Limited geospatiotemporal data (e.g. data about the income of people in Amsterdam in 2010)

Transcription

1 several geospatial references are called geospatial data, while data with several temporal references are called temporal data (Table 5-3). An example of geospatial data is data about the number of inhabitants per country in These data have multiple geospatial references ( Spain, Russia, India, Mexico, etc.) and one temporal reference ( 2002 ). An example of temporal data is data about the precipitation per month in Amsterdam. The temporal references are January, February, March, etc.). The data also has one geospatial reference ( Amsterdam ). Data with several geospatial and temporal references are called geospatiotemporal data. An example is data about outbreaks of Avian Flu in the world between 2003 and A point of discussion may be data about the world around us with only one geospatial reference and only one temporal reference, for example: data about the income of people in Amsterdam in 2010; or a photo taken at a certain location and certain moment in time. These data are hereby called limited geospatiotemporal data. In this dissertation, the term geodata is used to refer to data with at least one geospatial reference. So, geodata includes limited geospatiotemporal data, spatial data, temporal data, and geospatiotemporal data. Next to data with one or more geospatial and temporal references, there is also data without geospatial or temporal references: non-geospatiotemporal data. An example is data about the lifespan of a set of batteries. In this case, the location on Earth where the data are collected and the moment in time when the data are collected do not matter. It must be noted that some data are spatial but not geospatial. For example, when physicists study a mechanical system, they use a local coordinate system such as the table on which the system is set up. Such a system could be studied everywhere on Earth. The location of the table does not matter, and the local coordinate system is not linked to geographic coordinate systems. Geographers, on the other hand, use geographic coordinate systems when they collect and use geodata in order to study the characteristics, structures, organization and functioning of, or problems in, the world around us. Table 5-3: The different types of data about the world around us 0 temporal references 1 temporal reference >1 temporal references 0 geospatial reference 1 geospatial reference >1 geospatial references Non-geospatiotemporal data (e.g. data about the lifespan of a set of batteries) Limited geospatiotemporal data (e.g. data about the income of people in Amsterdam in 2010) Temporal data (e.g. data about the precipitation per month in Amsterdam) geodata Geospatial data (e.g. data about the number of inhabitants per Member State of the European Union in 2002) Geospatiotemporal data (e.g. data about the occurrence of outbreaks of Avian Flu in the world between 2003 and 2009) Anselin (1989) argued that geospatial data display two general properties: (1) spatial heterogeneity; and (2) spatial dependency. This means that: (1) the values of properties show specific distributions in space; and (2) the difference in the values of properties at various locations is related to the distance between those locations. 57

2 5.3 Geodata-based external representations about the world around us Geographers frequently use external visuospatial representations that are based on geodata when they study or communicate about the characteristics, functioning, or problems of the world around us. These geodata-based external representations about the world around us can be differentiated into statistical, temporal, and geospatial external representations (Table 5-4), depending on the type of data on which they are based, and the way these data are represented. Appendix F1 presents examples for every type of geodata-based external representation about the world around us. Table 5-4: Different types of geodata-based external representations about the world around us Type of data Non-geospatiotemporal Limited geospatiotemporal Geospatial Temporal Geospatiotemporal Statistical representation Temporal representation Geospatial representation Case-value dot plot Frequency dot plot Case-value bar chart Frequency bar chart Case-value pie chart Frequency pie chart Scatter plot Regression chart Temporal dot plot Temporal interval chart Temporal line chart Temporal bar chart True spatial model Map Cross-section Spatial dot plot Spatial line chart Spatial interval chart Maps are the most important kind of geodata-based external representation about the world around us used by geographers. The cartographic display of a map is determined by a number of things. First, it is determined by the extent, scale, and projection of the map. Second, it is 58

3 determined by the number of map layers and the order of those map layers. Third, it is determined by the type of the geodata in each map layer. It depends on the kind of map layer (vector or raster). For vector map layers, it also depends on the type of elements (points, lines, or polygons), and the format of the attributes. Fourth, it is determined by the content of the geodata. For vector map layers, it depends on the number of elements, the spatial distribution of those elements, and the values of the attributes. Fifth, it is determined by the way the elements and their attributes are visualized: the symbology, the labelling, and the transparency. The symbology shows the attribute geodata by means of varying the cartographic variables, which are the symbol type, symbol size, symbol orientation, colour, grey tone, or hatch (Ormeling and Van der Schans, 1997). Sixth and finally, it is determined by the layout of the map: the way map elements such as a scale bar, title, and legend are displayed in the map. Analogue maps have a fixed cartographic display. The display is determined by the producer of the map in such a way that communication of information is optimal. For digital maps in full GIS software, the user can adjust the cartographic display. 5.4 Knowledge about the world around us Two kinds of knowledge In order to be able to think geographically, one needs to have, among other things, knowledge about the meaning of geographic concepts, and knowledge about the world around us. Now follows a short description of the two types of knowledge. Bodies of verbal knowledge about the meaning of geographic concepts are called geographic definitions. There are two types. The first type of geographic definitions refers to bodies of knowledge in which different quantitative properties of a class are connected to each other. Examples are: The population density (of regions) is the population size (of those regions) divided by the surface area (of those regions) ; and The flood risk (in regions) is the chance of floods (in those regions) times the effect of floods (in those regions). The second type of geographic definitions refers to bodies of knowledge in which a qualitative property value is explained in terms of other property values. Examples are: A suburb is a type of neighbourhood that is far from the city centre, and has a large percentage of single-family dwellings ; and A Mediterranean climate is a type of climate with a hot and dry summer, and a wet and cool winter. Following the models of Baddeley and Hitch (1974) and Paivio (1971), knowledge about the world around us can have a visuospatial form or a verbal form. In this dissertation, the terms mental representations about the world around us and verbal knowledge about the world around us are used to refer to the two kinds of knowledge. Mental representations about the world around us are internal (in human memory) reflections of geodata-based external representations about the world around us. They can include all types mentioned in Table 5-4. Mental maps and mental photos are well-known mental representations about the world around us. Verbal knowledge about the world around us can often be subdivided into several bodies of verbal knowledge. Bodies of verbal knowledge that cannot be further subdivided are hereby called the primitive bodies of verbal knowledge. Five main types of primitive bodies of verbal knowledge were identified during the elaboration of the model for GIS-supported geographic 59

