comparisons in the spatial knowledge surfaces of subjects from canada and the united states

ANDREW CURTIS Department of Geography, Government and History, Morehead State University, Morehead, Kentucky 40351 (emai I : a.curtis@morehead-stedu)

U.S.A.

COMPARISONS IN THE SPATIAL KNOWLEDGE SURFACES OF SUBJECTS FROM CANADA AND THE UNITED STATES

This paper advances the spatial-choice modelling literature by further examining the way in which spatial knowledge is gained. The specific research purpose of this paper is to see how a major boundary (the U.S.A.- Canada border) will affect the generation of a spatial- knowledge surface. it is accepted that an important impact on the way an individual makes a spatial choice, such as a decision to migrate, is the amount and quality of the information he / she possesses about different locations. A positive influence on such a knowledge surface is the population size of the location. Negative influences include the separating distance between individual and location, and the degree of clustering the location faces in respect to other places around it. This paper investigates the way in which these influences also hold if a major boundary lies between a subject and the investigated research space. The paper uses a multivariate model calibrated on lists of recalled United States city names generated at 9 different Canadian test sites. These are then compared to similar model results from 22 U.S. test sites. The Canadian test results are more consistent than those for the United States. Also, for Canadian subjects, there is no distance decay in the probability of recalling a location unless the Canadian test site is located proximate to a major American border city. A strong relationship exists between the population size of the recalled location and its probability of being recalled. There is also further evidence to support a hierarchical method of knowledge processing, albeit in a weaker form than found in the US. test sites.

Key words: competing destinations, spatial choice, spatial knowledge

Cet article contribue 1 la documentation sur la modelisation des choix spatiaux en analysant comment on acquiert des connaissances sur I’espace. Le but spkifique de la recherche est dobserver comment une frontiere geographique (la frontiere entre les Etats-Unis et le Canada) influencerait la generation dune surface de connaissances spatiales. Lorsqu’un individu choisit un lieu dune perspective spatiale (et lorsqu’on prend une decision de migrer) la quantite et la qualit6 des ren- seignements qu’on possede au sujet des differentes situations in fluencent profondement sa decision. La population d’un lieu a une influence positive sur une telle surface de connaissances. Parmi les influences negatives il y a la distance qui separe I’individu du lieu dont i l s’agit, la proximite de ce lieu aux autres et le degre d’agglomeration d’un lieu par rapport aux autres dans les environs. Dans cet article nous essa yons de determiner comment ces influences fonctionnent si une fronti6re importante reste entre I’individu et I’espace qu’on etu- die. Cette investigation utilise un modele multivarie, calibre sur des listes de noms de villes aux Etats-Unis qu‘on rappelle et qui furent generes 1 9 sites canadiens differents. Nous faisons la comparaison entre ceux-ci et des resultats semblables des modeles de 22 sites aux Etats-Unis. Les resultats des tests au Canada sont plus uniformes que ceux des Etats-Unis. De plus, pour les canadiens la distance n’a aucune influence sur la

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54 Andrew Curtis

probabilite' de rappeler un lieu 2 moins que le lieu canadien ne se trouve pas tr& pres d'une ville importante ame'ricaine situee sur la frontigre. Une relation forte existe entre la population d'un lieu rappel4 et sa probabilite d'etre rappel&. D'autres faits suggerent egalement la validite' d'une me'thode hie'rarchique de traitement des connaissances, m&me si ces indications sout moins fortes que ce que /'on observe aux sites ame'ricains.

Mots-clb: destinations rivales, choix d'espaces, connaissances spatiales

There i s a perplexing amount of spatial information available to any individual at any location. The spatial-choice literature suggests that an individual's spatial behaviour, such as a decision to migrate, i s linked to the quantity and quality of this spatial knowledge. This means that an individual i s more likely to move to a destination they know more about, ceteris paribus, than one about which they know relatively little. This provides one explanation for three traditional results found in the migration literature. There is a distance-decay effect in the movement of people, which can be explained because the greater the distance between an individual and a city, ceteris paribus, the less is known about it. There is also a population-size effect: the larger a city is, ceteris paribus, the more people know about it through media accounts and increased personal interactions. The third effect is the spatial competition surrounding a city in respect to information originating from all other cities. People will know more about a relatively isolated city than, ceterisparibus, one that appears in the shadow of several other cities (Fotheringham 1983).

