. When the two angles are very different, people respond quickly. The research demonstrates that people show the same pattern with their visual images. According to Paivio (1978), this study demonstrates strong support for the proposal that people use analog codes, rather than propositional codes. Additional support for analog codes comes from research with visual images that represent more com- plex shapes. Shepard and Chipman (1970) asked participants to construct mental images of the shapes of various U.S. states, such as Colorado and Oregon. Then the participants judged the similarity between the 144 MENTAL IMAGERY AND COGNITIVE MAPS 7.0 Reaction time (in seconds) 6.6 FIGURE 7.3 The influence of angle 6.2 difference on reaction Low imagery time for high-imagery 5.8 and low-imagery people. 5.4 Source: Paivio, A. (1978). High imagery Comparison of mental 5.0 clocks. Journal of Experimental Psychology: 30° 60° 90° 120° Human Perception and Performance, 4, 61–71. Difference between the two angles two mental images, with respect to their shapes. For example—without looking at a map—do you think that Colorado and Oregon have similar shapes? How about Colorado and West Virginia? These same participants also made shape-similarity judgments about pairs of states while they looked at an actual physical sketch of each state (rather than only its name). The results showed that the participants’ judgments were highly similar in the two conditions. Once again, people’s judgments about the shape of mental images are similar to their judgments about the shape of physical stimuli. Let’s review our conclusions about the characteristics of visual images, based on the research we have discussed so far: 1. When people rotate a visual image, a large rotation takes them longer, just as they take longer when making a large rotation with a physical stimulus. 2. People make distance judgments in a similar fashion for visual images and for physical stimuli. 3. People make decisions about shape in a similar fashion for visual images and for physical stimuli. This conclusion holds true for both simple shapes (angles formed by hands on a clock) and complex shapes (geographic regions, like Colorado or West Virginia). Visual Imagery and Interference Many studies show that your mental image can interfere with an actual physical image (e.g., Baddeley & Andrade, 1998; Craver-Lemley & Reeves, 1992; Kosslyn et al., 2006; Richardson, 1999). Let’s examine the research related to interference, specifically focusing on visual imagery. Think about a friend whom you have seen in the last day or two. Next, create a clear mental image of this friend’s face. Keep this mental image in mind, and simultaneously let your eyes wander over this page. You will probably find that the task is difficult, because you are trying to “look” at your friend (in a visual image) at the same time that you are trying to look at the words on this page (a physical stimulus). Research has confirmed that visual imagery can interfere with your visual perception. Consider a classic study about interference, conducted by Segal and Fusella (1970). In part of this study, they asked participants to create a visual image, for example, a visual image of a tree. As soon as the participant had formed the requested image, the researchers presented a real physical stimulus, for example a small blue arrow. The researchers then measured the participants’ ability to detect the physical stimulus. Segal and Fusella’s (1970) results showed that people had more problems detecting the physical stimulus when the mental image was in the same sensory mode. For example, when the participants had been imagining the shape of a tree, they had trouble detecting the small blue arrow. The mental image interfered with the real visual stimulus. In contrast, when they had been imagining the sound of an oboe, they had no trouble reporting that they saw the arrow. After all, the imagined sound and the arrow—a visual stimulus—represented two different sensory modes. In another study on visual interference, Mast and his colleagues (1999) told participants to create a visual image of a set of narrow parallel lines. Next, they were instructed to rotate their mental image of  Factors That Influence Visual Imagery 145 this set of lines, so that the lines were in a diagonal orientation. Meanwhile, the researchers presented a physical stimulus, a small segment of a line. The participants were told to judge whether this line seg- ment had an exactly vertical orientation. The results showed that the imagined set of lines and the real set of lines produced similar distortions in the participants’ judgments about the orientation of that line segment. Visual Imagery and Other Vision-Like Processes So far, we have examined a variety of characteristics related to visual imagery. Let’s briefly consider another less-obvious characteristic of visual perception. We’ll see that a relatively unknown visual charac- teristic has a mental-imagery counterpart. Research in visual perception shows that people can see a visual target more accurately if the target is presented with vertical lines on each side of this target. Research by Ishai and Sagi (1995) shows that mental imagery produces the same masking effect. That is, people can see a visual target more accurately if they create mental images of vertical lines on each side of the target. This study on the masking effect is especially important because of a research-methods issue called “demand characteristics.” Demand characteristics