4 inquiry: (1) facts; (2) generalizations; (3) hierarchic definitions; (4) taxonomic definitions; and (5) rules. The structure of (integrated) bodies of verbal knowledge about the world around us can follow a sort of standard format. This standard format can be seen as the geographic grammar. The next section describes the content and structure of the different primitive bodies of verbal knowledge about the world around us The primitive bodies of verbal knowledge Facts Facts are hereby defined as bodies of verbal knowledge about the value of a property of entities (Figure 5-2). An example of a fact is: the Netherlands had an average winter temperature of 2 C in the 1990s. Facts always consist of the following components: (I) a subject; (II) a property name; (III) a property value; and (IV) a stamp. Facts about a quantitative property of an entity also contain (V) a property unit. In everyday language, people often do not make every component explicit. Facts may contain several entities, but the subject is the entity that is central. The stamp refers to the conditions for which the property values are true. This stamp can be an entity in itself. In the example, the subject is the Netherlands (a region) and the stamp is the 1990s (a time span). The property name is average winter temperature, the property value is 2, and the property unit is C. Facts with a stamp can often be transformed into facts in which the central entity and the entity in the stamp have switched position. For example, the fact in the example above can be transformed into the fact: The 1990s had an average winter temperature of 2 C in the Netherlands. In the new fact, the subject is the 1990s and the stamp is the Netherlands, but the property name, property value, and property unit stayed the same. The new and old fact have the same content and structure and can be seen as each other s equivalents. Figure 5-2: The structure of facts Fact Property Subject Property name (average winter temperature) Property value (2) Property unit ( C ) Stamp (1990s) Entity (the Netherlands) Example: The Netherlands had an average winter temperature of 2 C in the 1990s Note that the property value can contain an entity too. Table 5-5 presents examples of such facts. These facts can be converted into opposites, in which the entity in the subject and the entity in the property value have switched position. 60

5 Table 5-5: Examples of facts with a property value which contains an entity Examples of facts Subject Property Property value 1A 1B Amsterdam has more inhabitants than Utrecht Utrecht has less inhabitants than Amsterdam Amsterdam Number of inhabitants More than Utrecht Utrecht Number of inhabitants Less than Amsterdam 2A "Amsterdam is northwest of Utrecht Amsterdam Situation Northwest of Utrecht 2B Utrecht is southeast of Amsterdam Utrecht Situation Southeast of Amsterdam Facts can have four different standard formats: (1) a subject form; (2) a property name form; (3) property value form; and (4) a descriptive form. The subject is central in the first form. In the second and third form, respectively, the property name and property value are central. Descriptive versions of facts start with texts such as: There is... ; or There are. Table 5-6 presents examples of the four standard formats for facts with the same content. Table 5-6: Examples of the four standard formats for facts and generalizations Subject form Property name form Property value form Descriptive form Example of a fact The Netherlands had an average winter temperature of 2 C in the 1990s The average winter temperature in the Netherlands in the 1990s was 2 C 2 C was the average winter temperature in the Netherlands in the 1990s There was an average winter temperature of 2 C in the Netherlands in the 1990s Example of a generalization Countries in Africa generally had an average infant mortality rate of 80 deaths per 1000 newborns in 2006 The average infant mortality rate of countries in Africa was 80 deaths per 1000 newborns in deaths per 1000 newborns was the average infant mortality rate of countries in Africa in 2006 There were on average 80 deaths per 1000 newborns in countries in Africa in Generalizations Generalizations are hereby defined as bodies of verbal knowledge about the value of a property of classes or abstract entities (Figure 5-3). An example of a generalization is Countries in Africa had an average infant mortality rate of 80 deaths per 1000 newborns in Generalizations consist of (I) a subject; (II) a property name; and (III) a property value. If the property is a quantitative property, it also consists of (IV) a property unit. The subject of a generalization consists of a class. In the example above, the subject is countries in Africa in 2006, which is a class of countries (the closure class) with a spatial extent ( Africa ) and a temporal extent ( 2006 ). Generalizations can be converted to facts. The extent, or one of the extents, of the class of the generalization then becomes the central entity in the subject of the fact. The example of a generalization above can be transformed into the fact: Africa has countries with an average infant mortality rate of 80 deaths per 1000 newborns in Note that the property is now presence of countries with an average infant mortality rate of 80 deaths per 61

