Numbers Aren't Nasty: a Workbook of Spatial Concepts
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Numbers aren’t nasty: a workbook of spatial concepts David J. Unwin Emeritus Professor in Geography Birkbeck London University of London 2010 Table of Contents Acknowledgment 5 Copyright and intellectual property 6 Chapter 1, Purpose and Motivations develops a scheme for spatial concepts and then discusses the educational use of the workbook. 1.1 Introduction: 7 What is spatial literacy and what is a spatial concept? Developing a schema 1.2 Educational challenges and structure 19 1.3 References 24 Chapter 2, Location, Spaces and Distance deals with the spatial primitives of location, distance, space and projection/reference frame together with the standard geometric classification of objects. 2.1 Aims and Introduction 27 2.2 Exercise (1): Location - where do you live, and what do you live in or on? 27 2.3 Exercise (2): Scale and representation 30 2.4 Exercise (3): Adjacency and relations between elements of a set 33 2.5 Exercise (4): Conceptions of distance 37 2.6 Exercise (5): Some complications with ‘distance’ 39 2.7 Exercise (6): Projection and location 43 2.8 Exercise (7): Transforming locations 46 2.9 References 48 Chapter 3, Patterns of Point Objects, provides exercises mostly based in the CRIMESTAT package that explore second order concepts such as dispersion, density and pattern using as it examples point located objects. 3.1 Introduction 50 3.2 Exercise (8): Dotting the map 51 3.3 Exercise (9): Drawing your own pin map 54 3.4 Exercise (10): Proportionate symbol maps 59 3.5 Exercise (11): Centrography 62 3.6 Exercise (12): Nearest neighbor statistics 66 3.7 Exercise (13): Ripley’s K statistic 70 2 3.8 Further Exercises: Other things you can do with Crimestat III 75 3.9 References 76 Chapter 4, Lines on maps, looks at line objects and the associated concepts of length, direction and connection. 4.1 Introduction 77 4.2 Exercise (14): Lines on maps 78 4.3 Exercise (15): Measuring length 80 4.4 Exercise (16): Fractals 83 4.5 Exercise (17): Direction 87 4.6 Exercise (18): Analyzing tree networks 92 4.7 Exercise (19): Analyzing networks 96 4.8 References 100 Chapter 5, Area: the devil’s variable? Explores the idea of area and uses the OpenGeoda™ package to produce maps and autocorrelation measures of the concept of ‘pattern’. 5.1 Introduction 102 5.2 Exercise (20): Types of areas on maps 103 5.3 Exercise (21): Colour maps for area objects 106 5.4 Exercise (22): Choropleth maps for area objects 109 5.5 Exercise (23): Measuring area 113 5.6 Exercise (24): What do we mean by ‘shape’? 117 5.7 Exercise (25): Mapping area data using OpenGeoDa™ 119 5.8 Exercise (26): Using OpenGeoDa™ to compute a spatial weights matrix 127 5.9 Exercise (27): Spatial autocorrelation and pattern 131 5.10 Exercise (28): Global spatial autocorrelation using OpenGeoDa™140 5.11 References 147 Chapter 6: Fields provides a series of exercises associated with self-defining continuous fields such as continuity, gradient and trend, making use of the 3DField and E (Z)-Kriging public domain packages. 6.1 Introduction 149 6.1 Exercise (29): Continuity and isolining a field 150 6.3 Exercise (30): Isolining by machine 156 6.4 Exercise (31): Visualizing fields 161 3 6.5 Exercise (32): Trends in fields 163 6.6 Exercise (33): Spatial structure and spatial interpolation by kriging 167 6.7 Exercise (34): Spatial structure from the semi-variogram models 175 6.8 References 179 Chapter 7: Taking it Further does not attempt to list all the resources that an instructor wishing to develop these exercise further might call in, since to do so would involve an enormously long list. Rather it provides pointers to some web sources that will in turn lead into these materials. 7.1 Introduction 180 7.2 General Geography and Geographic Information Science projects of relevance 180 7.3 Spatial concepts 182 7.4 Software used in the Workbook 183 7.5 Linked Resources: Data Files 185 4 Acknowledgement This Workbook collects together materials I have used over many years and in many different educational contexts. I am grateful to Dr. Nick Tate, University of Leicester for his suggestion that they could be gathered together under a heading of ‘spatial literacy’ and to the SPLINT initiative for the Fellowship that enabled me to do this. In preparation, I am grateful for additional discussion with Sarah Witham Bednarz, Chris Brunsdon, Jason Dykes, Nick Tate, and Harvey Miller. Students at Universities in Leicester, London, Hamilton (NZ), Christchurch, and Redlands together with those enrolled on my course for http://www.statistics.com have often unwittingly helped in the development of almost all the ideas and exercises that are presented. Some of the exercises aren’t possible without use of software created by Luc Anselin, Ned Levine, the team that created 3Dfield, and Jo Wood. Alex Szumski ‘road tested’ the exercises and checked the manuscript for typos and the