are all the cues that might convey the experimenter’s hypothesis to the participant. Some critics of the analog approach have proposed that the experimental results in imagery experiments might be traceable to one or more of these demand characteristics (Pylyshyn, 2003, 2006). For example, participants may be able to guess the results that the experimenter wants. Perhaps they might guess that a visual mental image is supposed to interfere with visual perception. The masking effect, however, is virtually unknown to people who have not completed a psychology course in perception. The participants in the study by Ishai and Sagi (1995) would not know that visual targets are especially easy to see if they are surrounded by masking stimuli. Therefore, demand character- istics cannot account for the masking effect with mental images. As a result, we can be more confident that visual imagery really can produce the masking effect, just as visual perception can produce the masking effect. Visual imagery can indeed resemble visual perception. Researchers have also examined whether mental imagery resembles visual perception in other respects. For example, people have especially good acuity for mental images that are visualized in the center of the retina, rather than in the periphery; visual perception operates the same way (Kosslyn, 1983). Other studies demonstrate additional parallels between mental images and visual perception (Kosslyn, 2001; Kosslyn & Thompson, 2000; Kosslyn et al., 2006). Gender Comparisons in Spatial Ability When psychologists conduct research about individual differences in cognition, one of the most popular topics is gender comparisons. Talk-show hosts, politicians—and even university presidents—feel free to speculate about gender differences. However, they rarely consult the extensive psychology research about gender comparisons. As a result, they rarely learn that most gender differences in cognitive abilities are small (Hyde, 2005; Matlin, 2012; Yoder, 2007). Researchers have conducted literally hundreds of studies on gender comparisons in cognitive abilities. If we want to understand gender comparisons in spatial ability, for example, we cannot focus on just one study. When the research on a topic is abundant, psychologists often use a statistical technique called a meta-analysis. Meta-analysis is a statistical method for combining numerous studies on a single topic. Researchers begin by locating all appropriate studies on a topic such as gender comparisons in verbal abil- ity. Then they perform a meta-analysis that combines the results of all these studies. A meta-analysis yields a number called effect size, or d. For example, suppose that researchers conduct a meta-analysis of 18 studies about gender comparisons in reading comprehension scores. Furthermore, suppose that—on each of the 18 studies—females and males receive very similar scores. In this case, the d would be close to zero. Psychologists have conducted numerous meta-analyses on cognitive gender comparisons. Janet Hyde (2005) wrote an important article that summarized all of these previous meta-analyses. Table 7.1 shows a tally of the effect sizes for the meta-analyses that have been conducted in three major areas of cognitive ability. 146 MENTAL IMAGERY AND COGNITIVE MAPS Table 7.1 The Distribution of Effect Sizes (d) Reported in Meta-Analyses for Three Kinds of Cognitive Skills Magnitude of Effect Size Close to Zero Small Moderate Large (d < 0.10) (d = 0.11 to 0.35) (d = 0.36 to 0.65) (d = 0.66 to 1.00) Verbal Ability 4 1 0 0 Mathematics 4 0 0 0 Spatial Ability 0 4 3 1 Source: Based on Hyde (2005). As you can see in Table 7.1, four meta-analyses on verbal ability showed extremely small gender dif- ferences, with d values close to zero. One additional meta-analysis produced a d value considered to be “small,” and no meta-analyses yielded a d value considered to be either moderate or large. In other words, these studies show gender similarities in verbal ability. You can also see that all four meta-analyses on mathematics ability produced d values that are close to zero, once more showing gender similarities. These gender similarities in math ability are extremely important, especially because the headlines in the media usually claim that males are much better than females in their math skills (Hyde, 2005; Matlin, 2012). These math comparisons are consistent with an international study that focused on eighth-grade students in 34 different countries. Interestingly, the boys’ average was higher than the girls’ average in 16 countries, the girls’ average was higher than boys’ average in 16 countries, and girls and boys had the same averages in two countries (National Center for Education Statistics, 2004). Let’s now consider spatial ability, the topic related to our current discussion. Here, the gender differences are more substantial. Notice, however, that only one meta-analysis yielded a d value in the “large” category. An important point is that spatial ability represents several different skills; it is not unitary (Caplan & Caplan, 2009; Chipman, 2004; Tversky, 2005b). One skill is spatial visualization. A typical task would be to ask people to look at a sketch of a busy street to find hidden drawings of human faces. Gender differ- ences in spatial visualization are small, according to Hyde’s (2005) summary of meta-analyses. The second component of spatial ability is spatial perception. A typical task would be sitting in a dark room and adjusting an illuminated rod so