Systematic Distortions in Cognitive Maps - CiteSeerX

Systematic Distortions in Cognitive Maps: The North American West Coast vs. the (West) Coast of Israel Juval Portugali and Itzhak Omer ESLab (Environmental Simulation Lab) Department of Geography and the Human Environment, Tel Aviv University, Tel Aviv 69978, Israel {juval, omery}@post.tau.ac.il

Abstract. This article suggests a second thought on two papers published in Cognitive psychology in 1978 and 1981. Both articles deal with systematic distortions in cognitive mapping and both are based on experiments conducted along the North American West Coast. The first, by Stevens and Coupe, deals with distortions due to hierarchical organization while the second, by Tversky, with distortions due to rotation. Our second thought follows a set empirical results from a study conducted along the (West) coast of Israel. These results suggest that the experiments, on the basis of which the above two forms of systematic distortions were determined, could have resulted from another form of systematic distortion that we term the edge effect.

1. Introduction This paper suggests a second thought on two types of ‘systematic distortions in cognitive mapping’ [1] – distortions due to ‘hierarchical organization’ and ‘rotation’. The motivation to reexamine these distortions followed the analysis of a set of experiments conducted in Israel on the phenomenon of systematic distortions. On the one hand, these experiments have exposed systematic distortions that remind one of the above effects of hierarchy and rotation. On the other hand, they have also raised some doubts about the validity and generality of systematic distortions in cognitive mapping due to hierarchy and rotations as they currently appear in the literature. The first two sections of the paper introduce distortions due to hierarchy then examine the phenomenon critically in light of the results from Israel. The next pair of sections does the same to distortions due to rotation. The section that follows introduces a new form of systematic distortion termed the edge effect. It shows that the edge effect might explain several equivocal cases of rotation. The paper concludes by noting that in certain cases the edge effect might provide a better interpretive framework for both hierarchy and rotation.

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Juval Portugali and Itzhak Omer

2. From San Diego California to Reno Nevada In a paper entitled “Distortions in judged spatial relations” [2], Stevens and Coupe report on an experiment in which subjects in San Diego, California were asked to indicate from memory the direction to Reno Nevada (as well as to, and between, several other American cities). This, by drawing a line in the proper orientation on a circle with north noted at the top. Most subjects have indicated that Reno is northeast of San Diego [2], while from Fig. 1 it can be seen that it is, in fact, northwest.

Fig. 1. California and Nevada – The geographical context for Stevens & Coupe’s [2] and Tversky’s [4] studies.

Stevens and Coupe’s interpretation is that this distortion is due to hierarchical organization of spatial knowledge. That is, people tend to store in memory not the exact, or relative, location of all cities, but rather the relative location of states. Thus, when asked to make judgment about directions between cities, subjects infer the direction between cities from the spatial relations between the states. In our case such an inference can go like this: Since Reno is in Nevada and since Nevada is generally east of California, then every city in Nevada must be east of every city in California. Reno must, therefore, be east of San Diego. In terms of memory space, this way of hierarchical organization of spatial information is evidently more efficient and economical, but it has a price – systematic distortion in cognitive mapping due to hierarchy. Since its publication in 1978 several subsequent studies have found similar results, have elaborated various aspects and have established the working of systematic distortions in cognitive maps due to hierarchy. In all these studies, as well in several textbooks that have since appeared, Stevens and Coupe’s San Diego-Reno experiment stands as the seminal, paradigmatic case study. But is it really so? Does their

Systematic Distortions in Cognitive Maps: The North American West Coast vs. the (West) Coast of Israel

experiment really indicate the working of hierarchical organization in cognitive mapping?