6 1000 newborns. The generalization and the fact have the same content, but have a different property and property value. They are seen as each other s opposites. Generalizations can have the same four standard formats as facts (see Table 5-6). Figure 5-3: The structure of generalizations about the property of a class (above), and generalizations about the property of an abstract entity (below) Generalization Property Subject Property name (average infact mortality rate) Property value (80) Property unit (deaths per 1000 newborns) Class (countries in Africa in 2006) Example: Countries in Africa had an average infant mortality rate of 80 deaths per 1000 newborns in 2006 Generalization Property Subject Property name (average infact mortality rate) Property value (80) Property unit (deaths per 1000 newborns) Abstract entity (a country in Africa) Example: A country in Africa generally has a high average infant mortality rate There are actually three main types of generalizations. The first kind of generalization refers to bodies of verbal knowledge about the number of members of a class, or the total value of a property for a class. Examples are,, respectively,: People in Argentina number in total 40 million in 2008 ; and People in the Netherlands spend in total! 43 billion on food in The second kind of generalization refers to bodies of verbal knowledge about the variability shown by a class in terms of property values, space, and/or time, in other words, generalizations about distributions. As there are seven kinds of distributions (see Table 5-1), there are also seven kinds of generalizations about distributions. The generalization about the infant mortality rate of African countries is an example of a generalization about a property distribution. The third kind of generalization refers to bodies of verbal knowledge about the properties of a class compared to the properties of another class. An example is: Countries with bad safety conditions generally have a larger outflow of refugees than countries with good safety conditions. The examples of generalizations above deal with the properties of classes. Statements about the properties of abstract entities are also called generalizations. Examples of such generalizations are: A country in Africa generally has a high average infant mortality rate and A country with bad safety conditions generally has a larger outflow of refugees than a country with good safety conditions Hierarchic definitions Bodies of verbal knowledge about the position of concrete entities, abstract entities, or classes in hierarchies (see Section 5.1) are hereby called hierarchic definitions. Examples of hierarchic 62

7 definitions about entities are, respectively, The Municipality of Amsterdam is part of the Province of North Holland ; A municipality is part of a province ; and Municipalities are part of provinces. Figure 5-4 shows the structure of hierarchic definitions. Figure 5-4: The structure of hierarchic definitions Hierarchic definition 2 Super-entity (the Netherlands) Hierarchic definition 1 Entity (Province of North Holland) Sub-entity (Municipality of Amsterdam) Examples: (1) The Municipality of Amsterdam is part of the Province of North Holland ; (2) The Province of North Holland is part of the Netherlands Hierarchic definition 2 Abstract super-entity (a country) Hierarchic definition 1 Examples: (1) A municipality is part of a province (2) A province is part of a country Abstract entity (a province) Abstract sub-entity (a municipality) Hierarchic definition 2 Super-class (countries) Hierarchic definition 1 Examples: (1) Municipalities are part of provinces (2) Provinces are part of countries Class (provinces) Sub-class (municipalities) Taxonomic definitions In this dissertation, bodies of verbal knowledge about the position of entities and classes in taxonomies (see Section 5.1) are called taxonomic definitions. An example of a taxonomic definition is: Albania is a low-income country. Figure 5-5 shows the structure of taxonomic definitions. 63

8 Figure 5-5: The structure of taxonomic definitions Taxonomic definition 2 Higher-order abstract entity (a country) Abstract entity (a low-income country) Taxonomic definition 1 Entity (Albania) Examples: (1) Albania is a low-income country (2) A low-income country is a country Higher-order class (countries) Taxonomic definition Class (low-income countries) Example: Low-income countries are countries Rules A rule is hereby defined as a body of verbal knowledge about the relationship between two phenomena (Figure 5-6). There are two types of rules: (1) rules about associations, and (2) rules about direct causal relationships. Rules about causal relationships contain knowledge about the direction of the influence. It is known whether phenomenon influences phenomenon Y or whether phenomenon Y influences phenomenon. Rules about associations, on the other hand, just say that phenomena and Y show a correlation. There are then five different possibilities: (1) phenomena and Y do not influence each other and the presence of an association is coincidental; (2A) phenomenon influences phenomenon Y directly or indirectly; (2B) phenomenon Y influences phenomenon directly or indirectly; (2A + 2B) phenomena and Y influence each other directly or indirectly; and (3) phenomena and Y are both influenced directly or indirectly by a third phenomenon. 64

