Multidimensional geographic information science

Multidimensional Geographic Information Science

Multidimensional Geographic Information Science Jonathan Raper

London and New York

First published 2000 by Taylor & Francis 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Taylor & Francis Inc 29 West 35th Street, New York, NY 10001 Taylor & Francis is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledges’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” © 2000 Jonathan Raper All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Every effort has been made to ensure that the advice and information in this book is true and accurate at the time of going to press. However, neither the publisher nor the authors can accept any legal responsibility or liability for any errors or omissions that may be made. In case of drug administration, any medical procedure or the use of technical equipment mentioned within this book, you are strongly advised to consult the manufacturer’s guidelines. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Raper, Jonathan. Multidimensional geographic information science/Jonathan Raper. p. cm Includes bibliographical references (p. ). 1. Geographic information systems. 2. Spatial analysis (Statistics) I. Title. G70.212 .R367 2001 910'.285–dc21 00–062904 ISBN 0-203-30122-6 Master e-book ISBN

ISBN 0-203-35194-0 (Adobe eReader Format) ISBN 0-7484-0506-2 (Print Edition)—ISBN 0-7484-0507-0 (pbk.)

Publisher’s Note This book has been prepared from camera-ready copy provided by the author.

Contents

List of figures List of tables List of plates Acknowledgements Preface

PART I 1 2 3 4 5

The worldview of geographic information science Two-dimensional representations of space Multidimensional representations of space and time Multidimensional geo-representations for modelling Multidimensional geo-representations for exploration

PART II 6 7 8 9 10

vii ix x xii xvii 1 3 31 84 120 172 201

Hypermedia geo-representations for coastal management Geo-representation of dynamic coastal geo-phenomena Geo-representations of coastal change using virtual environments Three-dimensional modelling of coastal landforms Multidimensional geo-representation in coastal environments

205 212 218 224 232

References Index

250 293

List of figures 1.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 5.1 5.2 5.3 5.4 II.1

Construction of a world view Naïve geography and scientific geography trajectories through life The four conceptual spaces of Couclelis (1992a) How the Puluwatan navigate using the ETAK system—the reference point is an island which is lined up with a series of stars Axial lines drawn through convex urban spaces for part of Lisbon How rural village land can be consolidated by rebuilding houses and merging plots through land reform How Eratosthenes calculated the earth’s circumference Conic sections Topographic features required by map users Platonic solids Improvements in timekeeping Tissot’s Indicatrix and graticule for the orthographic projection Light cones and world lines Conceptualising identity Spatial processes Definitions of topological terms Geometric objects in pointset topology Coordinatised Euclidean geometry Geo-representation using rasters Parametric solids A classification of 3D data structures Octree encoding Simplices Three-dimensional tetrahedronisations are not unique A taxonomy of three-dimensional spatial functions Space-time prism Georeferencing video imagery VRML coordinate space Scheme of links between information elements and abstractions in a Hypertext application Latencies in a monitoring system Location of Scolt Head Island and other sites in Part II

6 37 39 54 55 60 64 65 72 89 93 95 100 122 124 133 134 141 143 145 148 149 151 152 160 166 175 178 186 192 201

II.2 Map of Scolt Head Island 6.1 The time-space diagram in the SMP 6.2 The use of the SMPviewer for the extraction of geographic information from imagery 7.1 Wave orthogonal mapping at Far Point on Scolt Head Island 7.2 Space-time path for two days surveying the Far Points spits on Scolt Head Island in March 2000 8.1 Scolt Head Island Far Point spits in a gallery in the Virtual GIS Room with the currently selected model displayed on the viewing table 9.1 The sedimentary logs of the recovered core for the south Privet Hill site 10.1 Two spit cross sections at the same spatial location but one month apart

203 207 208 213 215 220 226 235

List of tables 1.1 Hempel’s four modes of scientific explanation 13 2.1 A model of spaces and scales 45 2.2 Some examples of user language for space with regard to land and mining 78 surveying practice 127 4.1 Space-time structures supporting geo-representations 4.2 Generic spatial query and analysis functions in three-dimensional modelling and 158 their effectiveness under different data structures 226 9.1 Sieve aperture sizes used in mm (upper row) and phi ( ) (lower row)

