Acquired Map-Like Mental Constructs
Hans J. Stolle (Kalamazoo, USA)
< hans.stolle@wmich.edu >
Attempts to identify mental maps with the help of maps drawn from memory have unfortunately been quite disappointing. Based on the findings of Betty Edwards (1975/2012) and others, it can be concluded that in most cases these tests do not externalize specific map details, which have been intentionally committed to memory.
Instead, they provide us with an inkling of the individual's map-like mental constructs, which he or she has learned routinely for the purpose of recognition.
Keywords: recognition and recall, preferences of map viewing direction and illumiation, angle of viewing elevation and type of map surface, acquired map-like mental constructs
1. Recognition and recall
The recognition of a concrete object, as suggested by Frisby (1980) and others, is achieved when matching a perceived object's structural description against a stored memory trace occurs. Since we can still recognize a face after a cartoonist's radical surgery of simplification and exaggeration, it can be speculated that the matching of structural descriptions and memory traces occurs as long as the former fall within the envelop of probability or tolerance (Bronowski, 1973). This notion does not only help explain the tolerance of the human mechanism of recognition but why the degrees of identification certainty vary. In contrast, recall is the active and deliberate retrieval of information from memory, which requires previous learning of details and more precisely defined chunks of knowledge. The difference between recognition and recall becomes quite clear when we think of both in terms of the amount of knowledge needed to identify a tune or to hum every tone of its melody. As the participants of television game shows have proven, some tunes can be identified by as little as the melody's first three notes.
Assessing cartographic products in that light reveals that cartographers have not only been aware of the cognitive mechanism's tolerance of recognition, but have put it to use for quite some time. Realizing that world-projections cannot show the earth's correct shapes, areas and distances simultaneously, they have developed useful 'compromise-solutions'.
Understanding the mind's ability to compensate for shape distortions, they devised projections that sacrifice a region's shape in order to preserve its area or distance relations.
On cartograms the cartographer is going one step further by varying a geographic area’s size and shape to represent a given statistical quantity, presupposing that the user can recognize the distorted area and perform intellectual correlation between the statistical magnitude shown on paper and the region's geographic size recalled from memory.
The differences between recognition and recall, Sigel's (1978) picture recognition and picture comprehension, map reading and map interpretation are based on an automatized, seemingly passive mode on the one hand, and a deliberate, intellectual and active mode on the other. By teaching us how to 'look at maps’, the strategies put forth by some of the map- learning studies promise to help improve our recall or mental representations of map contents. In their work on map learning, Thorndyke & Stass (1979) have determined that the procedures of map learning consist of partitioning, sampling, verbal learning, spatial learning and evaluation. As defined in their study, partitioning makes it possible for the map
learner to focus his interest on regional or global (the entire map area) subsets of the map's content. Various procedures of sampling are found to provide the mechanism for guiding the learner's attention to particular map elements. For verbal learning, it is helpful to employ counting, mnemonics (acronyms) and associations with prior knowledge. By constructing a visual image of some portion of the map in memory, spatial learning is facilitated, while the process of labeling generates a verbal identification for each complex spatial configuration. In addition, spatial learning is found to include 'relation encoding' of detailed relationships between two or more objects and 'pattern encoding' of spatial detail or shape of a single map element. Finally, evaluation is performed by searching and retrieving information from memory and comparing it to the representation of a target element on the map. In other words, the use of partitioning, relation encoding and pattern encoding comprises a learning strategy of segmentation. For map learning, segmentation helps break up the map's complex content into graspable chunks of meaningful regional clusters of multi-category information or by extracting subsets of single category information from the entire map.