9 Figure 5-6: The structure of rules Property A (the number of children) Property B (the number of primary schools) Rule Phenomenon A (the number of primary schools in neighbourhoods in The Hague) Class (neighbourhoods in The Hague) Phenomenon B (the number of primary schools in neighbourhoods in The Hague) Example: The number of primary schools (in neighbourhoods in The Hague) is associated with the number of children (in those neighbourhoods) Phenomenon A (the distribution of law firms in New York) Phenomenon B (the distribution of banks in New York) Rule Class A (law firms in New York) Class B (banks in New York) Example: The distribution of law firms in New York is associated with the distribution of banks in New York Rules about associations can have a standard format, hereby called the! form. Examples are: The spatial distribution of law firms in New York is associated with the spatial distribution of banks in New York ; and The spatial-property distribution of the population density (of places in China) is negatively associated with the spatial-property distribution of the elevation (of those places in China). As there are four types of relationships and three types of pseudo relationships (see Table 5-2, there are also four types of rules and three types of pseudo rules. The rule about the relationship between the spatial association between the distribution of law firms and banks is a rule about a Type-2 relationship, while the rule about the association between the population density and elevation is a rule about a Type-4 relationship. The classes in the rules are, respectively, law firms in New York and banks in New York, and places in China and places in China. In correct rules, the classes always have the same analysis level and the same aggregation level. A rule like: The spatial distribution of primary schools in The Hague is associated with the spatial-property distribution of the number of children of neighbourhoods in The Hague is, in fact, incorrect. The classes in the example of a rule, 65

10 respectively, primary schools in The Hague and neighbourhoods in The Hague, have different analysis units. It is better to express the relationship in the form of a Type-2 or Type-4 rule: The spatial distribution of primary schools in The Hague is associated with the spatial distribution of children in The Hague ; or The spatial-property distribution of the number of primary schools (in neighbourhoods in The Hague) is associated with the spatial-property distribution of the number of children (of neighbourhoods in The Hague). In everyday language, the components distribution shown by, class, over space, and over time are often not always made explicit. People generally say things like: The number of primary schools (in neighbourhoods in The Hague) is associated with the number of children (in those neighbourhoods in The Hague). Rules about causal relationships can have three standard formats: the!1 form, the!2 form, and the! form. Examples of the three forms of rules about causal relationships are: The population density (of places in China) is influenced by the elevation (of those places in China) ; The elevation (of places in China) influences the population density (of those places in China) ; and The higher the elevation (of places in China), the higher the population density (of those places in China). The! form can only be distinguished for Type-1, Type-4, Type-5, and Type-7 rules in which the properties are quantitative properties. For other relationships, only the!1 form and!2 form can be distinguished. Table 5-7 presents examples of! and! form rules. Table 5-7: Examples of rules!-form Rule "-form Rule Distribution 1 Distribution 2 The higher the latitude (at places), the lower the temperature (at those places) The higher the distance to the city centre (of neighbourhoods), the lower the average rent per square metre (in those neighbourhoods) The higher the change in population size (in cities), the higher the change in the need for housing (in those cities) The higher the amount of natural resources (in countries), the higher the per capita income (of those countries) <does not exist> The better the safety conditions (in countries), the lower the outflow of refugees (in those countries) The temperature (at places) is negatively associated with the latitude (at those places) The average rent per square metre (of neighbourhoods) is negatively associated with the distance to the city centre (of those neighbourhoods) The change in the need for housing (in cities) is positively associated with the change in population size (in those cities) The per capita income (of countries) is associated with the amount of natural resources (in those countries) The soil type (of regions in the Netherlands) is associated with the situation (of those regions in the Netherlands) The outflow of refugees (in countries) is negatively associated with the safety conditions (in those countries) property 'temperature' of the class 'places in the world' property 'square metre rent' of the class 'neighbourhoods' property 'change in the need for housing' of the class 'cities' property 'per capita income' of the class 'countries property 'soil type' of the class 'regions in the Netherlands property 'magnitude of the outflow of refugees' of the class 'countries' property 'latitude' of the class 'places in the world' property 'distance to the city centre' of the class 'neighbourhoods' property 'change in population size' of the class 'cities' property 'amount of natural resources' of the class 'countries property 'situation' of the class 'regions in the Netherlands property 'safety conditions' the class 'countries' 66