It is also reasonable to assume that there is a locational variation in the quantity (how many places an individual has heard of) and quality (how well they know those places) of spatial knowledge. These variations in knowledge could occur depending on whether an individual lives in an information-rich environment - one with an increased number of personal and media contacts, such as Toronto - or an information-poor environment, such as rural Saskatchewan (see Gould 1975). There is a need for continued investigation into the connection between location and the content and structure of spatial knowledge in order to further our understanding of spatial behaviour. This paper considers two issues regarding spatial knowledge: the characteristics of locations that help form the spatial knowledge set, and variations in the knowledge set that result from the residence of the individual.

Previous research has directly considered the way in which spatial knowledge varies between different locations. This was achieved by comparing recall lists of U.S. city names generated by subjects at a series of different test sites. These studies have used multivariate models similar to those employed in migration studies. A strong correlation has been found between the probability of recalling a city and the separating distance from an individual to the recalled city, the population size of the recalled city, and the relative isolation of the recalled city (Curtis and Fotheringham 1995, 1998). The benefit this type of research has for applications using models of spatial choice is that the results bring us a step closer to understanding the locational variations in spatial knowledge. These, if removed from models of spatial choice, can help in the identification of other choice patterns. The overall similarity in the results of models calibrated on both migration-flow and city-recall data suggest that using these recall lists constitutes a valid approach to identifying the locational variations in spatial knowledge.

The specific contribution this paper makes to this literature i s in how a significant geographic border influences the characteristics of spatial knowledge. The question this paper poses is this: Will the traditional findings of spatial knowledge deteriorating with distance and spatial clustering, and increasing with population size, be changed if a significant geographic (in this case political /cultural) boundary is introduced between an individual (Canadian) and the investigated knowledge space (United States)?

This paper will use the same multivariate model approach as previously used in the investigation of city- recall lists generated at 22 different universities from the United States. It will then compare these to results generated at 9 Canadian universities.

The Representation of Spatial Knowledge

Research has considered the way in which spatial information i s encoded (Shepard 1975; Anderson 1983), whether this information is stored nonhierarchically (Byrne 1979; Sadella and Magel 1980; Sadella and Staplin 1980; Briggs 1983) or as a series of hierarchically arranged clusters (Hirtle and Jonides 1985; McNamara 1986; McNamara et al. 1989, Lloyd et al. 1996). How- ever, it is generally accepted in the research into revealed choice preferences that a consideration for a hierarchical storage of spatial information is required in the choice model. A hierarchical storage mechanism is utilized because of the voluminous amount of spatial information

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Comparisons in the Spatial Knowledge Surfaces of Subjects from Canada and the United States 55

accessible to an individual. Different aggregations of space (such as a neighborhood, a suburb, a regional centre) sit at different levels of this hierarchy. It is also likely that clusters found at any level of this hierarchy (such as cities being grouped into regions) wil l vary according to the amount of information the individual experiences. Therefore, the strength of these knowledge hierarchies - that is, the number of levels in the hierarchical tree and the number of clusters found at any one level of that tree - are likely to vary between geographic locations. This is because of variations between information-rich and information-poor locations.

Research has directly considered the connection between the way spatial information i s clustered and the effect these structures have on representation mecha- nisms (Stevens 1976; Cadwallader 1979; Sadella et al. 1979); McNamara 1992). For example, Wilton (1 979) found that test subjects consistently took longer to verify directional statements when the distances involved were between objects on either side of a cluster boundary, rather than existing within the same cluster. Other work has examined the actual variations and errors in the spatial-knowledge surfaces, particularly at the national level (Gould and White 1974; Downs and Stea 1977; Stevens and Coupe 1978; Holyoak and Mah 1982; Birnbaum et al. 1989). For example, Stevens and Coupe (1 978) found that their test subjects reported Reno, Ne- vada, to be further east than Los Angeles, California. This was as a result of lower-level information (city location) being inferred from a higher level of the hierarchical structure (the relative location of the states).

The question this paper asks is, How will a significant geographic boundary influence an individual’s knowledge of spatial locations? It also goes a step further by seeing how this border effect varies between different locations. Indeed a criticism of some of the previous research into spatial-knowledge surfaces i s that they are location specific and do not test for spatial stability in the results. Models of spatial choice which have used the competing destination formulation have indirectly considered these locational variations in spatial-knowledge surfaces (Fotheringham 1983, 1986, 1991).