List of plates (Between pages 236 and 247) 6.1 The 1:50,000 scale Ordnance Survey topographic map of the North Norfolk coast around Brancaster in Arcview GIS, overlaid with the <5m elevation flood hazard zone on the mainland, aerial photographs points representing the location of photographic images 6.2 An SQL connect operation using Open Database Connectivity (ODBC) in Arcview GIS, which links to a table in Microsoft Access database containing geometric and attribute data for coastal landforms 6.3 The 1:50,000 scale Ordnance Survey topographic map of the North Norfolk coast around Brancaster loaded into Panoramap and overlaid with aerial photograph footprint 7.1 Four sequential video frames of breaking waves filmed from the air 7.2 A strip map made from aerial video imagery for the mouth of the Ore River at Shingle Street in Suffolk 7.3 Surveys of elevation at Scolt Head since 1993 (label gives month and year of survey) 8.1 A hilltop view over the coastal plain showing Brancaster Staithe and Scolt Head Island (land on right hand side of the channel extending away from the viewer) 8.2 The equivalent ‘virtual’ view of the virtual geo-representation of Plate 8.1 made by draping a terrain model with a satellite image 8.3 VRGIS 1.0. The virtual world is displayed on the right with a moving aircraft and the terrain grid cell vertically below it being highlighted as it moves. The map on the left shows the track of the aircraft and its current position inside the yellow rectangle. 8.4 VRGIS 2.0 with controls for viewing and querying the virtual world and the map 8.5 Two surface models (with different geographical data coverage) of the Far Point spits for September 1993 and March 1994, shaded by elevation 8.6 The change of elevation between September 1993 and March 1994 for the Far Point elevation surfaces calculated using TIN techniques and visualised using a dichromatic legend palette from red (deposition) to blue (erosion) 8.7 Surface model of the sea wall and marsh south of Scolt Head Island, captured using laser surface-profiling LIDAR techniques and shaded for elevation. Data is copyright Environment Agency. 9.1 Three-dimensional minimum tension isosurface model of the spit section at the Privet Hill south site shaded by mean grain size phi ( ) units 9.2 Three-dimensional tetrahedra model of the spit section at the Privet Hill south site shaded by attribute ranges

10.1 Surface models showing coastal sedimentary landforms generated by SEDSIM experiments 10.2 The 15,000 superset of all data points collected for elevation surveys at Scolt Head over eight years

Acknowledgements Cover The book cover’s three-dimensional image courtesy of Simultec AG, Zurich, Switzerland.

Figures Figure 2.2 The four conceptual spaces of Couclelis (1992a) (Couclelis, Helen, ‘Location, Place, Region and Space’. From Geography’s Inner Worlds, ed. By Ronald F.Abler, Melvin G, Marcus, and Judy M.Olson. Copyright © 1992 by Rutgers, The State University. Reprinted by permission of Rutgers University Press. Figure 2.8 Topographic features required by map users (from Rhind 1991, after Smith 1979). Reproduced with permission from Walter Smith. Figure 3.2 Improvements in timekeeping. Reproduced by permission of Oxford University Press from Whitrow, G.J. Time in history, © 1988. Figure 3.3 Tissot’s Indicatrix and graticule for the orthographic projection (from the Projector program, courtesy of J.Wood) Figure 4.9 Octree encoding (from Lattuada 1998, courtesy R.Lattuada) Figure 4.11 Three-dimensional tetahedronisations are not unique (from Lattuada 1998, courtesy R.Lattuada) Figure 5.4 Latencies in a monitoring system (from McCarthy 1999, courtesy T.McCarthy)

Plates Plate 6.1 Reproduced by kind permission of Ordnance Survey © Crown Copyright NC/00/1136. The 1:50,000 scale topographic map of the North Norfolk coast around Brancaster in Arcview GIS overlaid with points representing photograph locations Plate 6.3 Reproduced by kind permission of Ordnance Survey © Crown Copyright NC/00/1136. The 1:50,000 scale topographic map of the North Norfolk coast around

Brancaster in Panoramap overlaid with orange points representing the location of photographic images, two of which are shown with their respective fields of view. Courtesy of the Virtual Field Course (J.Dykes). Plate 7.1 Four sequential video frames of breaking waves filmed from the air. Courtesy of Airborne Videography Ltd. Plate 7.2 A strip map made from aerial video imagery for the mouth of the Ore River at Shingle Street in Suffolk. Courtesy of Airborne Videography Ltd. Plate 8.7 Surface model of the sea wall and salt marsh south of Scolt Head Island, captured using laser surface-profiling LIDAR techniques and shaded for elevation. Data is copyright Environment Agency.