that it is in an exactly vertical position. The two meta-analyses that specifically focused on spatial perception both produced d values of 0.44, a moderate gender differ- ence (Hyde, 2005). The third component of spatial ability is mental rotation. As you know from Demonstration 7.1, a typical task would be to look at two geometric figures and then decide whether they would be identical if you rotated one of the figures. Males are more likely than females to respond quickly on this task. The two meta-analyses that specifically focused on mental rotation produced d values of 0.56 and 0.73 (Hyde, 2005). For the sake of comparison, however, consider the gender differences in people’s height. For height, the d is a substantial 2.0. In other words, mental rotation is the only cognitive skill where a group of males is likely to earn higher scores than a group of females. However, we must emphasize that some studies report no gender differ- ences in mental rotation. Furthermore, some studies report that the gender differences disappear when the task instructions are changed and when people receive training on spatial skills (Matlin, 2012; Newcombe, 2006; Terlecki et al., 2008). In addition, a large portion of the gender differences in spatial rotation can be traced to the fact that boys typically have more experience with toys and sports (and perhaps even video games) that emphasize spa- tial skills (Voyer et al., 2000). In other words, this one area of cognitive gender differences can be reduced by providing girls with experience and training in spatial activities. Auditory Imagery Most research on the topic of mental imagery has tended to focus heavily on visual imagery, and it turns out that people tend to report more visual imagery than other types of mental imagery. Stephen Kosslyn and his coauthors (1990), for example, asked students to keep diaries about their mental imagery. They  Auditory Imagery 147 reported that about two-thirds of their images were visual. In contrast, images for hearing, touch, taste, and smell were much less common. Psychologists show a similar lopsidedness in their research preferences. Most of the research focuses on visual imagery, though the research on auditory imagery has increased during the last decade. In contrast, psychologists rarely investigate smell, taste, or touch imagery. As we noted at the beginning of this chapter, auditory imagery is our mental representation of sounds when these sounds are not physically present. For example, can you create a vivid auditory image of a close friend’s laughter? Can you create a vivid auditory image for the first few bars of a favorite song? What other categories of auditory images can you create in your “mind’s ear”? We can typically identify a variety of “environmental sounds,” even though we might not use that par- ticular term. For example, can you create an auditory image of the whining sound made by an almost-dead car battery? In addition, we typically have auditory imagery for the distinctive noises made by a variety of animals (Wu et al., 2006). This section on auditory imagery provides an introduction to the topic. Psychologists have lamented the relative lack of research on auditory imagery (e.g., Kosslyn et al., 2010; Vuvan & Schmuckler, 2011). For example, Timothy Hubbard (2010) reviewed the research on the topic. The first paragraph of Hubbard’s article begins, “Despite the resurgence in imagery research begin- ning in the late 1960s and early 1970s, auditory forms of imagery have received relatively little interest” (p. 302). Hubbard also discovered that some previous articles had claimed that they had found evidence of auditory imagery, but the evidence was not convincing. As you know from the studies on visual imagery, the research methods need to be carefully designed to demonstrate clear-cut evidence of mental imagery. Is auditory imagery less vivid than visual imagery? Rubin and Berentsen (2009) asked people in the United States and Denmark to recall an event from their life and rate its vividness. In both countries, peo- ple reported higher imagery ratings for visual imagery than for auditory imagery. Even so, the relative lack of research on auditory imagery is puzzling. Researchers have explored some characteristics of auditory imagery such as loudness (e.g., Hubbard, 2010; Vuvan & Schmuckler, 2011). In this section, we will briefly consider two topics that have clear implications for mental imagery: (1) auditory imagery and pitch and (2) auditory imagery and timbre. Auditory Imagery and Pitch One prominent feature of auditory imagery is pitch. Pitch is a characteristic of a sound stimulus that can be arranged on a scale from low to high (Foley & Matlin, 2010; Plack & Oxenham, 2005). One of the classic studies on pitch was conducted by Margaret J. Intons-Peterson, who was one of the creators of the impor- tant Brown/Peterson & Peterson technique for assessing short-term memory. (See Chapter 4.) Intons- Peterson and her coauthors (1992) examined how quickly people could “travel” the distance between two auditory stimuli that differ in pitch. For example, Intons-Peterson and her colleagues asked students to create an auditory image of a cat purring. Then they asked the students to “travel” from the cat-purring image to an image with a slightly higher pitch, such as a slamming door. The participants pressed a button when they reached this slightly higher pitch. The results showed that the students needed about 4 seconds to travel that relatively short auditory