like. Any remaining errors are of course entirely my own responsibility. I am grateful to Karl Grossner for permission to use Figure 1.1, to John Davis for permission to reference and use data (STRIAE and NOTREDAM) from his text Statistics and Data Analysis in Geology and to Wiley & Sons (New York) for permission to redraw and reuse my own figures 4.1, 4.3, 4.6, 5.4, 5.13, and 6.2 from O’Sullivan and Unwin (2003 & 2010) Geographic Information Analysis. David Unwin December 22nd 2010 5 Copyright and Intellectual Property In the post World Wide Web, e-learning, world, attribution of Copyright to materials such as those in this Workbook isn’t easy. There are ideas and possibly short sections of text that could be claimed by John Wiley & Sons, Birkbeck London, University of Leicester, University of Redlands (USA), Karen K Kemp (with whom I worked in Redlands) and myself. As sponsors of the project that has assembled them and provided their raison d’etre in a spatial literacy context, the SPLINT Centre for Excellence in Teaching and Learning might well also lodge a claim. Where there might be doubt, I have indicated this by use of an appropriate qualifying phrase such as ‘source’ or ‘taken from.’ In this form and context these materials have been authored entirely by myself, so it is reasonable to claim them as © David J. Unwin (2010) and to assert the moral rights of authorship. They are made available under the understanding that they can be used in teaching and modified to suit local circumstances without and claim or charge provided that the source is recognized by the statement: These materials have been developed from the Workbook ‘Numbers aren’t Nasty’ assembled by David J. Unwin under the auspices of the (UK) Spatial Literacy in Teaching Initiative, (2010). Any repurposing for commercial gain is subject to the usual ‘all rights’ © claim given above. 6 Chapter 1: Purpose and Motivations 1.1 Introduction What is spatial literacy and what is a spatial concept? This little workbook provides a series of relatively simple, usually numerical or computer-based, exercises that together illustrate some of the basic spatial concepts whose mastery might be held to be a component of what has been termed spatial literacy. The exercises themselves have been drawn from experiences teaching geography at University level in a variety of institutions and have in most cases been tried and tested many times. A few are newly minted to fill some of the more obvious gaps in the coverage. In developing them I am aware that for those of a modern cultural-geographic persuasion the exercise, and the concerns to develop geography as ‘spatial science’ that they address, will seem both naive and irrelevant to the discipline as they define it. To compound this alleged sin the emphasis on numerical argument will also seem old- fashioned and, through some guilt-by-association argument, ‘positivist’. I do not accept either of these critiques. Following Gatrell (1983, page 7) I hope earnestly that the book will not be seen simply as ‘spatial science’, since I think the path charted here shows us that a concern for space transcends the artificial partitioning of geography into distinct research traditions and ultimately the artificial separation of disciplines in science. Work by psychologists (summarized in Golledge, 2002, page 3-4) seems to indicate that ‘geographers’ do ‘think differently’ from other academics, and suggests that this difference is characterized by an ability to reason about space and to represent its complexities graphically (mostly but not entirely by maps) in ways that are not matched elsewhere by any other discipline. I suggest that increasingly there is a need to include within the term ‘geographer’ not just those who have had the benefit of some instruction in the academic discipline, but also all those, scientists and the general public, who now routinely acquire and use spatial information through media such as GPS, GIS, satellite navigation systems, location based services, on-line mapping systems, virtual globes and even location-based games such as ‘geocaching’. All of these activities require individuals to demonstrate some measure of spatial literacy, which can be defined as the ability to think and act in any context that requires the recognition that location in space is important. Within this, spatial thinking has itself been defined by a group established by the (US) National Research Council (2006, page 12) as a collection of cognitive skills 7 comprised of knowing concepts of space, using tools of representation, and reasoning processes. These three abilities – knowing spatial concepts, representing them and reasoning from and about them - are not the same as what, in his Presidential Address to the Association of American Geographers, Golledge (2002) refers to as knowledge of space, which is the accumulation of facts about the spatial arrangement and interactions comprising human- environment relations.