2. The experiment
It is believed that map-like mental constructs are a product of using maps and acquiring real-world knowledge. Based on the premise that optimum recognition is achieved when a viewed map’s depiction matches a viewer’s map-like mental constructs, a number of tests were designed to find out if students of similar background share map-like mental constructs of their home state. An experiment, applying preference rankings of view variations of one and the same map, was designed to help assess degrees by which descriptions of the map and the viewer's mental map-like constructs correspond. To attract eighty student test subjects, a chance to win a cash prize was offered. One hundred and five different views of a raised-relief map of Wisconsin, as seen from different directions and viewing elevations, illuminated from different directions and represented as a flat or earth- like curved surface, were produced by photography. Thirty-three of them were eliminated by a number of pretests. The main tests, consisting of two different but converging investigations applied repetitive tasks of ranking to progressively eliminate all but the most preferred views. While participants of the first test looked at seventy-two variations to arrive at their most preferred view, those of the second test used only seventeen. As both tests employed the same test materials, it was postulated that similar outcomes of both approaches would verify that Wisconsin students share map-like mental constructs of the home state’s viewing direction, viewing elevation, direction of illumination and type of surface. Testing the strength of each individual’s most preferred view, he/she was asked to choose between it and an orthogonal (correct shape), but disoriented, view of the map.
In preparation, a raised relief map of Wisconsin at a scale of 1:633,600 (see Figure 1) was painted gray and black in areas outside the state. The borders of adjacent states were drawn in white and their names, printed in white on black labels, could be moved or rotated to suit each photo’s viewing direction. For constant lighting control, all of the photography was done in total darkness using an electronic flash for exposure. The camera's viewing elevation angles were measured with a clinometer. For quick camera-map set-ups of viewing azimuths, the horizontal angles of viewing direction were marked in the margins of the map.
Figure 1. The raised relief map of Wisconsin
As discussed earlier, the purpose of producing a large variety of views of one and the same map was to allow test subjects to rank them and choose their most preferred views.
Once defined, the identified ranks of preference would be viewed as degrees of coincidence between the descriptions shown on the test maps and the subject's acquired map-like mental constructs. Since the production of test maps by photographing the raised relief map, changing one perspective parameter at a time, would have resulted in hundreds of variations, several pretests were administered to reduce that number.
2.1. Pretest 1, Viewing Direction Preferences
The first pretest was designed to identify preferences of viewing directions. Starting from the south, the State of Wisconsin was photographed as seen from the eight cardinal directions at a viewing elevation of 40° and an illumination from the left. To be sure one extra direction from the south-southeast was added. After ten test subjects had viewed and ranked the printed views according to their likes and dislikes, the results, plotted in Figure 2 and shown in Table I, identified the extra view from south-southeast, or 165°, as the most preferred direction. It is of interest that the viewing directions of most block-diagrams are between cardinal directions.
Figure 2. Pretest 1, Viewing Direction Preferences
Table 1. Preference Scores of Nine Viewing Directions
Therefore, starting at this direction the map was photographed again at intervals of thirty degrees, which resulted in twelve new views from an elevation angle of 40° and a left side illuminations.
2.2. Pretest 2, Preferred Directions of Illumination
In order to find if directions of illumination affect preferences of viewing the three- dimensional relief, each of the twelve state views was photographed two more times.
Besides the first set illuminated from the left, the second was illuminated from the viewing (camera) direction and the third from the right. All photographs were taken at a viewing elevation (camera angle) of 40°.
Twenty new test subjects were asked to view the three illuminations of each direction and rank them according to their likes and dislikes. As shown in Table 2, the results indicate that none of the viewing (camera) directions were chosen. With the exception of views I, V, IX, X and XII, the group preferred illuminations from the left. Despite a seven/five preference for left illuminations, directions of illumination do not seem to be a fixed map- like mental construct but appear to vary with the shape of the illuminated object. Figure 3 shows the preferred direction of illumination, photographed from an elevation angle of 40°, for each of the twelve directional views.
Table 2 Preference Scores of Illumination Directions
The fact that only some maps show topography by relief shading may be a reason why individuals do not have well-developed map-like mental constructs of relief. Thus, we may conclude that the pretests, which had been designed to reduce the number of map variations, have also identified a consensus of some map-like mental constructs, which were most likely developed by experience and interaction with maps.