distance. The researchers also asked students to “travel” longer auditory distances, for example, from a cat purr- ing to the sound of a police siren. The participants needed about 6 seconds to travel this relatively long dis- tance. In the case of pitch, the distance between the two actual tones is indeed correlated with the distance between the two imagined tones. Auditory Imagery and Timbre Another important characteristic of a sound is called “timbre” (pronounced “tam-ber”). Timbre describes the sound quality of a tone. For example, imagine a familiar tune—such as Happy Birthday—played on the flute. Now contrast that sound quality with the same song played on a trumpet. Even when the two versions of this song have the same pitch, the flute tune seems relatively pure. Consider a study by Andrea Halpern and her coauthors (2004), which focused on people’s auditory imagery for the timbre of musical instruments. These researchers studied young adults who had completed at least 5 years of formal training in music. This requirement was necessary so that the participants would be familiar with the timbre of eight musical instruments, such as the basoon, flute, trumpet, and violin. Each participant first listened to the sound of every instrument, until he or she could name them all easily. 148 MENTAL IMAGERY AND COGNITIVE MAPS To assess auditory imagery for timbre, Halpern and her colleagues asked each participant to rate the similarity of timbres in two conditions. In the perception condition, the participants listened to a 1.5-second segment of one musical instrument, followed by a 1.5-second segment of another instrument. They heard all possible pairings of the eight different instruments. For every pair, the participants rated the similarity of the two perceptual stimuli. In the imagined condition, the participants heard the names of the instruments, rather than their sounds. They heard all possible pairings of the eight names for the different instruments. The results showed that the ratings for timbre perception and for timbre imagery were highly correlated with each other r.84. In other words, the participants showed that their cognitive representation for the timbre of an actual musical instrument is quite similar to the cognitive representation for the timbre of an imagined musical instrument. Clearly, researchers with an interest in imagery can explore many new topics that compare the relationship between auditory perception and auditory imagery. Cognitive Maps Have you had an experience like this? You’ve just arrived in a new environment, perhaps for your first year of college. You ask for directions, let’s say, to the library. You hear the reply, “OK, it’s simple. You go up the hill, staying to the right of the Northumbria Building. Then you take a left, and Meliora Hall will be on your right. The library will be over on your left.” You struggle to recall some landmarks from the orientation tour. Was Seashore Hall next to Uris Hall, or was it over near Johnson Hall? Valiantly, you try to incorporate this new information into your discouragingly hazy mental map. So far, this chapter has examined the general characteristics of mental images. This discussion primar- ily focused on a theoretical issue that has intrigued cognitive psychologists: Do our visual and auditory mental images resemble our perception of actual visual and auditory stimuli? Now we consider cognitive maps, a topic that is clearly related to mental imagery. However, the research on cognitive maps focuses on the way we represent geographic space. More specifically, a cognitive map is a mental representation of geographic information, including the environment that surrounds us (Shelton & Yamamoto, 2009; Wagner, 2006). Notice, then, that the first two sections of this chapter emphasize our mental representations of sights and sounds. In contrast, this third section emphasizes our mental images of the relationships among objects, such as buildings on your college campus. Let’s discuss some background about cognitive maps, and then we’ll see how distance, shape, and rela- tive position are represented in these cognitive maps. We’ll conclude this chapter by examining how we create mental maps from verbal descriptions. Try to picture a home that you know quite well. Now picture yourself walking through this home. Does your cognitive map seem fairly accurate, or is this map somewhat fuzzy about the specific size and location of a room? A cognitive map can also represent larger geographic areas, such as a neighbor- hood, a city, or a country. In general, our cognitive maps represent areas that are too large to be seen in a single glance (Bower, 2008; Poirel et al., 2010; Wagner, 2006). As a result, we create a cognitive map by integrating the information that we have acquired from many successive views (Shelton, 2004; Spence & Feng, 2010). In general, the research on cognitive maps emphasizes real-world settings, as well as high ecological validity. Research on cognitive maps is part of a larger topic called spatial cognition. Spatial cognition primarily refers to three cognitive activities: (1) our thoughts about cognitive maps; (2) how we remember the world we navigate; and (3) how we keep track of objects in a spatial array (Shelton, 2004; Spence & Feng, 2010). Furthermore, spatial cognition is interdisciplinary in its scope. For example, computer scientists create models of spatial knowledge. Linguists analyze how people talk about spatial arrangements. Anthropologists study how different