3. From Haifa to Be’er Sheva Our doubts regarding Stevens and Coupe’s interpretation of the San Diego–Reno experiment followed a systematic distortion we’ve found in the relations between the cities Haifa and Be’er Sheva in Israel (Fig. 2), as described in Experiment 1. N

Fig. 2. Map of Israel – The geographical context for experiments conducted in the present study

Experiment 1: Two groups – 28 undergraduate geography students and 25 undergraduate architecture students at Tel Aviv University – participated in this experiment, that was conducted within the frame of a “cognitive geography” class. The subjects of the first group were asked to judge the direction from Be’er Sheva to Haifa, while those from the second group from Haifa to Be’er Sheva. The subjects were asked to draw a line from the center of a 2.7 cm radius circle according to the following instructions: Imagine that Beer Sheva is at the center of the circle and that you are in Be’er Sheve. Draw a straight line from Be’er Sheva to the direction of Haifa. Make sure that the line reaches the edge of the circle.

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At the outset of the experiment the experimenter made sure that the subjects understand the task. At the end of the experiment the responses were screened and distortions of over 60° from the true direction were taken out. As can be seen, our experimental set-up was almost identical to Stevens and Coupe’s. Comparing Fig. 1 with Fig. 2 one can see that both the North American West Coast and the Israeli coastline run in a general north-south direction and that both bend somewhat from the exact north-south axis: The West Coast towards SE, while the Israeli coastline towards SW. Furthermore, Haifa in Israel has a geographical position similar to San Diego in California – both are located “on the sea”; while Be’er Sheva in Israel is the parallel of Reno in the USA – both are inland, far from the coastline. The two experimental setups differ, however, in two respects. First in scale; the Israeli coast is some 250 km long, while the North American one some 2,200 km long. Second, and this is of major significance in the present context, the Israeli study area is not subdivided into states – there are no parallels to California and Nevada here. True, one can still claim that Be’er Sheva is in the Negev – Israel’s southernmost region. But all that can be said about the Negev is that it is south of any other region in Israel, not east nor west of it. The results from experiment 1 are presented in Fig. 3. The average discrepancy from the true direction of the two sets of judgment is 21°. As can be seen, the systematic distortions in Israel are identical to those found by Stevens and Coupe in the US West Coast. But in Israel, as noted, there is no California and Nevada and the systematic distortion in the cognitive maps of Israelis cannot be a consequence of hierarchical organization of spatial geographical relations. What is it then?

Be’er Sheva - Haifa

Haifa – Be'er Sheva

Fig. 3. Experiment 1: distribution of responses. Bold lines indicate the true directions

In a seminar that took place in Israel in 1988, Barbara Tversky suggested that since the coastline of Israel bends from north to SW, it is rather likely that it might cause


systematic distortions in cognitive mapping due to rotation (See report on that seminar in [3]). The notion of rotation effect was first introduced by Tversky [4] in a study where she asked subjects to judge the direction between several cities located along the Bay Area coastline. Most subjects correctly indicated that Berkeley, for example, is north of Palo Alto, but they incorrectly indicated that Berkeley is east of Palo Alto. Similar systematic distortions were identifies by Tversky with respect to other cities along the Bay Area. Tversky’s interpretation to the above distortions was that, in their minds, people tend to rotate geographical objects so that they will correspond the exact N-S frame of reference. As a consequence, in cases where the orientation of a geographical object is somewhat in “conflict” with the “natural” 90 degrees N-S axis, the N-S frame of reference tends to “win” and people wrongly judge spatial relations. Since in the Haifa – Be’er Sheva case ‘hierarchy’ as a cause for systematic distortion must be ruled out, we thought that Tversky’s ‘rotation effect’ might provide an alternative and more appropriate interpretational framework. The logic of this interpretation might be as follows: The Israeli coastline runs from north to SW, but people tend to rotate it, in their mind, to the exact N-S axis. And since Haifa is on the coastline itself and Be’er Sheva some 60 km east of it, people wrongly infer or imagine that it must be SE of Haifa. And vice versa: When considering the task from the point of view of Be’er Sheva, they imagine/infer that Haifa’s direction is NW. Cases of systematic distortion due to rotation were typically identified between pairs of cities located along, or close to, the coastline – along the San Francisco Bay Area, for example. Now, Haifa in Israel is indeed on the coastline, but Be’er Sheva is some 60 km from the sea. The latter case study thus indicates that the effect of rotation might extend beyond the area of the coastline. Is such an extended rotation effect active only in the Israeli case or is it a general property active also in the west coast of California and its Bay Area were the systematic distortions due to hierarchy and rotation were originally identified? The goal of experiment 2 was to answer this question, concerning the spatial relations between San Diego and two sites in north California: the city of Sacramento and Lake Tahoe. Both places are located far from the coastline; Sacramento is within California while Lake Tahoe is divided between Californian and Nevada. No hierarchy affect could be at work with respect to Sacramento. Experiment 2: This experiment was conducted with the help of Ms. N. Taylor – a graduate student at Tel Aviv University and a former undergraduate student at San Diego. 22 undergraduate students, living in San Diego, participated voluntarily in the experiment. They were asked to judge the direction from San Diego to Sacramento and Lake Tahoe. The procedure and method employed was identical to experiment 1. The subjects were asked the following: Imagine that San Diego is at the center of the circle: 1. Draw a straight line from San Diego to the direction of Sacramento. Make sure that the line reaches the edge of the circle. 2. Draw a straight line from San Diego to the direction of Lake Tahoe. Make sure that the line reaches the edge of the circle.