Figure 3: Twelve Directions with Preferred Illumination seen at 40°
In preparation for the main test, the twelve directional views (Figure 3; Stolle, 1984) were photographed two more times at smaller elevation angles of 30° and 35°, using each view’s chosen direction of illumination. To simulate the earth's shape, a 'realistic curvature’
of Wisconsin was determined by the author to have a radius 4 times smaller than the earth.
rightrrrrr
To adjust for the new angular relationships between the film plane and curved map surface, three elevation angles of 20°, 30° and 40° were chosen to photograph the curved map, which resulted in a total of six viewing elevation/surface variations for each of the twelve directions, shown in Figure 4 (ibid.) for direction I (165°).
Figure 4: Six viewing elevation-surface variations viewed at 165°
To provide test subjects with a fixed viewing direction seven by eight-inch test cards, Figure 5, were printed and each of the views was glued on one.
Figure 5: test card
2.3. Map view variation preferences, test I
To record each participant’s viewing preferences, the test form Figure 6 was produced.
21 new subjects were asked to find which viewing direction, viewing elevation, and type of map surface best match their map-like mental constructs. Each was shown the six variations of flat and curved maps seen from different elevations of one directional view, which he/she ranked according to his/her likes and dislikes. Once the order of preference was recorded, the procedure was repeated for each of the other eleven viewing directions.
Having thus identified the most preferred viewing angle/type of surface variation for each
Figure 6: The test form, Test I
of the twelve viewing directions, all of the first choices were placed in front of the subject to select the most preferred view. As final task, participants were asked to choose between their final choice and the disoriented orthogonal relief map of the state shown in Figure 7.
Figure 7: An orthogonal but disoriented relief view
2.4. Map View Variation Preferences, Test II
For the second test, another group of twenty-five subjects partook in a shortened test, Figure 8. To find their preferences of viewing direction, viewing elevation and type of map surface, each viewer was first shown the twelve directional views of the relief maps, Figure 3. After the subjects had chosen their most preferred directional view, only its six variations of flat and curved surfaces, seen from three camera angles of elevations, were shown to select their most preferred view. Thus, viewers of Test II viewed only seventeen variations, while participants of Test I had viewed seventy-two. As final task they were also asked to choose between their most preferred perspective view and the map’s correctly shaped (orthogonal), but disoriented, view. In the event that the results of both tests turned out to be similar, the hypothesis that preferred map directions, viewing elevations and types of map surface are part of the students’ shared map-like mental constructs of their home state, could be accepted.
Figure 8: The test form, Test II
Viewing Direction Preference Comparisons, Tests I and II
For an evaluation of the ranked viewing direction scores, it was necessary to weight them. All first choice scores were multiplied by twelve, second choice scores by eleven and so forth. The weighted direction preference scores for Test I and Test II, shown in Table III, are seen to be quite similar. Adding the scores of each tests and dividing them by twelve finds an average score of 162.5, which every view would have received had there been no difference in preference. Plus signs indicate scores above the average and negative scores are below it. Both tests identified viewing direction I as first choice, direction II as third and view X as fifth pick. The second and fourth preferences of Test I for views XI and XII are reversed as views XII and XI in Test II.
3. Results
3.1. Statistical Comparisons of Viewing Direction Preference Scores
To test the strength of relationships between the scores of both tests, the Wilcoxon matched-pairs signed-ranks test was applied (Blalock, 1972). As seen in Table IV, the calculated differences of scores for each pair of the tests are quite similar and the sums of positive and negative differences indicate a high agreement between both tests. Ignoring their signs, all differences were ranked using the smaller of the two ranked sums as the test’s critical value T. If it equals or is less than the value T found in the Wilcoxon test’s T table (ibid.), the no-difference hypothesis is rejected. For n=12 the table shows that a value of T=14 or smaller rejects the no-difference hypothesis at the .05 level, a 10 or smaller to reject at the .02 level, and a T=7 or smaller to reject at the .01 significance level. Since the calculated T=27.5 is much larger, the no-difference hypothesis cannot be rejected at any reasonable level of significance, verifying that the scores for both tests are not significantly different in a statistical sense.