cultures use different frameworks to describe locations. Geographers examine all of these dimensions, with the goal of creating efficient maps. The topic is also relevant when architects design build- ings and when urban planners construct new communities (Devlin, 2001; Tversky, 1999, 2000b). In addition to theoretical issues related to spatial cognition, psychologists study applied topics. These include topics related to entertainment, such as video games (Spence & Feng, 2010). They also study life-and-death topics such as the communication of spatial information between air traffic controllers and airplane flight crews (Barshi & Healy, 2011; Schneider et al., 2011). As you might expect, individual differences in spatial-cognition skills are quite large (Shelton & McNamara, 2004; Smith & Cohen, 2008; Wagner, 2006). However, people tend to be accurate in judging  Cognitive Maps 149 their ability to find their way to unfamiliar locations (Kitchin & Blades, 2002). In other words, your metacognition about your spatial ability may be reasonably correct. Furthermore, these individual differences in spatial cognition are correlated with people’s scores on tests of the visuospatial sketchpad (Gyselinck & Meneghetti, 2011). Spatial-cognition scores are also correlated with performance on the spatial tasks that we discussed in the first section of this chapter (Newcombe, 2010; Sholl et al., 2006). For example, people who are good at mental rotation are more skilled than others in using maps to find a particular location (Fields & Shelton, 2006; Shelton & Gabrieli, 2004). Fortunately, people with poor spatial skills can improve their performance. Suppose that you are visit- ing an unfamiliar college campus (Smith & Cohen, 2008). You park your car, and you set out to find a specific building. You’ll increase your chances of finding your way back to your car if you periodically turn around and study the scene you’ll see on your return trip (Heth et al., 2002; Montello, 2005). As you might expect, it’s also important to notice specific landmarks along this route (Ruddle et al., 2011). These strategies should improve the accuracy of your cognitive maps. Try Demonstration 7.4 before you read further. This demonstration is based on research by Roskos- Ewoldsen and her colleagues (1998), which we will discuss shortly. Our cognitive maps typically include survey knowledge, which is the relationship among locations that we acquire by directly learning a map or by repeatedly exploring an environment. Now look back at Dem- onstration 7.4. Which of the two tasks was easier? Your cognitive map will be easier to judge and more accurate if you acquire spatial information from a physical map that is oriented in the same direction that you are facing in your cognitive map. In Question 1 of this demonstration, your mental map and the physical map have the same orientation, so this task should be relatively easy. In contrast, you need to perform a mental rotation in order to answer Question 2, so this task is more difficult. Research confirms that judgments are easier when your mental map and the physical map have matching orientations (Devlin, 2001; Montello, 2005; Montello et al., 2004). Now we will consider how our cognitive maps represent three geographic attributes: distance, shape, and relative position. Theme 2 of this book states that our cognitive processes are generally accurate. This generalization also applies to cognitive maps. In fact, our mental representations of the environment usu- ally reflect reality with reasonable accuracy, whether these cognitive maps depict college campuses or larger geographic regions. According to Theme 2, however, when people do make cognitive mistakes, these mistakes can often be traced to a rational strategy. The mistakes that people display in their cognitive maps usually “make sense” because they are systematic distortions of reality (Devlin, 2001; Koriat 2000; Tversky, 2000b). These mistakes reflect a tendency to base our judgments on variables that are usually relevant. They also reflect a tendency to judge our environment as being more well organized and orderly than it really is. At this point, we need to introduce a useful term in cognitive psychology, called a “heuristic.” A heuristic (pronounced “hyoo-riss-tick”) is a general problem-solving strategy that usually produces a correct solution... but not always. As you will see, people often use heuristics in making judgments about cognitive maps. As a result, they tend to show systematic distortions in distance, shape, and relative position. Demonstration 7.4 Learning from a Map Study the diagram at the bottom of this demonstration for about 30 seconds, and then cover it completely. Now answer the following 1 questions: 4 1. Imagine that you are standing at Position 3, facing Position 4. Point to Position 1. 2. Now, glance quickly at the diagram and then cover it com- 2 3 pletely. Imagine that you are now standing at Position 1, facing Position 2. Point to Position 4. 