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The results from experiment 2 are presented in Fig. 4. Although the pairs of locations represent different principle geographical positions, the results show the same systematic error: The subjects judge the direction between the locations as running southwest to northeast instead of southeast to northwest.

Fig. 4. Experiment 2: Distribution of responses.

5. Systematic distortion due to rotation – a second thought The above results about the extended rotation effect entailed two questions: Firstly, how far from the reference line the rotation effect is active? Secondly, does it effect also the perceived spatial relations between cities that are far from the reference line? To answer these questions we’ve conducted Experiment 3. Experiment 3: 27 students from Tel Aviv University participated voluntarily in this experiment in the context of an urban geography class. The procedure and methodology employed here are identical to the previous two experiments. The subjects were asked to draw a line between the following pairs of cities in Israel (see map in Fig. 2), when each of the four tasks was implemented separately: a. From Haifa (on the sea) to Tel-Aviv (on the sea). b. From Tel-Aviv (on the sea) to Ashkelon (on the sea). c. From Haifa (on the sea) to Jerusalem (inland – further east of Be’er Sheva). d. From Be’er Sheva (inland) to Jerusalem (inland). The results of experiment 3 are presented in Fig. 5. Firstly, as we’ve already seen above (Fig. 3), there are significant systematic distortions in the pair Haifa-Be’er Sheva (The average distortion from the true direction is 47 °). Secondly, as can be seen, there are also significant distortions with respect to the pair Haifa–Jerusalem.


Thirdly, no distortions were found when subjects were asked to judge the direction from Be’er Sheva to Jerusalem and vice versa. Fourthly, and this is a rather surprising finding, no significant distortions were found between the pairs Haifa–Tel Aviv and Tel Aviv–Ashkelon.

Fig. 5. Experiment 3: Distribution of responses. Bold lines indicate the true directions

The intermediate conclusions from the above are straightforward: What we’ve considered so far as the rotation effect is active when one site/city of the pair in question is on the reference line and the other is inland; it is not active when both sites are not related to the reference line – people do not rotate the entire country, in their mind, in line with the exact N-S axis. Furthermore, it is not effective either when the pairs of sites are on the reference line itself – the Israeli coastline in our case.