To Geraldine

Preface This book has been a long time in the making. The origins of the ideas in this book lie in 1990 when I attended a NATO-funded Advanced Study Institute in Las Navas del Marqués in Spain on ‘Cognitive and Linguistic Aspects of Geographic Space’, organised by Andrew Frank and David Mark. After a long gestation, I started to write the first draft in the spring of 1995 when on a term’s sabbatical leave from Birkbeck College, London. At that, time I thought I would simply update and expand my 1989 edited collection on three-dimensional GIS. However, despite my best efforts I was unable to finish the book before returning to Birkbeck after my sabbatical. Perhaps that was for the best, as over the course of the next year doubts began to grow that my 1995 book outline was the right one. I attended the NCGIA GIS and Environmental Modelling Conference in Santa Fe, New Mexico in January 1996 and I helped to organise the ESF-funded GISDATA meeting on ‘Spatial socio-economic units’ in Nafplion, Greece in May 1996, where new ‘multidimensional’ ideas took root. The rest is history. I dipped my toe in philosophy, I gathered material on spatial and temporal representation from many disciplines outside geography and informatics, and four years went by while I developed the new outline. I eventually began writing again in earnest in the summer of 1999 and I finished the manuscript in July 2000. Over its five years of development, this book has been written in a variety of places with help from many different people. During my 1995 sabbatical, I wrote substantial parts of the book at the Environmental Spatial Analysis Group (GASA) in the New University of Lisbon, and at the US National Center for Geographic Information and Analysis (NCGIA) in Santa Barbara. I would therefore like to thank Antonio Câmara of GASA and Mike Goodchild of NCGIA for their hospitality and support. I also wrote parts of the book at the Palacky University of Olomouc in the Czech Republic, at GISDATA conferences in Rostock, Nafplion and Strasbourg, at the NCGIA Initiative 21 meeting in San Antonio, at the NCGIA Varenius initiative on Discovering Geographic Knowledge and backstage at the Theatre on the Bay in Cape Town! Fittingly, given the location of the case studies in part II, some of the book has even been written in the Hut on Scolt Head Island! In a five-year book writing project, an author accumulates a large number of debts to individuals that I would like to acknowledge here. I have benefited especially from the advice of my former colleagues David Unwin, Richard Kelly and Diane Horn in the Department of Geography and Charlie Bristow in the Department of Geology, at Birkbeck College, and from my current colleagues in the Department of Information Science at City University, London, especially David Nicholas, lan Rowlands and Tamara Eisenschitz. In addition, the members of the Virtual Field Course project team Peter Fisher, Jo Wood, Alan Jenkins, Jason Dykes, Kate Moore, David Mountain, Timothy McCarthy and Nathan Williams have all given me a great deal of help and inspiration over the last five years. I am further indebted to my postgraduate students

including Rachael McDonnell, Eisa João, Rui Reis, Roman Krzanowsky, Roberto Lattuada, Maha Al-Faraj, Timothy McCarthy, Armanda Rodrigues and Roger Longhorn. A large number of colleagues around the world have given me advice and food for thought, including: David Rhind, Peter Burrough, Keith Turner, Art Paradis, John Harbaugh, Andrew Frank, Mike Goodchild, Antonio Câmara, Mike Worboys, Menno-Jan Kraak, Stan Openshaw, Doreen Massey, Myke Gluck, Josef Blat, Rui Gonçalves Henriques, David Mark, Tim Unwin, Nuno Neves, Nelson Neves, Robert Weibel, Alexandra Fonseca, Henk Scholten, Keith Riddell, Max Egenhofer, Mark Gahegan, Vit Vozelilek, Jürgen Broschart and Barry Smith. In addition Kim Styles, Melissa Currie, Paul Davies, Mark Smithard, Nick Fairfax, Sîan John, Claire Mellish, Eisa João, Andrew Thompson, Simon Lewis, Geraldine Garner, Sally-Ann Garner, Chris Garner, Nathan Williams, David Mountain, Tim Adams and Phil Raper have all endured the rigours of fieldwork on Scolt Head island, which has been facilitated by the successive wardens Colin Campbell, Mike Everitt and Mike Rooney. I would also like to thank Tina Scally and Geraldine Garner who drew a number of the diagrams, and Neil Hardie and Greg Eades who provided the desk on which the book was written at home. I have also benefited from the advice, good humour and supreme tolerance of my publisher Tony Moore whose patience I have sorely tested over the last five years. Finally, I would like to single out the particular help I have had from Roberto Casati who answered my philosophical questions and commented on the 1995 draft. I also wish to acknowledge the significant contribution that David Livingstone has made as a research colleague over the last decade to much of the work in this book. My wife Geraldine, parents, parents-in-law and my family at large have also made this book possible by tolerating my absences both physical and mental over the last few years. I would also like to pay tribute to my late grandfather William Pritchard who did not live to see this project completed. Their help has been invaluable, but the responsibility for what follows in mine, although music from Steve Allee, Sky, Focus, AfroCelt, Mike Oldfield, Urban Hype, Dimitri from Paris, Madredeus and sundry house music, may also be to blame! Jonathan Raper London October 2000 Links to work in this book can be found at the following web page: http://www.soi.city.ac.uk/~raper/