Spatial Choice

A spatial choice originates from a different process of information storage and retrieval than for most aspatial choices, such as choosing a coffee brand (Fotheringham and O’Kelly 1989). An explanation for this i s the sheer volume of potential spatial choices. There are too many choices for an individual to simultaneously compare all

elements in the spatial set. It would therefore seem likely that the individual clusters this information into more manageable groups, with similarly cognized places being grouped together. It is also likely that these clusters have a hierarchical arrangement, such as the grouping of certain small cities together because they surround a larger regional centre. At a higher level of the tree, regional centres will be clustered into a larger region. The identification of such a spatial hierarchy and its incorporated cluster boundary has long been a problem in models of spatial choice.

Spatial knowledge clustered in this way presents a modelling situation too complex to simply apply existing aspatial choice theory (Fotheringham 1986; Fother- ingham and O’Kelly 1989). For example, it is inappropri- ate to apply standard aspatial choice models to model migration flows, because of the underlying premise that choices result from an evaluation of all possible alternatives. As has been suggested, the size of a spatial- choice set is too immense to allow an individual to evaluate all possible alternatives. It i s likely that a hierarchy i s constructed, with the levels of the hierarchy vary- ing according to the amount of information available. An individual will identify relevant spatial clusters (such as the northeast) and then begin to evaluate those locations contained within this cluster. The hierarchies will vary according to the residence of the individual. Those from more centrally located areas wil l possess more evolved spatial maps, because they have an increased number of contacts as compared to those from isolated areas (Gould 1975).

Another influence this hierarchical clustering of spatial locations has on resulting spatial choices is that there i s an increased likelihood for individuals to underestimate the number of elements within the cluster as its size increases (Fotheringham 1987). This means that an individual is more likely to underestimate opportunities within a densely populated region because of an information shadow spreading from each large centre.

The competing-destination model has been used previously to investigate spatial choices, usually in the form of migration flows, because of its ability to incorporate such a hierarchical organization of spatial knowledge (Fotheringham 1987; Fotheringham and Curtis 1992). Therefore, spatial choice decisions, such as choosing a migration destination, wi l l in part reflect variations in an individual’s underlying spatial-knowledge surface. The competing destination model has also been used to investigate spatial knowledge surfaces directly by cali- brating them on lists of recalled city names (Fother- ingham and Curtis 1998). However, although these in-

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56 Andrew Curtis

Table 1 Parameter Estimates for the Canadian Test Sites

Dist POP Accs Dummy AdjR"

Vancouver (Simon Fraser University) Edmonton (University of Alberta) Regina (University of Regina) Winnipeg (University of Manitoba) Windsor (University of Windsor) London (University of Western) Hamilton (McMaster University) Kingston (Queen's University) St. John's (Memorial University of Newfoundland)

Stan. Dev. Upper Lower Mean

U.S. Subjects

Lower Mean

Upper

-0.44 (-2.3 3 )' -0.35* (-0.89) -0.20; (-0.51) -0.30* (-0.94) -0.25 (-2.07) -0.14' (-0.88) -0.40 (-2.52) -0.54 (-3.25) o.oo* (0.01)

0.16 0.00

-0.54 -0.29

-0.28 -0.91 -0.55

1.15 (10.69) 1.27 (10.19) 1.22 (10.26) 1.10 (9.00) 1.33 (10.06) 1.25 (10.96) 1.22 (10.77) 1.15 (10.11) 1.48 (10.99)

0.1 1 1.48 1.1 1.24

1.2 0.78 0.93

-0.40* (-1.52) -1.02 (-3.27) -0.92 (-3.66) -0.77 (-3.3) -0.76 (-2.43) -0.67 (-2.06) -1.01 (-2.92) -1.68 (-4.53) -0.48* (-1.06)

0.35 -0.4 -1.68 -0.86

-0.64 -1.98 -1.24

0.06' 0.65 (0.35) 0.29' 0.65 (1.48) 0.32* 0.65 (1.82) 0.24; 0.57 (1.24) 0.03* 0.63 (0.14) -0.05' 0.65 (-0.29) 0.33. 0.66 (1.88) 0.27* 0.65 (1.49) -0.1 1 * 0.64 (-0.53)

0.03 0.66 0.57 0.64

0.74 0.4 0.62

NOTES:

1 Figures in parentheses are t-values. * Indicates statistically nonsignificant value.

vestigations have modelled data collected at several different test sites, they have not considered the impact a significant boundary would have on the information flows leading to the formation of a spatial-knowledge surface (and therefore any resulting spatial choice). More specifically, how will the results differ for subjects that live on either side of a major boundary, even if those test sites are geographically proximate?