Table 3: Viewing Direction Preference Comparisons
The fact that both tests have identified very similar viewing preferences, although both tests had employed different approaches and participants, suggests that the tested individuals share a strong preference for maps oriented toward north. The fact that the viewers of the second test had viewed only 1/5 of the variations to arrive at their directional choice, supports this conclusion further. It is quite certain that map orientation is a strong map-like mental construct learned by viewing and using maps, conventionally oriented to the north. For that reason, most map users expect to see maps with their north at or near the top. As seen in Figure 9, the tests' most preferred view directions are view I, II, XII and XI. Since the results of both test groups were found to be statistically very similar, it is highly unlikely that they were produced by chance.
In his study on Orientation and Form of familiar figures, Rock (1973) states that attempts of assigning non-conventional directions to familiar figures are as a rule un- successful since figures, like familiar faces or lettering, have their own (intrinsic) axes regardless of their orientation. Much like Rock's familiar figures, the perspective maps of Wisconsin were rotated. Unlike Rock’s test, the subjects of the Wisconsin experiment were not asked to identify the rotated map, but to rank the rotated views according to their perceived preferences. Despite the differences in objectives, the results of both studies concur that rotating a familiar figure, which has an intrinsic or natural axis, has a negative effect on viewer response. This supports the Wisconsin experiment's assumption that a
Table 4: Computations for Wilcoxon Matched-pairs Test(Viewing Direction Preferences)
Figure 9: Viewing Direction Preference Scores
viewer's ranks of maps by various amounts of rotation indicates the degree with which each rotated map's descriptions coincides with, or differs, from the viewer's map-like mental constructs. Comparing Rock's recognition scores of rotated familiar figures, shown in Figure 10, with preference scores of the rotated map of Wisconsin, taken from Table VII and re- presented in Figure 11, reveals their similarities in quantitative terms.
Figure 10: Orientation and Recognition
(after Rock, 1973 ) Figure 11: Orientation and Preference of Tests I and II (Stolle, 1984)
This evidence implies that the mental traces needed for the recognition of Rock's familiar figures and the universal map-like mental constructs, which were used to judge the rotated views of Wisconsin may be of the same kind. The fact that all test participants were familiar with their home state's map, suggests that the task of ranking each variation of the familiar figure was performed by mentally assessing the fit between the map-like mental constructs learned from maps, and the descriptions of the test maps before them. This leads to the third conclusion that the human mechanism of cognition cannot only match an object's descriptions and its mental constructs, but it can mentally rotate a disoriented object's descriptions in order to do so. Moreover, it seems to be able to express the extent of rotation at an ordinal scale. In the case of viewing direction, this means that the state map's object constancy, like Rock's familiar upright faces, weakens as the rotation between the shown object's natural axis and its mapped axis increases. As the orientation of most printed maps is toward geographic north, a long-time cartographic convention, mental comparisons are apparently made in reference to it.
3.2. Viewing Elevation Angle and Map Surface Preferences
The second part of the Wisconsin experiment identified viewing elevation angle and map surface preferences. From the results shown in Table V, we know that the views of the flat and curved maps from an elevation of 40° were preferred most by both groups. The views of 35° of the flat and 30° of the curved maps were found to be the groups' third and fourth choice. This may be attributed to the fact that a 40° view optimizes the visibility of a map’s raised-relief. Hence, we may conclude that map-like mental constructs of angle of viewing elevation are products of interacting with raised-relief maps, models and map-use ergonomics.
The ranked preference scores for viewing angle and surface variations of each subject were weighted next. First choices were multiplied by six, second choices by five and so on.
Their cumulative values are shown in Table V. Again, close relationships are seen to exist between the scores of the two tests. Both test groups found the views from a 40° elevation of the flat and curved surfaces to be their first and second most preferred variation. The view from 35° of the flat surface and from 30° of the curved surface are seen to be the third and fourth choices in reversed order for Tests I and II.