Part I INTRODUCTION This book is about representation—which is what happens when we attempt to make our concepts of the world concrete. Since much representation is explicitly grounded in space and time and referenced to the earth, ‘geo-representation’ is of interest to many disciplines, and may be foundational in many forms of knowledge. But precisely what drives ‘geo-representation’ is rarely articulated and few synoptic accounts are available. This book aims to fill that gap by reviewing the theory and developing some new applications. The book title ‘multidimensional geographic information science’ is intended to identify a new research area and to enlarge the scope of geo-representation from the limited two-dimensional perspective of many current geographic information systems (GIS), to the greater richness that three- and four-dimensional representation brings. Such limitations on representation in conventional GIS derive from the characteristics of maps, and yet maps are limited in this way due to their paper form. Multidimensional georepresentations can now escape the ‘flatland’ representational limitations of the twodimensional paper map and engage the user in a reflexive cycle of conceptualisation, representation, reflection and evaluation. Yet while our cognitive experience is powerfully four-dimensional we do not have many methodologies for designing multidimensional representations. This book aims to explore the potential of multidimensional representation by following the information lifecycle from conceptualisation to evaluation. This book can be read in different ways. For those who are familiar with GIS and who use them at present, I hope that this book will act as a critique of the current systems and their representational basis. While there is much that is valuable in current GIS and they will remain central to much work with geographic information, there are clearly new frontiers of representation which may not be found by extending the design of the current systems. For those who do not use GIS but who do use modelling tools that incorporate space and time (such as geoscientists, environmental scientists, anthropologists, economists and so on), some of the applications shown in the book may tempt them to look at the new generation of systems discussed below. This book can be read as a philosophical history of representations of space and time: this is the focus of chapters one and two. This book can also be read as a technical foundation for multidimensional representation: this is the focus of chapters three to five. In the last decade, there has been huge progress in the development of three-dimensional and four-dimensional GIS, which are surveyed here. Finally, part II of the book presents some case studies drawn from application of these techniques to geomorphology and

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environmental science in the area of coastal management. These can be read as indications of the potential of these techniques. Since the applications section presents original work in these fields that I, my research students and collaborators have carried out over the last decade, the selection of work included is restricted in scope. This book does not seek to present a comprehensive cross section of applications but instead aims to encourage others to rethink multidimensional representation and modelling in the context of their own research problems.

CHAPTER 1 The worldview of geographic information science FOUNDATIONS Definitions Geographic information science (GISc) is a new field of study that has emerged since the early 1990s. It is still developing rapidly and the scope of GISc research is in a state of flux. This youthful nature makes it important to define and contextualise GISc as a foundation for the knowledge claims being made by the discipline. This book is an attempt to develop a theoretical basis for GISc and to sketch out a manifesto for future research based on philosophical foundations. Setting out these foundations is the goal of this first chapter. The nature of GISc has changed subtly since its inception. Initially, GISc was seen as the theoretical context for the development of geographic information systems (GIS) in software. The term GISc was first used in the title of Goodchild’s (1992b) paper, in which he expressed a (foresighted) concern that users of GIS needed: ‘…to ensure that GIS, and spatial data handling technology, play their legitimate role in supporting those sciences for which geography is a significant key, or a significant source of insight, explanation and understanding’ (p32). In the late 1990’s new and more generic definitions of GISc have been proposed that go beyond the technological concerns of GIS and widen the disciplinary context beyond geography. Goodchild et al. (1999) defined GISc as follows: ‘Information science generally can be defined as the systematic study according to scientific principles of the nature and properties of information. GISc [is] the subset of information science that is about geographic information’ (p737) Goodchild et al. (1999) argued that both this information-oriented view and the earlier GIS software-oriented definition of GISc are valid and complementary, together defining an enduring GISc research agenda. Some researchers prefer the term ‘geocomputation’ to describe the connection of computation with space and time, especially in the formulation of models (Couclelis 1998). However, the geocomputation focus is more narrowly on GIS and modelling software issues, and it is mostly inductive in methodological terms (MacMillan 1998). Hence Openshaw (2000) described geocomputation as ‘the application of a computational science paradigm to study a wide range of problems in geographical and earth systems…contexts’ (p3). GISc remains free of these theoretical