Methodology

Subjects from nine Canadian universities were asked to recall as many cities as possible. The locations of the nine Canadian test sites can be seen in Figure 1, and their names can be found in Table 1. A time-limit of 15 minutes was imposed on the exercise, though this time period was unknown to the subjects, in order to minimize any framing that such a limit could cause. Subjects were also asked to include the host-state name for each city recalled, in order to help identify cities with the same name. However, the state-identifier criterion was down

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played in order to minimize any framing that this condition could impose. On conclusion of the test, students were asked to give their age, sex, comments on any approach they had implemented during the recall, and a list of their cities of residence during the previous 10 years. Only recall lists from students who had resided in the local area for all of the previous 10 years were selected. This was because the purpose of the investigation was to construct aggregate-information surfaces specific to each test location. The number of recall lists meeting this criteria and therefore used in the model can be seen in Table 2 (subjects n).' The exact set of instructions given to each of the test administrators can be seen in Note 2.

It immediately became obvious that there was consid- erable variation in the types of cities recalled by the subjects. This presented a problem in an unbiased selection of a correct recall list on which to calibrate the model. There were some errors as to what some of the subjects thought was a city located in the conterminous United States. In order to compensate for this, only the

Comparisons in the Spatial Knowledge Surfaces of Subjects from Canada and the United States 57

Canadian Teat

3. Regina 4. Winnipeg 5. Windsor

*’ 8. Kingston 9. St. John’s

Figure 1 Canadian test sites

Table 2 Newlerseyas a Consistent Error in the Recall Lists

The numnber of recalls Subjects, R of ‘New lersev’

Vancouvei Edmonton Regina Winnipeg Windsor London Hamilton Kingston St. John‘s

25 44 30 34 44 30 28 35 35

8 15 9 3 13 3 10 7 18

probability of recalling major population centres was modelled for each test site. The metropolitan population was used in the model, as this gives a closer approxima- tion to the cognized settlement size, because in many instances, the political definition of a citywill result in an underbounded population size. One further selection in using a list of the largest metropolitan areas was the condition of the area being based around a definable, named centre. Therefore, those metropolitan areas which result from the clustering of medium-sized settle- ments, such as Lakeland in Florida, were not included in the model. New York City and Los Angeles were also removed from the model because of the overwhelm- ing size of these metropolitan areas (New York City’s population is 18 million and Los Angeles’s population is 14.5 million). This was because the inclusion of these

two metropolitan areas could bias the parameter estimates. Although there is a limit to the recall for any one city per site (being n number of test subjects), population size is essentially unlimited. This also reduced the need to use a logistic regression, as the association between the probability of recall and the investigated variables are approximately linear (Curtis 1995). The resulting model was calibrated on a set of 76 metropolitan areas.

The following model was then calibrated:

Rjj = exp(k) . Pi* . Dip C j y . exp(hSj) (1 1

where Rjj i s the number of times metropolitan area j i s recalled at site i (maximum value = 44); f j i s the metropolitan area population of j ; Djj i s the straight-line distance between i and j ; Sj i s a dummy variable which takes the value of I whenever metropolitan area j i s a state capital and 0 otherwise; and Cij is a spatial competition variable which measures the degree of competiton faced by city j from other cities (Fotheringham 1983; Fother- ingham and O’Kelly 1989). Spatial competition i s meas- ured as:

This places metro area j within an overall surface of accessibility, where metro area jwould have a high value if it i s in close proximity to other large population centres, or a low value if it is isolated from other population centres. It i s expected that the resulting parameter estimate associated with this value will be negative. This is because, ceterisparibus, cities found in areas of high city density will be more likely to be underrepresented by an individual because the strength of information flowing from them is masked by other flows originating from the same area (e.g., the city of Poughkeepsie which i s close to New York City). The summation as found in Equation 2 was performed on the one hundred largest metropolitan areas and not just those used in the calibration of the model. This is in order to place city j within as large as possible a representative selection of population centres. Both sides of Equation 1 are logged in order to make the model linear. The estimation of the parameters was by using ordinary least-square regression (see Curtis and Fotheringham 1995). There was a separate calibration for the data collected at each test site. The results were then compared to recall lists compiled in an identical fashion for subjects from 22 test locations from across the United States.