3.3. Statistical Evaluation of Viewing Elevation and Surface Preference Scores
To assess the degrees of relationship between the viewing elevation and surface preference scores of Tests I and II, the Wilcoxon matched-pairs signed-ranks test was used again. The differences for each pair were calculated and ranked, ignoring their signs, as shown in Table VI. Since the sum of the positive differences equals the sum of the negative differences, for n=6, T=0 and we can conclude that there are no significant statistical differences between the scores of both tests. This in turn indicates that most participants of both tests share partialities about viewing elevation angles from which maps ought to be viewed, while preferences on whether the mapped state of Wisconsin should look flat or curved are equally divided. Both findings support the hypothesis. that viewing elevation and type of surface are map-like mental constructs, most likely learned from viewing space imagery or weather satellite images and the use of globes. Based on the results of both tests, whose statistical agreement ruled out results by chance, we can conclude that the tested students shared constructs of learned viewing elevation and earth curvature. It is interesting to note that the experiment's first choice of viewing elevation concurs with the findings of Jenks & Crawford (1967), who recommend perspective map viewing angles between 30° and 40°. Since a 'normal' sitting or standing position results in an 'average' reading angle between 30° and 45°, it may explain the tests' viewing elevation preference. Finally, it is possible that the 40° view is favored since it maximizes visibility of raised-relief details.
Hence, we may conclude that map-like mental constructs of viewing elevation angles are a product of reading positions used for viewing raised-relief maps or maps in general.
To test the theory that certain map-like mental constructs may be more important than others, all test subjects were given the opportunity to trade their most preferred perspective choice of Wisconsin for a planimetrically correct relief map (Figure 7) which had been oriented to the west-northwest. Eighty-four percent of test group I and seventy- two percent of group II preferred to keep their best perspective view although a considerable number of subjects commented that if they could turn the orthogonal map to a northern orientation, they would choose it. This fact supports further that map-like mental constructs of map orientation are the primary, overriding construct, while the state's shape is a secondary attribute of shared constructs.
4. Summary
For objects, too large to be viewed and learned by individuals on the ground, real- world surrogates such as space imagery, photo- or line maps are used. As a result, map users develop and use map-like mental constructs, which are not necessarily based on real-world properties but the characteristics of the memorized surrogates. Based on the outcomes of the experiment, the hypothesis that the tested students share given preferences of their home state map’s viewing direction, viewing elevation angles, earth curvature and shape,
Table 5: Preference Score Comparisons for Viewing Elevation Angle and Surface
was verified. Preferences of map illumination direction, on the other hand, were found to be less consistent, perhaps due to an individual’s real-world images or knowledge.
Thus, the experiments' results suggest that some map-like mental constructs are universal, while a few vary with specific situations. Evidence, that the mental construct of orientation carries more weight than shape, was confirmed. The choices of viewing directions and elevation angles that result in maximum surface visibility, should be of interest to mapmakers, especially those working with interactive computer systems. Since all conclusions were based on the response of eighty individuals who shared similar backgrounds of residence, education and exposure to maps, future tests involving less homogeneous groups are recommended to find if their responses are similar or vary with each tested individual’s level of education, occupation, age and personal interests.
5. References
Blalock, H. M. (1960). Social statistics. McGraw-Hill.
Bronowski, B. (1973). The Ascent of Man. Little, Brown and Company.
Edwards, B. (1975/2012). Drawing on the right side of the brain: The definitive. Penguin.
Frisby, J.F. (1980). Illusion, Brain and Mind. Oxford University Press.
Jenks, G. F., & Crawford, P. V. (1967). Viewing points for three-dimensional maps. Department of Geography, University of Kansas.
Rock, I. (1973). Orientation and Form. Academic Press.
Sigel, I. E. (1978). The development of pictorial comprehension. In S. Randhava & W. E. Coffman (eds.): Visual learning, thinking and communication, 93-111. Academic Press.
Stolle, H. J. (1984). Symbol Structure, Information Content and Visual Form: A Carto-semiotic Theory of Map Signs (Unpublished doctoral dissertation). University of Wisconsin, Madison, USA.
Thorndyke, P. W., & Stasz, C. (1979). Training Procedures for Map Learning. Rand Note prepared for the Office of Naval Research (No. RAND/N-1018-ONR).
Article history:
Received July 21, 2016 Accepted March 18, 2017 Table 6: Computations for Wilcoxon Matched-pairs Test(Viewing Elevation and Surface Preferences)