150 MENTAL IMAGERY AND COGNITIVE MAPS Distance and Shape Effects on Cognitive Maps How far is it from your college library to the classroom in which your cognitive psychology course is taught? How many miles separate the place where you were born from the college or university where you are now studying? People’s distance estimates are often distorted by factors such as (1) the number of intervening cities, (2) category membership, and (3) whether their destination is a landmark. Distance Estimates and Number of Intervening Cities In one of the first systematic studies about distance in cognitive maps, Thorndyke (1981) constructed a map of a hypothetical geographic region with cities distributed throughout the map. Between any two cit- ies on the map, there were 0, 1, 2, or 3 other cities along the route. Participants studied the map until they could accurately reconstruct it. Then they estimated the distance between specified pairs of cities. The number of intervening cities had a clear-cut influence on their estimates. For example, when the cities were really 300 miles apart on this map, people estimated that they were only 280 miles apart when there were no intervening cities. In contrast, these target cities were estimated to be 350 miles apart with three intervening cities. Notice that this error is consistent with the concept of heuristics. If cities are ran- domly distributed throughout a region, two cities are usually closer together when there are no intervening cities between them. In contrast, two cities are likely to be further apart when there are three intervening cities. Distance Estimates and Category Membership Research shows that the categories we create can have a large influence on our distance estimates. For example, Hirtle and Mascolo (1986) showed participants a hypothetical map of a town, and they learned the locations on the map. Then the map was removed, and people estimated the distance between pairs of locations. The results showed that people tended to shift each location closer to other sites that belonged to the same category. For example, people typically remembered the courthouse as being close to the police station and other government buildings. However, these shifts did not occur for members of different cat- egories. For instance, people did not move the courthouse closer to the golf course. People show a similar distortion when they estimate large-scale distances (Tversky, 2009). For instance, Friedman and her colleagues asked college students to estimate the distance between various North Ameri- can cities (Friedman et al., 2005; Friedman & Montello, 2006). Students from Canada, the United States, and Mexico judged that distances were greater when they were separated by an international border. Spe- cifically, they judged two cities to be an average of only 1,225 miles from each other if the cities were located in the same country. In contrast, they judged two cities to be an average of 1,579 miles from each other if they were located in different countries. In other words, the estimated difference was 354 miles when the cities were separated by an interna- tional border. In reality, however, the actual difference was only 63 miles (Friedman & Montello, 2006). Students make a similar error when they estimate distances on their own college campus, and there is an invisible border between two parts of the campus (Uttal et al., 2010; Wagner, 2006). They are reluctant to say that two buildings could be near each other if they are on different sides of that invisible border. According to a phenomenon called border bias, people estimate that the distance between two specific locations is larger if they are on different sides of a geographic border, compared to two locations on the same side of that border. Border bias can have far-reaching consequences. For example, Arul Mishra and Himanshu Mishra (2010) asked participants to imagine that they were thinking about buying a vacation home in the mountains, and their final choices were currently in either Oregon or Washington. While they were deciding, one group was told that an earthquake had hit Wells, Oregon, in a location 200 miles from both of these vacation homes. Another group received identical instructions, except that the earthquake had hit Wells, Washington. A third group (the control group) received the same initial instructions, but no earthquake was mentioned. Figure 7.4 shows the results. Even though the epicenter of the earthquake was the same distance from both vacation homes, the participants in the “Oregon earthquake group” were 20% more likely than the control group to choose a Washington home. Similarly, the participants in the “Washington earthquake group” were 25% more likely than the control group to choose an Oregon home. Notice that this study demonstrates a “same-category heuristic.” It’s generally a good strategy to guess that two cities are closer together if they are in the same state, rather than in adjacent states.  Cognitive Maps 151 Vacation Home in Washington 90 Vacation Home in Oregon FIGURE 7.4 An 80 76.60 example of border bias: percentage of partic- 70 68.50 ipants choosing each vacation home, as a 60 56.60 function of which state had experienced an Choice (%) 50 earthquake. 