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Hypotheses

In comparing the results of the multivariate analysis for subjects from Canada and the United States, the following differences were expected. Even though many of the test locations were geographically close (such as Van- couver and Seattle, Hamilton and Buffalo, Windsor and East Lansing), it is likely that the presence of a significant cultural / political boundary will disturb the traditional decay-with-distance effect found in other models of revealed choice. As a specific hypothesis, and in a similar fashion leading from the results found by Stevens (1 976):

It is expected that distance has little effect on the probability of a subject recalling a city if that city and the subject are on different sides of a major cluster boundary.

In previous studies of revealed choice, a consistent finding is that the larger the population size of a city, ceteris paribus, the more is known about it. One of the reasons for this is the positive correlation that exists between the size of a city and its media coverage. The similarity in media coverage in both Canada and the United States (news, television shows, films, etc.), and participation of Canadian teams within American professional sports leagues, would lead to the expectation of a strong positive correlation between population size and probability of recall for the Canadian subjects. In this case, the cluster boundary has far less impact on the flow of information. For this reason, it is also likely that there will be little variation in the parameter estimate for population size between the Canadian test sites.

In previous recall research using subjects solely from the United States (Curtis and Fotheringham 1995), an example of a form of nonspatial knowledge was modelled by the inclusion of a dummy variable measuring whether the recalled city was a state capital or not. The justification for this was that students from the United States rote-learned state capitals at school and that this knowledge set still exists even though it may not be linked spatially to other knowledge. Canadian school children are not taught these capitals in the same fashion as school children from the United States. Therefore, it i s expected that the inclusion of the same dummy variable would not be significant for the Canadian test locations.

As a specific hypothesis:

There will be a positive correlation between the probability of a city name being recalled and the size of that city. Also, the parameter measuring this probability should be relatively stable across all test locations. The probability of a city being recalled is not influenced by the fact that the city is a state capital.

It is expected that the number of personal contacts, such as meeting travellers from different areas of the United States, is less than what would be expected for the subjects from the United States. Therefore, subjects from Canada will have less information and possess weaker spatial knowledge hierarchies about the United States. This will be seen in the model as a relatively weak spatial competition parameter. It is also doubtful whether the variation in the number of contacts between ‘central- ized’ and ‘isolated’ Canadian sites wi l l be enough to identify any systematic geographic variation in hierarchical storage strength. As a specific hypothesis:

Subjects from Canada possess enough information about the United States to employ a hierarchical clustering of spatial knowledge. The strength of this hierarchy will be weaker for the Canadian subjects than for their counterparts from the United States. There will be no systematic geographic variation in the strength of this hierarchical processing for the different Cana- dian test sites.

Results

Table 1 shows the parameter estimates for the 9 Cana- dian test sites, as well as a summary for the 22 test sites from the United States. It is encouraging to note the general consistency in the parameter estimates for the Canadian sites. This trend is also seen in the Adjusted R- square, which shows only one test location, Winnipeg, straying more than one standard deviation from the mean. Although the mean for the Canadian and Ameri- can test groups are similar, there is a greater variation in the Adjusted R-square for the U.S. test sites. This suggests that the subjects from the United States tend to use different sources of information for an exercise such as this and that these sources may vary between different areas of the country.

The most noticeable difference between the Canadian test subjects and their counterparts from the United States is the impact that separating distance plays on the probability of recalling a given city. Although the strength of the distance parameter i s not as large as traditionally found in migration studies, there was still a significantly negative relationship between distance and the probability of recall at all the test sites from the United States. This contrasts sharply with the Canadian subjects, where five of the nine test locations show no such significant relationship. Even at the four sites where there is a significantly negative relationship, the strength of the distance parameter is generally lower than for the sites in the United States. It i s also interesting to note that the four test sites are within two hours’ drive of a

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Comparisons in the Spatial Knowledge Surfaces of Subjects from Canada and the United States 59 - -

major city in the United States (Hamilton to Buffalo, Vancouver to Seattle, Windsor to Detroit, and Kingston to Syracuse).