11 Table 5-7: Examples of rules (cont.)!-form Rule "-form Rule Distribution 1 Distribution 2 The better the safety conditions (in countries), the higher the inflow of refugees (in those countries) The higher the magnitude of the outflow of refugees (in countries), the higher the decrease in the number of inhabitants (in those countries) The higher the magnitude of the inflow of refugees (in countries), the higher the increase in the number of inhabitants (in those countries) The higher the average travel time (of flows of migrants between countries), the lower the magnitude (of those flows of migrants between countries) <does not exist> <does not exist> <does not exist> The higher the number of banks (in neighbourhoods in New York), the higher the number of law firms (in those neighbourhoods) The better the natural transportation possibilities (in regions in Europe), the higher the population density (in those regions in Europe) The higher the number of solar spots (of years), the higher air temperature (of those years) The inflow of refugees (in countries) is positively associated with the safety conditions (in those countries) The decrease in the number of inhabitants (in countries) is positively associated with the magnitude of the outflow of refugees (in those countries) The increase in the number of inhabitants (in countries) is positively associated with the magnitude of the inflow of refugees (in those countries) The magnitude (of flows of migrants between countries) is negatively associated with the average travel time (of those flows of migrants between countries) The spatial distribution of law firms in New York is associated with the spatial distribution of banks in New York The spatial distribution of large cities in Europe is associated with the spatial distribution of large rivers in Europe The occurrence of years with many solar spots is associated with the occurrence of years with a high air temperature The number of law firms (in neighbourhoods in New York) is positively associated with the number of banks (in those neighbourhoods in New York) The population density (in regions in Europe) is positively associated with the quality of the natural transportation possibilities (in those regions in Europe) The air temperature (of years) is related to the number of solar spots (of those years) property 'magnitude of the inflow of refugees' of the class 'countries' property 'change in population size' of the class 'countries' property 'change in population size' of the class 'countries' property 'magnitude' of the class 'flows of migrants between countries' Spatial distribution of the class Law firms in New York Spatial distribution of the class large cities in Europe Temporal distribution of the class years with solar spots property 'number of banks' of the class 'neighbourhoods in New York' property population density of the class regions in Europe property air temperature of the class years property 'safety conditions' of the class 'countries' property 'magnitude of the outflow of refugees' of the class 'countries' property 'magnitude of the inflow of refugees' of the class 'countries' property 'average travel time' of the class 'flows of migrants between countries' Spatial distribution of the class banks in New York Spatial distribution of the class large rivers in Europe Temporal distribution of the class years with a high air temperature property 'number of banks' of the law firms 'neighbourhoods in New York' property quality of natural transportation possibilities of the class regions property number of solar spots of the class years 67

12 Rules can contain information about the direction and strength of the relationship. However, rules do not contain information about the causal mechanism. They do not show why phenomenon influences phenomenon Y, or vice versa. Statements about causal relationships in which the causal mechanism is known are called interpretations about direct causal relationships. They consist of a rule and a body of verbal knowledge about the causal mechanism. Statements about phenomena that indirectly influence each other are called interpretations about indirect causal relationships. The structure and content of interpretations is discussed later on in Section Primitive key bodies of verbal knowledge and key concepts Altogether, more than 200 types of facts, generalizations, hierarchic definitions, taxonomic definitions, and rules were distinguished during the elaboration of the model for GIS-supported geographic inquiry. Every primitive body of verbal knowledge is connected to a key concept. The key concepts are organized in a taxonomy with five levels. At the highest level, there are four key concepts: property ; hierarchy ; taxonomy ; and relationship. These 1 st -order key concepts are connected to, respectively, facts and generalizations, hierarchic definitions, taxonomic definitions, and rules. The key concepts property and relationship more or less coincide with the main concept groups number and relationship distinguished by Abler et al. (1977). The main difference is that in this dissertation, the 2 nd -order key concept situation (see the example of a body of verbal knowledge Bombay is situated in India ) is assigned to the 1 st - order key concept property, and not under the 1 st -order key concept relationship, as this key concept is always connected to facts. Table 5-8 presents a summary of the list of key concepts (1 st - to 3 rd -order key concepts), and Appendix G presents the complete list (1 st - to 5 th -order key concepts). The appendix also presents examples for every key body of verbal knowledge, and analyses the structure and content of these examples in detail. 68

13 Table 5-8: Summary of the list of key concepts (KC) Key Concept Body of knowledge 1 st -order KC 2 nd -order KC 3 rd -order KC F G H T R Location in space* Location Location in time Location in space and time* Shape in space* Shape Shape in time Shape in space and time* Situation in Situation in space* space/time Situation in time Situation in space and time* Situation in a Situation in a spatial network* network Situation in a temporal network Situation in a social network Situation in a flow Situation in a spatial flow network * network Situation in a temporal flow network Situation in a social flow network Authentic property Field property Property Computed property Categorized property Classified property Summarized / aggregated property! Comparative property Cause & Effect property Evaluated property Predicted property Estimated property Inductively estimated property Deductively estimated property Frequency distribution Spatial distribution* Temporal distribution Distribution Spatial-property distribution* Temporal-property distribution Spatial-temporal distribution* Spatial-temporal-property distribution* Consistency To a summarized property To a relationship Spatial hierarchy* Hierarchy Temporal hierarchy Social hierarchy Taxonomy Association Relationship Causal relationship Interaction Note: F = fact; G = generalization; H = hierarchic def.; T = tax. def.; R = rule; * = spatial concept. 69

14 The list of key concepts shows a high degree of logic. For example, the 2 nd -order key concepts location, situation, shape can be differentiated in the same way for the dimension space and time (see Table 5-9). Spatial gradients and processes can also be seen as each other s equivalents. They are connected to, respectively, the 4 th -order key concepts change in space and change in time (Table 5-10). Table 5-9: Examples of facts (A) Examples of facts 1 st -order KC 2 nd -order KC 3 rd -order KC 4 th -order KC Amsterdam is located at N 4 53 E Property Location The Tsunami occurred on 26 December 2004 Property Location Rome is south of Milan Property Situation The Weichselian Glacial occurred later than the Saalien Glacial Property Shape The Polish coast is 500 km long Property Shape World War II lasted 6 years Property Shape Location in space Location in time Situation in space Situation in time Shape in space Shape in time Horizontal Date Direction Direction Length Length Table 5-10: Examples of facts (B) Examples of facts 1 st -order KC 2 nd -order KC 3 rd -order KC 4 th -order KC The elevation decreases between Delhi and Calcutta The population of New York increased between 1900 and 2000 Property Property Distribution Distribution Spatial-property distribution Temporal-property distribution Change in space Change in time Facts with the same property can often be connected to different key concepts. See for example the facts: Jordan had an increase in population of 250 thousand inhabitants in 2006 ; Jordan had an increase in population size of 4 per cent in 2006 ; Jordan had a larger increase in population size than Syria in 2006 ; and Jordan had an large increase in population size as a result of an inflow of refugees from Iraq in The property in these facts is increase in population size. The property values are, respectively, 250 thousand, 4 per cent, larger than Syria, large as a result of the inflow of refugees from Iraq. Table 5-11 shows the key concepts that are connected to these four facts. 70