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6. Rotation or edge? The above findings, in particular the fourth point, put a question mark on the whole idea of systematic distortion due to rotation: If people really tend to rotate the coastline in line with the N-S axis, then in the above tests they should have responded that Tel Aviv is south of Haifa and Ashkelon is directly south of Tel Aviv. The analysis of their responses indicates that they make no such mistakes; they know that the Israeli coastline bends toward SW and that as a consequence Tel Aviv is SW of Haifa and Ashkelon is SW of Tel Aviv. In other words, the effect of the Israeli coastline on systematic distortions is not unequivocal. In some cases it indeed causes distortions, but in other cases it “helps” subjects to judge spatial relations accurately. We suggest calling this equivocal effect of the coast as a reference line the edge effect. The notion of ‘edge’, as is well known, goes back to Lynch’s [5] The Image of the City. According to him edges are very useful elements when dealing with perceived spatial relations in large-scale extended environments such as cities – they provide a very prominent reference line. Thus, unlike Tversky’s notion of ‘rotation,’ that has the “negative” effect as a cause of distortions, Lynch’s notion of edge is associated with the “positive” effect of improving legibility. Edges belong to a set of five elements (edge, path, landmark, node, district) that according to Lynch are specifically significant in making the city and its image legible. As we’ve just seen, due to the edge effect of the bending Israeli coastline, our subjects were rather accurate when judging spatial relations between the three ‘edge cities’: Haifa, Tel Aviv and Ashkelon. The difficulty started when they were asked to judge the relations between the edge city Haifa and the “floating point” cities Be’er Sheva and Jerusalem. Most subjects simply underestimated the cumulative effect of a bending edge. That is to say, that what to the eye looks as a slight inclination westward, off the N-S axis, near Haifa, might accumulate to some 60 km at the south part of the country, close to 200 km down the coastline south of Haifa. On the Israeli coastline this is particularly prominent because as can be seen from the map (Fig. 2), the Israeli coastline bends westward “exponentially” in a nonlinear fashion; and nonlinear relations are counter-intuitive and hard to perceive and judge.

7. Concluding notes The above results from Israel and California have direct implications to the original Steven and Coupe interpretation of the San Diego–Reno systematic distortions: The actual direction of the Californian coast is NW-SE. San Diego is on the coastline itself, while Reno is inland, far away from the reference line of the west coast; exactly like Be’er Sheva in Israel and Sacramento and Lake Tahoe in California. In light of the above results, the edge effect might explain the San Diego–Reno distortion without the need to employ the hierarchical organization effect, nor the rotation effect. There is no way to tell, of course, whether the systematic distortions made by Stevens and Coupe’s subjects were due to hierarchical organization, as it is commonly


assumed, or due to the other effects discussed above. That is to day, due to the rotation effect, or due to the edge effect – that to our view explains the systematic distortions we’ve identified between cities in Israel, as well as in relation to Sacramento and probably also Lake Tahoe in California – or possibly due to several effects. But, it can clearly be stated that from the point of view of Popper’s principle of falsification, the experimental results from Israel and California falsify the interpretation suggested by Stevens and Coupe. Certainly it would be hasty to claim that our results falsify the very possibility of the hierarchical organization effect, the rotation effect and the very possibility of systematic distortions due to them. In fact, several other studies have demonstrated the effect of hierarchy in different circumstances, even when the area concerned had no prior hierarchical subdivision [6]. Our results falsify only what has become a canonical interpretation of the Stevens and Coupe’s experiment – that the distortions of their subjects were due to hierarchy only. The lesson from the above is rather interesting; it shows that a fallacious interpretation might entail true results – but this is an issue that goes beyond the short research note we are engaged with here.

References 1. Tversky, B.: Distortions in Cognitive maps. Geoforum, 23 (1992) 131-138. 2. Stevens, A., & Coupe, P.: Distortions in Judged Spatial Relation. Cognitive Psychology 10 (1978) 422-437 3. Glicksohn, J.: Rotation, Orientation and Cognitive Mapping. American Journal of Psychology 107 (1994) 39-51 4. Tversky, B.: Distortions in Memory for Maps. Cognitive Psychology 13 (1981) 407-433 5. Lynch, K.: The Image of the City. Cambridge: Mit Press (1960) 6. McNamara, T.: Spatial Representation. Geoforum 23, 39-150