This result suggests that the information boundary between Canada and the United States i s more perme- able at certain access points. If this is the case, the one problematic test location would be London, which is approximately two hours from Detroit. We cannot accept the first hypothesis as given, that there is no relationship between separating distance and probability of recall because of a border effect. Obviously, there is a need for further investigation to see if an amendment to this rule would be needed if the test site was in close proximity to a large US. city with a border crossing.

The population parameter i s significantly positive for all test locations. As expected, the subjects are more likely to know more about, and therefore recall, a city with a large population, as compared to one with a small population. The strength of the parameters for the Cana- dian test sites are greater than for all the test sites from the United States except one: Stevens Point in Wisconsin. One explanation for this could be the degree to which the Canadian subjects develop a cognitive surface of the United States from various nonexperiential sources, such as the number of times they are mentioned either in the media or in association with different sports. Therefore, the source of spatial knowledge as identified in an exercise such as this could dominate far more than for subjects from the United States. Interestingly enough, the strongest relationship between population size and the probability of recall i s with St. John’s. This test site in Newfoundland is relatively inaccessible by conventional travel routes. It i s therefore plausible that knowledge surfaces of the United States are far more dependent on media sources at this site than in any of the other Cana- dian test sites.

The state capital dummy variable is not significant at any of the test sites. This shows that there is no increased probability of recalling a city if it is a state capital. This is different from the findings for the test groups from the United States, where 18 of the 22 test sites had a significant and positive value for the dummy variable. A likely explanation for this is the difference found in the two education systems. The stability of the population parameter and the nonsignificant finding for the state capital dummy parameter means we can accept the second hypothesis.

The spatial competition parameter i s significantly negative at seven of the nine test sites. This means that the probability of recalling a city is less likely if it comes from a ’clustered’ environment full of other large cities

which overshadow it. Also, as expected, the mean of this parameter is less negative than for the US. test sites. An explanation for the nonsignificant result for St. John’s might be because of its relative isolation, though the nonsignificant estimate for Vancouver is more problematic to explain. There is no systematic geographic variation in the strength of the competition parameter. Even those locations close to a large US. city with an easy border crossing are not likely to possess such a disparity in experiential information contact as to develop significantly more complex hierarchies. The second hypothesis can therefore be accepted.

The standardized residuals generated by the models calibrated on the recall data sets were also analyzed. Cities that had a greater probability of being recalled by subjects from the United States beyond their population size, separating distance, and spatial competition included Las Vegas, Orlando, New Orleans, San Diego, and Cincinnati. A similar trend is found for the Canadian subjects, expecially with the recall of Las Vegas and Orlando. Presumably this is because of nonspatial con- nections: the subjects are all potential consumers, and these cities are permanent consumption points through their tourist associations.

Conclusion

A multivariate model was calibrated on a list of U.S. cities recalled by subjects at nine Canadian universities. The results of this model showed that there i s less locational variation in the recall of cities for Canadian subjects than there i s for subjects from the United States. The relative consistency found in the estimates for Popu- lation size, for Spatial Competition, and in the Adjusted R-Square suggests a more ‘similar’ knowledge surface for all Canadians, independent of location. The one variation comes with the effect distance plays on the probability of recalling a city’s name. There was no relationship between the probability of recalling a city and separating distance to the city if the test site was not immediately accessible to a US. border city. However, the majority of the test sites that were located close to a major American border city displayed a significantly negative relationship between the probability of recall and separating distance, though the strength of this parameter was still lower that for test groups from the United States. One explanation for this could be the presence of accessibility ‘holes‘ in the cluster boundary between Canada and the United States. The boundary effect i s apparent for the other test sites and cannot be explained away simply by a lack of access routes into the United States. Indeed,

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60 Andrew Curtis

equally remote test sites in the United States study (such as Marquette in upper Michigan) still displayed a significant distance decay of information.