15 Table 5-11: Examples of facts (C) Examples of facts 1 st -order KC 2 nd -order KC 3 rd -order KC 4 th -order KC Jordan had an increase in population of 250 thousand inhabitants in 2006 Jordan had an increase in population size of 4 per cent in 2006 Jordan had a larger increase in population size than Syria in 2006 Jordan had an increase in population size as a result of an inflow of refugees from Iraq in 2006 Property Property Property Property Computed property Computed property Comparative property Explanatory property Rate Rate Absolute change Relative change One third of the 3 rd -order key concepts have in space or spatial in their names, such as location in space and spatial distribution. These key concepts can be seen as typically spatial key concepts. Relationships between two property distributions in which one of the properties is connected to a spatial key concept are hereby called spatial relationships. Examples of rules about spatial relationships are: The increase in real estate prices (in regions) is influenced by the magnitude of the inflow of migrants (in those regions) ; and The average square metre rent (in neighbourhoods) is influenced by the distance to the city centre (of those neighbourhoods). In the first rule, the property increase in real estate prices is connected to the 2 nd -order nonspatial key concept change in time (process), and the property magnitude of the inflow of migrants is connected to the 2 nd order spatial key concept situation in a spatial flow network. In the second rule, the property average square meter rent is connected to the non-spatial 2 nd - order key concept internal property distribution and 3 rd -order key concept mean. The property distance to the city centre is connected to the 2 nd -order spatial key concept situation in space. Besides the relationships between two property distributions in which one of the properties is connected to a spatial key concept, also relationships between two spatial distributions can be seen as spatial relationships. So what is the difference between Van Westrhenen (1987) and this dissertation? Table 5-12 shows how the eight types of bodies of verbal knowledge distinguished by Van Westrhenen (1987) can be classified according to the classification scheme presented in this dissertation. 71

16 Table 5-12: Comparison between Van Westrhenen (1987) and this dissertation Van Westrhenen (1987) This dissertation Example of a body of verbal knowledge 1F Amsterdam has 800,000 inhabitants Type Type Key concepts 1 st -category factual knowledge 2F Amsterdam is a city 2 nd -category factual knowledge 3F Amsterdam has more inhabitants than Utrecht 4F There s a daily flow of 9,000 commuters from Amstelveen to Amsterdam 3 rd -category factual knowledge (taxonomic relationship) 4 th -category factual knowledge (dependency relationship) Fact! entity = Amsterdam! property = number of inhabitants! property value = 800,000 Taxonomic definition! entity = Amsterdam! class = cities Fact! entity = Amsterdam! property = number of inhabitants! property value = more than Utrecht Fact! entity = the flow of commuters from Amstelveen to Amsterdam! property = magnitude! property value = 12,000 1KC = Property 2KC = Aggregated property 3KC = Total value 1KC = Taxonomy 1KC = Property 2KC = Comparative property 1KC = Property 2KC = Aggregated property 3KC = Total value 1C Cities have many inhabitants 1 st -category conceptual knowledge 2C Cities are settlements 2 nd -category conceptual knowledge 3C Cities have more inhabitants than villages 4C The crime rate (in cities) is related to the number of inhabitants (in those cities) 3 rd -category conceptual knowledge (taxonomic relationship) 4 th -category conceptual knowledge (probabilistic/causal relationship Generalization! class = cities! property = number of inhabitants! property value = many Taxonomic definition! class = cities! higher-order class = settlements Generalization! class = cities! property = number of inhabitants! property value = more than villages Rule! phenomenon A = the crime rate (in cities)! phenomenon B = the number of inhabitant (in cities) 1KC = Property 2KC = Property distribution 3KC = Lower-order class with a high/low value 1KC = Taxonomy 1KC = Property 2KC = Comparative property 1KC = Relationship 2KC = Causal relationship 72