43.40 When people hear about an 40 earthquake, they prefer to 31.50 select a home in a different state, rather than a home 30 23.40 that is equally close, but in the same state (Mishra & 20 Mishra, 2010). Source: Mishra, A., & Mishra, H. (2010). Border 10 bias: The belief that state borders can protect against 0 disasters. Psychological Control Earthquake in Oregon Earthquake in Science, 21, 1582–1586. Washington Copyright © 2010. Reprinted by permission of SAGE Condition Publications. Distance Estimates and Landmarks We have some friends who live in Rochester, the major city in our region of upstate New York. We some- times invite them to come down for a meeting in Geneseo, about 45 minutes away from Rochester. “But it’s so far away,” they complain. “Why don’t you come up here instead?” They are embarrassed when we point out that the distance from Geneseo to Rochester is exactly the same as the distance from Rochester to Geneseo! The research confirms the landmark effect, which is the general tendency to provide shorter esti- mates when traveling to a landmark—an important geographical location—rather than a nonlandmark (Shelton & Yamamoto, 2009; Tversky, 2005b, 2009; Wagner, 2006). For example, McNamara and Diwadkar (1997) asked students to memorize a map that displayed various pictures of objects. The map included some objects that were described as landmarks, and some objects that were not landmarks. After learning the locations, the students estimated the distance on the map (in inches) between various pairs of objects. Consistent with the landmark effect, these students showed an asymmetry in their distance estimates. In one study, for instance, students judged distances on an informal map (McNamara & Diwadkar, 1997). They estimated that the distance was an average of 1.7 inches when traveling from the landmark to the nonlandmark. However, the estimated distance was an average of only 1.4 inches when traveling from the nonlandmark to the landmark. Prominent destinations apparently seem closer than less-important destina- tions. This research also demonstrates the importance of context when we make decisions about distances and other features of our cognitive maps. Cognitive Maps and Shape Our cognitive maps represent not only distances but also shapes. These shapes are evident in map features such as the angles formed by intersecting streets. Once again, the research shows a systematic distortion. In this case, we tend to construct cognitive maps in which the shapes are more regular than they are in reality. Consider the classic research by Moar and Bower (1983), who studied people’s cognitive maps of Cambridge, England. All the participants in the study had lived in Cambridge for at least five years. Moar and Bower asked people to estimate the angles formed by the intersection of two streets, without using a map. The participants showed a clear tendency to “regularize” the angles so that they were more like 90-degree angles. For example, three intersections in Cambridge had “real” angles of 67, 63, and 50 degrees. How- ever, people estimated these same angles to be an average of 84, 78, and 88 degrees. As you may recall, 152 MENTAL IMAGERY AND COGNITIVE MAPS the sum of the angles in a triangle should be 180 degrees, but in this study, the sum of the estimated angles was 250 degrees. Furthermore, this study showed that seven of the nine angles were significantly biased in the direction of a 90-degree angle. What explains this systematic distortion? Moar and Bower (1983) suggest that we employ a heuristic. When two roads meet in most urban areas, they generally form a 90-degree angle. When people use the 90-degree-angle heuristic, they represent angles in a mental map as being closer to 90 degrees than they really are. You may recall a similar concept in the discussion of memory schemas in Chapter 5. It is easier to store a schematic version of an event, rather than a precise version of the event that includes all the trivial details. This 90-degree-angle heuristic has also been replicated in other settings (Montello et al., 2004; Tversky, 2005b; Wagner, 2006). Relative Position Effects on Cognitive Maps Which city is farther west—San Diego, California, or Reno, Nevada? If you are like most people—and the participants in a classic study by Stevens and Coupe (1978)—the question seems ludicrously easy. Of course, San Diego would be farther west, because California is west of Nevada. However, if you consult a map, you’ll discover that Reno is in fact west of San Diego. Which city is farther north—Detroit or its “twin city” across the river, Windsor, in Ontario, Canada? Again, the answer seems obvious; any Canadian city must be north of a U.S. city! Barbara Tversky (1981, 1998) points out that we use heuristics when we represent relative positions in our mental maps—just as we use heuristics to represent the angles of intersecting streets as being close to 90-degree angles, and just as we represent curves as being symmetrical. Tversky points out that these heuristics encourage two kinds of errors: 1. We remember a slightly tilted geographic structure as being either more vertical or more horizontal than it really is (the rotation heuristic). 2. We remember a series of geographic structures as being arranged in a straighter line than they really are (the alignment heuristic). The Rotation Heuristic According to the rotation heuristic, a figure that is slightly tilted will be remembered as being either more vertical or more horizontal than it really is (Taylor, 2005; Tversky, 2000b, 2009; Wagner, 2006). For example, Figure 7.5 shows that the coastline of California is obviously slanted. When we use the rotation heuristic for our cognitive map of California, we make the orientation more vertical by rotating the coast- line in a clockwise fashion. Therefore, if your cognitive map reflects the distorting effects of the rotation heuristic, you will conclude (erroneously) that San Diego is west of Reno. Similarly, the rotation heuristic encourages you to create a horizontal border between the United States and Canada. Therefore, you’ll make the wrong decision about Detroit and Windsor. In reality, Windsor, in Canada, is south of Detroit. Let’s look at some research on the rotation heuristic. Barbara Tversky (1981) studied people’s mental maps for the geographic region of the San Francisco Bay Area. She found that 69% of the students at a FIGURE 7.5 The correct locations of San Diego and Reno. Reno This figure shows that Reno is farther west than San Diego. According to [ San Francisco ] the rotation heuristic, however, we tend to rotate the coastline of California into a more nearly vertical San orientation. As a result, we Diego incorrectly conclude that San Diego is farther west than Reno.  