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commitments. This book aims to attempt to develop a more holistic view of GISc than these earlier approaches that is not dependent either on geography as a disciplinary context, information as a commodity, or GIS as a software platform. The cornerstone of this view of GISc is the process and product of representation. The process of representation is defined here as the projection of the entities, relationships and processes of the conceptualised world onto symbolic ‘facsimile’ objects with their associations and transformations. Spatial representation is the simplest and most general process as it is based on a two-dimensional projection, whereas multidimensional representation is the more complex process as it uses three- and four-dimensional projections. When the product of representational processes is referenced to the earth as part of the projection process then the result can be termed a ‘geo-representation’. When a geo-representation incorporates three dimensions of space and/or one dimension of time, it can be referred to as a multidimensional geo-representation. This approach to GISc brings new areas of concern beyond the cartographic perspective typical of much GIS such as geographic ontology, spatio-temporal behaviour, socio-spatial theory, geographic information lifecycles, spatio-temporal metrics and multidimensional exploration. From this perspective, the high level issues in GISc are a concern with the conceptualisation of representation and the flow of information it generates. Such a view brings with it wider theoretical commitments, which are explored in this chapter. Discipline As a new area of research forged in the 1990s, GISc is a rapidly evolving collage of disciplines, methodologies, practices and technologies. In the disciplinary sense GISc has origins in geography, cartography, survey engineering, mathematics and computer science and has now engaged philosophers, cognitive scientists, psychologists, archaeologists, anthropologists and social theorists in its multidisciplinary research projects (e.g. the Varenius project, Goodchild et al. 1999). Methodologically GISc is for the most part self-consciously ‘neo-positivist’ in orientation but it has engaged in a dialogue with post-positivism; this book is a contribution to that debate. This chapter aims to show where GISc is situated within science and how it is integrated with it, given the wide-ranging critical examination that science has undergone in the last two decades. The ethical and professional practices of GISc are those belonging to geography and engineering, which are now fusing with computing, information science and social science; the recent commodification of geo-representations has introduced commercial practices. In technological terms GISc is both influencing and influenced by the ‘digital transition’ currently being experienced by developed societies (Pickles 1999b), whose information handling functions are now moving to employ digital technologies. In this environment ‘representation’ is being further changed by computation. GISc today is a dynamic and multidisciplinary framework rich in new opportunities for research. In a general sense this book aims to contextualise GISc as a contribution to the debate about the claims and insights that this new sub-discipline makes (chapters 1 and 2). In a specific sense, and working from this new methodological platform, it is argued

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here that the multidimensional nature of the new geo-representations being developed in GISc opens up some radically new theoretical perspectives (chapters 3, 4 and 5). The case studies in the second half of the book aim to illustrate the potential of the new georepresentations in conceptual, representational and informational terms.

THEORETICAL COMMITMENTS OF THE GISc WORLDVIEW The GISc worldview Research in GISc requires methodological and ethical self-awareness; without it the assumptions and commitments on which it is based remain unstated and unevaluated. Many of the insights that GISc claims to make can only be taken seriously by other disciplines and by the community at large, if a proper audit of these issues is carried out. Such an audit allows an internal consistency check on the thinking underlying GISc and allows a debate on unresolved issues. Typically, the assumptions and commitments of a discipline are inherited in part from the research programme to which it is most closely related. Since, axiomatically, GISc belongs to the science tradition it is first necessary to examine the science ‘worldview’ and contrast its position with the alternatives (chapter 1), before looking at the specific multidimensional issues in GISc (chapters 2 to 5). A worldview can be seen as a set of assumptions and commitments to which a ‘research programme’ subscribes (Kuhn 1962). A worldview must develop a set of positions on at least the following fundamental issues: • the theoretical grounding and conceptualisation of ‘world’ employed (metaphysics); • the methodology by which the contents of the conceptualised world are defined, ordered and signified (ontology); • the procedures by which knowledge of the conceptualised world is established and evaluated (epistemology); • the nature of human knowledge of the conceptualised world (philosophy of mind); • the nature of language and its role in communication and the construction of meaning (linguistics); • processes of cognition, the nature of intelligence and the functioning of the mind (cognitive science); and • the nature of computation employing symbolic and informational representations of human knowledge (informatics). Since representation in general is central to each of these questions, any view that GISc should be concerned with spatial and temporal representation, such as the one advanced in this book, requires an explicit consideration of the debates on representation. Figure 1.1 shows how metaphysics and ontology can provide a foundation for epistemology and how mind and language play a key role in cognition. Representation takes part in a reflexive relationship with cognition and epistemology. The methodological issues listed above are often difficult and unresolved, and are still fiercely debated. Since concepts of space and time have played an important part in the

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philosophical debates about these fundamental questions, it is argued here that geographic information scientists should contribute to these debates. It is also important to consider these issues further so that we may understand the ground on which GISc is being constructed, and what the alternatives are. Furthermore, some of the recent theoretical critiques of GISc (e.g. Pickles 1995) pose methodological challenges that can only be answered by reference to these issues, even if many of the critiques have focussed on technologies rather than the underlying discipline. In the current climate, not to expose your methodological and philosophical position on these issues risks a charge of research naivety or blind reliance on longstanding ‘norms’ when the original authors may even have abandoned them! Accordingly, these issues are reviewed and summarised in this chapter.