17 When we compare the two classification schemes, we can see that Van Westrhenen s (1987) classification scheme is not complete: it contains only a fraction of the key concepts distinguished in the classification scheme presented in this dissertation. Key concepts which are important in a regional-geographic approach, such as situation, are missing. Second, we can see that Van Westrhenen s (1987) classification scheme is not very consistent. For example, the bodies of verbal knowledge There s a daily flow of 9,000 commuters from Amstelveen to Amsterdam and The crime rate (in cities) is related to the number of inhabitants (in those cities) are both seen as bodies of verbal knowledge about relationships, although they have a completely different content and structure. According to the classification scheme presented in this dissertation, the first body of verbal knowledge about the world around us is a fact about the magnitude of a flow, while the second is a rule about a relationship between two phenomena. Also, Van Westrhenen does not distinguish between generalizations and rules, and does not distinguish hierarchic definitions. A third problem is that Van Westrhenen s (1987) classification scheme cannot be used to analyse the structure of every body of verbal knowledge about the world around us in detail. The figures about the structure of the different primitive bodies of verbal knowledge presented in this dissertation (see Figure 5-2, Figure 5-3, Figure 5-4, Figure 5-5, and Figure 5-6) do allow people to decompose verbal knowledge and classify every component. With the help of these figures, it is possible to turn knowledge to data Combinations of primitive bodies of verbal knowledge Primitive bodies of verbal knowledge about the world around us are often combined in one statement. For example, the statement London and Paris have a large number of inhabitants consists of two facts that are connected via an overlap in property: London has a large number of inhabitants and Paris has a large number of inhabitants. The statement Cape Town (South Africa) has a warm and dry summer consists of two facts that are connected via an overlap in subject: Cape Town (South Africa) has a warm summer and Cape Town (South Africa) has a dry summer. Hierarchic definitions can also be combined in one statement. The same applies to taxonomic definitions. Examples of such statements are, respectively, North Holland can be subdivided into, among other things, the Municipality of Amsterdam, the Municipality of Haarlem, and the Municipality of Alkmaar ; and Congo, Tanzania, Malawi, and Ghana can be assigned to the class poor countries. Statements about relationships in which two phenomena influence each other actually consist of two rules. An example is the statement: The number of primary schools (in neighbourhoods) and the number of children (in those neighbourhoods) influence each other. This combined rule consists of the rules: The number of primary schools (in neighbourhoods) influences the number of children (in those neighbourhoods) ; and The number of children (in neighbourhoods) influences the number of primary schools (in those neighbourhoods) Integrated verbal knowledge Facts, generalizations, hierarchic definitions, taxonomic definitions, and rules can be integrated into comparisons, interpretations, causal explanations, causal descriptions, predictions, evaluations, solutions to problems, and estimations. This section describes the structure of the different statements. 73

18 Comparisons Comparisons are statements about the difference or similarity in the value of a property between two entities or two classes. They consist of a combination of two facts or two generalizations. Examples of comparisons are: New York has 17 million inhabitants, while London has 10 million inhabitants ; and Countries with bad safety conditions generally have a large outflow of refugees, while countries with good safety conditions generally have a small outflow of refugees. Note that the body of verbal knowledge New York has more inhabitants than London is a fact, and that the body of verbal knowledge Countries with bad safety conditions generally have a larger outflow of refugees than countries with good safety conditions is a generalization. The first is a body of verbal knowledge about the property number of inhabitants of the entity New York, while the second is a body of verbal knowledge about the property outflow of refugees of the class countries with bad safety conditions. The property value in the fact and generalization are, respectively, larger than London and larger than for countries with good safety conditions. Knowledge about relationships can be expressed in the form of rules, but also in the form of comparisons or generalizations. For example, the relationship between the latitude (at places) and the temperature (at those places) can be expressed as: (comparison) Places at high latitudes generally have a low temperature, while places at low latitudes generally have a high temperature ; (generalization) Places at high latitudes generally have a lower temperature than places at low latitudes ; (!-form rule) Places at high latitudes generally have a lower temperature than places at low latitudes ; or (!-form rule) The temperature (at places) is negatively associated with the latitude (at those places). This does not count for Type-2, Type- 3, and Type-6 relationships. These types of relationships can only be expressed in the form of a generalization or!-form rule. Appendix I presents more examples of series of comparisons, generalizations, and rules about relationships Interpretations Interpretations about direct causal relationships describe the relationship between two phenomena and explain why there is a relationship. They consist of a rule and a body of verbal knowledge about the driving force behind the relationship (the causal mechanism). These interpretations can be differentiated into interpretations about direct deterministic causal relationships, and interpretations about direct probabilistic causal relationships. Interpretations about direct deterministic causal relationships express the belief that any state is predetermined by another state. An example is: The influx of solar radiation (at places) is determined by the aspect towards the sun (of those places) via the (simplified) mathematic law influx of solar radiation = cosine(aspect towards the sun) * radiation at 150 million km from the sun. The body of verbal knowledge about the driving force in statements about deterministic causal relationships often consist of mathematical, physical, or chemical knowledge. The body of verbal knowledge in the example of an interpretation consists of mathematical knowledge: The influx of solar radiation is the cosine of the aspect towards the sun times the radiation at 150 million km from the sun. Interpretations about direct probabilistic causal relationships express the belief that any state is likely to occur. These interpretations are often connected to the behaviour of humans and other actors. This behaviour is never completely predictable, as people have free will that permits 74