There was a positive relationship between the population size of a city and its probability of being recalled. The strength of this relationship is also greater than for similarly tested subjects from the United States. This could be the result of an increased reliance on spatial information gained through media mention. Canadian subjects, unlike their counterparts from the United States, do not have a tendency to favour the recall of state capitals, because of differences in early schooling prac- tices. The results for the Canadian subjects, except for those in Vancouver and the remotely located St. John’s, also support the hypothesis of hierarchical information processing. However, these hierarchies are less well de- fined than for their counterparts from the United States.

There is a need for further investigation into other aspatialsources that lead to the creation of the Canadian subjects’ knowledge surface. From the subjects’ written comments collected after the test, it became obvious how important sports associations were in the recall task. Indeed, Table 2 shows a recall ‘mistake‘ that was con- stantly made at all the test sites. New jersey is the only well-established hockey team to be named after a state and not a city. In a similar vein, it would be interesting to see the change in the results for Florida if the tests were to be repeated after a period of 10 years. Other ‘mistakes’ of likely sporting origin included Colorado, Minnesota, and New England. It would be interesting to see to what degree a spatial knowledge surface of the United States can be approximated by a Canadian test site’s local sporting connection.

There i s also a need for an investigation into the stability of these results over time. Curtis (1997) has found that recall lists taken at the same university at different time periods are indeed stable. This helps to justify this approach of investigating knowledge surfaces by using these types of recall lists. It would be prudent to extend this temporal testing to all the Canadian test sites to see whether they show the same degree of stability.

The use of university students provides a limited set of results for one particular cohort of society. This provides consistency in comparing results between test sites. However, the work needs to be extended to include the knowledge surfaces of other test cohorts, such as by different age or class structure.

Acknowledgments

G. Handcock (Memorial University of Newfoundland); J. Holmes

(Queen’s University); G.P. Kershaw (University of Alberta); A. Trenhaile (University of Windsor); R.H. Foster (University of Manitoba); R. Widdis (University of Regina); R.W. Butler (University of Western Ontario); P. Schaus for drafting Figure 1.

Notes

1 Thecomplete data set can be viewed at http://ww.wlu.ca/-wwwtcg. 2 instructions for administering the test.

Could you please make a Xerox of the enclosed sheet, or if you prefer, let the students use their own paper. Could you then ask the students to write down as many cities from the continental United States as possible. After 15 minutes have passed, please stop them. Please don’t tell the students how long they will have for this test, as this may change how they recall information.

Before the test starts could you ask the students to write the state identifier next to each city in order to help me discern which city they are thinking about. It should be stressed, though, that this is not important. If they don’t know which state it is in, then just write down the city name.

At the end of test, could you ask the students to write down their age, their sex, and in which cities they’ve lived during the last 10 years. Could you also ask them to write down any comments they have as to how they approached the taskof recalling cities (e.g., Did they use any system or order?). Ideally, I am looking for 40 students from the host state - but I will take whatever size of class you are able to perform the test on.

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Submitted 08 / 96; Revised 06 / 97; Accepted 0 7 / 97

PHILIP 1 . STOOKE Department of Geography, University of Western Ontario, London, Ontario, Canada N6A 5C2 (ernail: [email protected])

MAPPING WORLDS WITH IRREGULAR SHAPES

Near-spherical worlds may be mapped using conventional techniques, but many solar system objects with diameters less than 500 km have very irregular shapes and pose special problems for cartographers. I describe the history and current status of exploration and mapping of these bodies with emphasis on cartographic problems, their solutions, and unusual cases requiring novel approaches to mapping. These include binary and multi- lobed objects, and faceted shapes for which near-global maps may be simultaneously equivalent and conformal.

Keywords: cartography, geodesy, map projections, planets, space exploration

On peut faire des cartes de corps celestes qui ont une forme presque spherique en utilisant des techniques conventionnelles, mais la plupart des petits corps ce‘lestes (diamstre de moins de 500 km) sont loin d6tre spheriques et pr4sentent des problemes particuliers pour les cartographes. Je discute de I’histoire et de I’etat actuel de /’exploration et de la cartographie de ces corps

The Canadian Geographer/ Le Cbgraphe canadien 42, no 1 (1998) 61-78 @/ 1998 Canadian Association of Geographers/ L’Association canadienne des geographes

comparisons in the spatial knowledge surfaces of subjects from canada and the united states

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