Figure 1.1 Construction of a worldview

Metaphysics Metaphysics originated with the ancient Greek philosopher Aristotle who regarded it as the study of ‘first causes’ (for him, ultimately God) (Loux 1998). Through the Middle Ages in Europe Aristotelian metaphysics underpinned the biblical view that the world was created by God with humankind playing a privileged part within it. As such the Church dictated that science could only reveal progressively more and more of that creation; alternative views were punished by the Inquisition. In the 15th century the observations and experiments of Copernicus and Kepler began to produce evidence that was inconsistent with the biblical account of creation by suggesting that the earth orbited the sun and not vice versa. If the earth orbited the sun as he thought, then it seemed inexplicable to Copernicus that there was no observed parallax with the light from the

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stars as the earth moved around the solar system. The observation suggested that the stars were at a vast distance from the earth, which was incompatible with the biblical scheme (Burtt 1932). In the 16th century, Galileo’s physical experiments showed that behaviour in nature, e.g. motion, could be described mathematically. He reasoned from this that phenomena, like motion, position, magnitude and number, were qualitatively different from the impressions they made on the senses. This implied that humankind was not part of the mathematical domain. To him this then implied that human beings were set apart from nature and that there might be an independent world external to the senses (‘Dialogues’, 1632). Since Galileo, one focus of metaphysics has been this relationship between the conceptualised world and human knowledge of it (often referred to as special metaphysics—Loux 1998). The origin of metaphysics can also be traced to Plato’s philosophy of categories in his ‘Parmenides’. In reasoning about possible philosophical inventories Plato argued that categories of things in the world could be defined by looking for their repeatable attributes (e.g. colour, shape), known as ‘universals’. Plato and Aristotle differed on the kinds of universals that they thought were possible. Plato allowed unexemplified (never existent) as well as exemplified universals in his scheme. Aristotle argued that this arrangement would require at least two separate worlds, and that this was unreasonable metaphysically. This debate founded the metaphysical study of the nature and structure of existence and being, specifically, questions of what kinds of things exist (often referred to as general metaphysics—Loux 1998). Questions of existence in and knowledge of the world were central to the philosophy of the 16th and 17th centuries. While Galileo’s conception of a separate mathematically defined external world defined a metaphysical position that came to be known as ‘materialism’ other views were proposed. Descartes argued that while the external world was ‘a vast plenum of matter and motion’ called the ‘res extensa’, there must also be a world of ‘unextended spirits’ called the ‘res cognitans’, a metaphysical position which became known as ‘dualism’ (‘Oeuvres’ 1637). In contrast, the philosopher (and bishop) Berkeley argued that there was no external world only a collection of experiences and ideas in the mind (Principles 1710), a metaphysical position known as ‘idealism’. Although to Berkeley the existence and concordance of such a mental world were due to God, Mill (1843) proposed a version of idealism in which the mental world was purely contingent, i.e. dependent on local circumstances (also known as ‘phenomenalism’). In other words, according to phenomenalists there is no order in experience, there is just a brute reality (Musgrave 1993). These early positions suggested that metaphysics was a choice between accepting that the external world was not accessible because it did not exist (and choosing idealism) or that it was accessible because it did exist (and choosing materialism or dualism). However, the philosopher Kant argued that while the external world does exist (accepting materialism), human minds do not have direct access to it. Kant suggested that human knowledge is produced by the interaction between the innate abilities of the mind and the sensory data being produced by the external world. Kant divided metaphysics into the ‘transcendental’ kind concerned with what lies beyond sensory experience and the ‘critical’ kind concerned with the most general structures in our thought about the world

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(Kant 1781). The means by which these ‘general structures in our thought’ could be investigated were termed ‘conceptual schemes’ by Kant and have become a focus of much contemporary research. In the 19th century metaphysics was criticised by positivists such as Comte (1830–42) and Mach (1883) who argued against the unobservable objects and untestable propositions of metaphysics. This view was further elaborated by the logical positivists of the Vienna Circle of the 1930s and even today by modern physicists such as van Fraassen (1980). Contemporary ‘neo-Kantian’ philosophers argue that whether or not the external world exists, it can only be accessed through conceptual schemes (Putnam 1990). This approach renders metaphysics unnecessary as the world is only approached through the language used in the conceptual scheme. Metaphysics is also criticised by postmodernists such as Lyotard (1985) who argue that science relies (unjustifiably) on metaphysics as a legitimation for its activities. Postmodernism argues instead that there are no universal truths and knowledge is specific to discourses taking place at certain times and places by certain people. In modern times these classical metaphysical positions have become ‘nuanced’ through sustained critiques and the development of diverse opinions on their meaning. Hence, idealism does not necessarily require a commitment to God as a source of experience and ideas in the mind; the 19th century German philosopher Hegel invoked the ‘geist’ or collective historical consciousness as a source. Idealism has largely been replaced by phenomenology in the 20th century, although some researchers maintain that the implications of quantum theory require idealism (Harrison and Dunham 1998). Materialism is regarded today as implying that the universe is deterministic, a claim that modern physics has called into question. Materialism has been largely replaced in science by a (metaphysical) realism that argues for an independent, indeterministic reality. There are some such as Putnam (1981) who argue that this does not necessarily confer a ‘God’s eye’ view on an external reality, as the sum total of the conceptual schemes is the reality. Today, much (most?) of science including GISc intrinsically supports metaphysics in general and within it, the realist position, as it allows a grounding of science in relation to an external world. The support of scientists is widespread despite criticisms of the realist position, even if the support is implicit and not usually articulated. Trigg (1993) argues that the realist position is still viable since the regularities in the world that science continues to successfully demonstrate show that there is indeed a structure to an external reality. To abandon this position in favour of idealism or phenomenalism would require us to pay a heavy theoretical price: • we have to argue that the immense complexity of the universe will be comprehensible by our minds since it is we who must create it; • the universe must be highly tuned to our existence with an ‘anthropic’ principle involved in its creation, as humankind could not have arisen by chance if we are actually creating it; • the world will be in some sense dependent upon our minds, and causal relations between the mind’s various elements cannot be maintained without a circularity of reasoning. Most (geographic information) scientists are not prepared to pay this price. They would