19 them to act according to their individual needs and means. However, when dealing with large classes of people, it is often possible to draw some generalizations. An example of an interpretation about a direct probabilistic causal relationship is: The demand for housing (in neighbourhoods) is influenced by the distance from the city centre (in those neighbourhoods), because many people prefer to live near the city centre. Note that we use is determined by in rules about deterministic relationships, and is influenced by in rules about probabilistic relationships. In statements about probabilistic causal relationships, the knowledge about the driving force usually consists of sociological, political, economic, or ecological knowledge. In the example of an interpretation, the body of verbal knowledge consists of sociological knowledge: People often prefer to live near the city centre. It is a generalization about the preference of the class people. Interpretations about indirect causal relationships consist of a series of two or more rules or interpretations about direct causal relationships. An example of such an interpretation is: The mean year temperature (at places) is determined by the influx of the solar radiation (at those places), which is determined by the aspect towards the sun (at those places), which is determined by the latitude (at those places). This statement consists of a series of three rules: (I) The mean year temperature (at places) is influenced by the influx of the solar radiation (at those places) ; (II) The influx of the solar radiation (at places) is influenced by the aspect towards the sun (at those places) ; and (III) The aspect towards the sun (at places) is influenced by the latitude (at those places) Causal explanations and causal descriptions Geographers generally distinguish between causal explanations, historic explanations, and functional explanations (Abler et al., 1977, p.371). Causal explanations try to explain why a property of an entity or class has a specific value. They usually consist of two facts or two generalizations and one or more rules. The fact or generalization that has to be explained is called the consequence. The fact or generalization that explains is called the antecedence. An example of such a causal explanation is: The neighbourhood Leidsche Rijn has a large number of primary schools because it has a large number of children, and the number of primary schools (in neighbourhoods) is influenced by the number of children (in those neighbourhoods). The consequence and antecedence in this explanation are, respectively, The neighbourhood Leidsche Rijn has a large number of primary schools and The neighbourhood Leidsche Rijn has a large number of children. The explanation consists of one rule: The number of primary schools (in neighbourhoods) is influenced by the number of children (in those neighbourhoods). Although not made explicit, one also needs a taxonomic definition to link the facts to the rule. In this case, one would need the taxonomic definition: Leidsche Rijn can be assigned to the class neighbourhoods. The example above is an example of an explanation in which the value of a property can be explained with a direct causal relationship. An example of an explanation in which the fact is explained with an indirect causal relationship is: Jordan had a large increase in real estate prices as a result of a large inflow of refugees from Iraq, because the change in real estate prices (in countries) is influenced by the change in population size (in those countries), and the change in population size (in countries) is influenced by the inflow of refugees (in those countries). This explanation contains two rules: The change in real estate prices (in countries) 75

20 is influenced by the change in population size (in those countries) ; and The change in population size (in countries) is influenced by the inflow of refugees (in those countries). Causal explanations can be converted into statements that describe how a property of an entity results in another property of that entity. They consist of a consequence and an antecence, just like causal explanations, but they have a different position. Examples of causal descriptions are: The neighbourhood Leidsche Rijn has a large number of children, which explains the large number of primary schools, as the number of primary schools (in neighbourhoods) is influenced by the number of children (in those neighbourhoods) ; and Jordan had a large inflow of refugees from Iraq in 2006, which resulted in a large increase in population size. Explanations in which the value of a property of an entity or class is an obvious cause-andeffect of the value of another property can be converted to a fact. For example, the explanation above can be converted to: Jordan had a increase in population size in 2006 as a result of a large inflow of refugees from Iraq. In everyday language, people are more likely to use property versions: The inflow of refugees from Iraq resulted in a increase in population size in Jordan in Predictions, evaluations, solutions, and estimations Predictions are statements about how the value of a property of an entity or class will develop in the future. They have the same structure as causal explanations, which can actually be seen as postdictions. An example of a prediction is: Cambodia will have a decrease in infant mortality rate in the near future, because it will have an increase in the accessibility to health care in the near future, and the infant mortality rate (in countries) is influenced by the accessibility of health care (in those countries). The antecedence is: Cambodia will have an increase in the accessibility to health care in the near future ; and the consequence is Cambodia will have a decrease in the infant mortality rate in the near future. Evaluations are statements about whether a value of a property of an entity or a specific event is desirable or not for a specific actor. An example of an evaluation is: The dike enforcement programme is a bad thing for the people who have a house on the dike, because the dike enforcement programme implies that the houses on the dike have to be dismantled, and dismantling of people s houses is sad for those people. Solutions are statements about how the value of a property of an entity or class could be changed. An example of a solution is: The high infant mortality rate of Cambodia could be decreased by making health care more accessible for poor people, as the infant mortality rate (in countries) is influenced by the accessibility to health care (in those countries). This statement consists of two facts and a rule. There are two types of estimations: (1) estimations about the property value of an entity; and (2) estimations about the property value of a class. An example of the first type is: Nigeria (probably) has a low per capita income, based on the taxonomic definition that Nigeria is an African country, and the generalization that African countries generally have a low per capita income. This estimation consists of a fact, a taxonomic definition, and a generalization about the summarized property of a class. Another example of the first kind of estimations is: Congo (probably) has a high per capita income, based on the fact that it has a large amount of natural resources, and the rule that the per capita income (in countries) is positively related to the 76