Cognitive Maps 153 Bay Area university showed evidence of the rotation heuristic. When the students constructed their mental maps, they rotated the California coastline in a more north-south direction than is true on a geographically correct map. However, keep in mind that some students—in fact, 31% of them—were not influenced by this heuristic. We also have evidence for the rotation heuristic in other cultures. People living in Israel, Japan, and Italy also tend to mentally rotate geographic structures. As a result, these structures appear to have either a more vertical or a more horizontal orientation in a mental map than in reality (Glicksohn, 1994; Tversky et al., 1999). The Alignment Heuristic According to the alignment heuristic, a series of separate geographic structures will be remembered as being more lined up than they really are (Taylor, 2005; Tversky, 1981, 2000b; 2009). To test the alignment heuristic, Tversky (1981) presented pairs of cities to students, who were asked to select which member of each pair was north (or, in some cases, east). For example, one pair was Rome and Philadelphia. As Figure 7.6 shows, Rome is actually north of Philadelphia. However, because of the alignment heuristic, people tend to line up the United States and Europe so that they are along the same latitude. We know that Rome is in the southern part of Europe. We also know that Philadelphia is in the northern part of the United States. Therefore, we conclude— incorrectly—that Philadelphia is north of Rome. Tversky’s results indicated that many students showed a consistent tendency to use the alignment heu- ristic. For example, 78% judged Philadelphia to be north of Rome, and 12% judged that they were at the same latitude. Only 10% correctly answered that Rome is north of Philadelphia. On all eight pairs of items tested by Tversky, an average of 66% of participants supplied the incorrect answer. Other researchers have confirmed that people’s cognitive maps are especially likely to be biased when northern cities in North America are compared with southern cities in Europe (Friedman et al., 2002). The rotation heuristic and the alignment heuristic may initially sound similar. However, the rotation heuristic requires rotating a single coastline, country, building, or other figure in a clockwise or coun- terclockwise fashion so that its border is oriented in a nearly vertical or a nearly horizontal direction. In contrast, the alignment heuristic requires lining up several separate countries, buildings, or other figures in a straight row. Both heuristics are similar, however, because they encourage us to construct cognitive maps that are more orderly and schematic than geographic reality. The heuristics we have examined in this chapter make sense. For example, our city streets tend to have right-angle intersections. Furthermore, a picture is generally hung on a wall in a vertical orientation, rather than at a slant. In addition, a series of houses is typically lined up so that they are equally far from the street. However, when our mental maps rely too strongly on these heuristics, we miss the important details that make each stimulus unique. When our top-down cognitive processes are too active, we fail to pay enough attention to bottom-up information. In fact, the angle at an intersection may really be 70 degrees. Fur- thermore, that coastline may not run exactly north-south. In addition, those two continents are not really arranged in a neat horizontal line. FIGURE 7.6 The correct locations of Philadelphia and Rome. Rome This figure shows that Philadelphia Philadelphia is farther south than Rome. According to the alignment heuristic, however, we tend to line up Europe and the United States. As a result, we incorrectly conclude that Philadelphia is north of Rome. 154 MENTAL IMAGERY AND COGNITIVE MAPS Creating a Cognitive Map In everyday life, we often read or hear a description of a particular environment. For instance, a friend calls to give you directions to her house. You have never traveled there before, yet you create a cognitive map as you hear her describing the route. A cognitive map is a mental representation of geographic information, including the environment that surrounds us. Similarly, a neighbor describes the setting in which his car was hit by a truck, or you may read a mystery novel explaining where the dead body was found in relation to the broken vase and the butler’s fingerprints. In each case, you typically create a cognitive map. It’s important to emphasize that our cognitive maps are not perfect “map-in-the-head” replicas of geo- graphic reality (Shelton & Yamamoto, 2009). However, they do help us represent the spatial aspects of our environment. When we encounter a description of a spatial setting, we do not simply store these isolated statements in a passive fashion. Instead—consistent with Theme 1—we actively create a cognitive map that represents the relevant features of a scene (Carr & Roskos-Ewoldsen, 1999; Tversky, 2005a, 2005b). Furthermore, people combine information from separate statements an