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prefer to live with the realisation of our insignificance in the universe and with the difficulties brought on by studying its frequently open and indeterministic nature with our limited knowledge. The implications of this position for GISc are subtle. If realism is accepted, then there is in fact a point to representation: it can succeed because correspondence with an external world is possible within the terms set for it by its creator (the ‘interested act’ of Harley 1989, 1990). If the representation coheres with the world through explanation, it may be capable of producing a generalisable regularity, which, in association with contingent events, can have significant value to understanding. If GISc can succeed in these terms then its purpose and insights cannot be denied per se, as some have claimed (Cuny 1998). It is argued here that realist metaphysics can provide a rational justification for scientific method as science claims truth by reference to reality and not by reference to itself (Trigg 1993). Hence, it is reasonable to believe that metaphysics and realism can survive the tests of their integrity and purpose posed by idealism and phenomenalism. However, the realist position cannot be accepted uncritically, and its acceptance should not be taken to suggest that a specific ontology and epistemology follow from it. Although it might be affirmed that there is an external world, human knowledge of it and the language used to speak about it, play an important role in underpinning action in that world. The world is much more than a constellation of objects as it involves discourses, identities and relations and these must find a place in the conception of world employed. Since knowledge and language are framed by concepts of space and time and they are increasingly represented as information, comprehensive accounts of nature and society require an ‘ecumenical’ perspective. Ontology The study of ontology is the methodology by which the contents of the conceptualised world are defined, ordered and signified; essentially, an ‘ontology’ is concerned with concepts of identity. The study of ontology can be traced to Plato’s study of categories as a philosophical inventory. Following Plato, ‘metaphysical realists’ argue that everything can be divided into ‘particulars’ (individual things), and ‘universals’ (repeatable phenomena). Universals can be further defined by their ‘properties’ (such as shape), the ‘kinds’ of which they are members (e.g. taxonomic group) and the ‘relations’ (e.g. topological) they enter into. Consequently, every particular can be said to ‘exemplify’ a set of universals. By contrast, ‘nominalists’ believe that there are no universals and that all properties are particular. The existence of repeatable ‘universals’ among things in the world is identified with an acceptance of implicit structure and regularity in that world. This implies that it is possible to create ontologies with a direct correspondence to these structures in an external reality. Ontologists search for conservative and logical methods to define such ontologies. Chisholm (1996) used a Pragmatic approach (see below) to divide things into the ‘necessary’ and the ‘contingent’ based on intentional, psychological, spatial, temporal and nomological criteria. In an alternative scheme Thomasson (1997) uses types of dependence on intentional states and spatio-temporal entities to create a decision-matrix for the classification of phenomena.

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Amongst ontologists, nominalists argue that phenomena are ontologically basic and do not depend on attributes. By contrast metaphysical realists give ontological accounts of identity that are either based on bundles of attributes, ‘bare’ substrata conferring identity, or ‘essences’. If identity is based on essences then Aristotelian essentialists argue that there are ‘natural kinds’ that confer identity upon phenomena. In geographic information science, Smith and Mark (1998) have argued that geographic kinds can be defined from a mereological actualist position (see chapter 2). In the 20th century some philosophers have added ‘propositions’ to the ontology of particulars and universals in order to encompass the abstract things we create by thinking, speaking and acting. These abstract things may be concrete with an existence at a specific place and time or they may be imaginary. Propositions can be defined as languageindependent assertions about these abstract things, which can be either true or false. For those who can’t accept that there are true propositions about things that don’t exist, it can be argued more simply in an alternative scheme that propositions are ‘properties’ of the more generic ‘states of affairs’, which can be either real or imaginary (Plantinga 1976). ‘States of affairs’ have been used to develop an ontology of information (Fox 1984). Since ontology is the means to discover the structures and generalities in reality that (metaphysical) realism predicts, ontology is a crucial part of the science worldview. By contrast, idealists such as Heidegger (1927) reject the ‘objectivist’ view that there are a set of categories to be discovered. They argue instead that ontology must be identified with the phenomenology of being. From this perspective entities emerge from social action rather than being given by the structure of the external world. Lakoff (1987) argued the case for an intermediate position, experientialism, in which realism is accepted but the process of developing an ontological catalogue of categories was highly embodied and metaphoric. Ontological methods should motivate the definition and classification of phenomena in scientific disciplines. Since most ontological schemes use spatial and temporal concepts, GISc often serves as an ontological precursor to the design or discovery of phenomena in scientific investigations. However, it is also easy to make ontological assumptions about what exists based on the set of phenomena that make up the ‘mesoscopic world’ of localised human experience. Much GISc is based on the use of commodified georepresentations like maps whose ontologies reflect an ‘interested’ view of one kind or another. The new generation of digital geo-representations now make it possible for each geographic information scientist to design their own ontologies for the task at hand. Epistemology Epistemology is the study of knowledge and is classically defined as justified, true belief (Musgrave 1993). Such a definition raises questions of how knowledge can be grounded, what standards for truth there are and how belief can be acquired. These questions are in turn dependent on attitudes towards metaphysics as a brief historical account will show. (Re) examination of these issues is critical for GISc in order to situate its methods in a wider context. The earliest epistemologists were the ancient Greeks who divided into the supporters of scepticism (we cannot know anything for certain and the choice between theories is

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arbitrary) and the majority view of dogmatism (we can know some things successfully). This ancient debate between (respectively) Socrates and Plato was later diminished by the successes of the dogmatists during the Renaissance in Europe. In the 17th century the views of the dogmatists became polarised into ‘rationalism’ which argued that some knowledge is innate to human beings (e.g. Descartes), and ‘empiricism’ which argued that all knowledge must ultimately be derived from sense experience (e.g. Locke). By the early 20th century empiricism had displaced rationalism and was driving science; more recently scepticism in a postmodern form has challenged dogmatism once more. The early critique of rationalism by empiricists such as Bacon in the early 17th century focussed on whether mathematical knowledge, for example, the geometry found in Euclid’s theorems was innate in the mind. Descartes attempted to defend this view by reference to the role of God ‘the first creator’ starting from his famous ‘I think, therefore, I am’ axiom. But this led him into a circularity of deductive reasoning and, with the reference to God, into metaphysical dualism. By contrast, Kant’s ‘Prolegomena’ in the late 18th century argued that innate knowledge is not knowledge of the world-in-itself but is indirect knowledge of the world embedded in a ‘conceptual scheme’. This led Kant into a form of metaphysical idealism since he suggests that our knowledge is not of the external world but instead of the world of ‘appearance’ in the conceptual scheme. In the 19th century, rationalism was severely tested by the discovery of new non-Euclidean geometries by Gauss and others, which showed that Euclidean geometry is not a privileged form of innate knowledge as the Rationalists had claimed. Rationalism was largely abandoned by the late 19th century but still provided further insights. The ‘Gestalt’ psychologists of the 1930s argued that cognitive processes could produce knowledge without experience (e.g. like that produced in certain optical illusions), and these ideas are still accepted. By contrast with rationalism, empiricism argued that the path to knowledge must be through the accumulation of sense experience and nothing else. Alternative empirical perspectives on sense data and our reasoning about it have been very important in the epistemology of the 19th and 20th century. The view that sense experience is the only path to knowledge was first stated comprehensively by Comte (1830–42) and became known as positivism. Positivism in Comte’s conception originally stood for the view that propositions could only be regarded as true or false if there was some way to settle their truth value. He regarded empirical sense experience as the only source of such truth values. In Comte’s view the development of positivism was the way to banish metaphysics, which at that time was seen as associated with rationalist epistemology or dualist theology. Positivist thinking played an important part in the physical discoveries in the late 19th century and early 20th century in which experimentation had a crucial role (Mach 1887). Comte’s positivism developed into the ‘logical positivism’ of the ‘Vienna Circle’ in the early to mid 20th century involving among others Schlick, Neurath, Carnap, Ayer and Wittgenstein. The logical positivists added a concern with logic, meaning and the analysis of language to Comte’s original set of positivist views. Today the term positivism is often used as a shorthand for the rationalist scientific method, i.e. empiricism and the instrumental power of authority, rather than the anti-metaphysical character of the original form defined by Comte (Hacking 1983).

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Empiricist epistemology argues that sense experience is the most important source of our belief since it supplies the raw material for reasoning. Since sense experience is primarily gathered through perception and held in memory these functions have been the focus of investigation in psychology from the late 19th century. Perception can be regarded as a means of belief justification, since the origin of the sense experience can be regarded as a cause of the belief, whether realist or phenomenalist in motivation. When belief is acquired through testimony from others the justification can be regarded as passing through a chain from the ultimate source. Memory can also be a source of belief: realists regard mental representations as the source, while phenomenalists account for memory by positing a transformation of present experiences using the imagination. Belief can also stem from consciousness: phenomenalists regard the source of this belief as pure introspection, while realists appeal to mental image-making (Kosslyn 1990). On the basis of ‘justified, true belief’ from any or all of these sources, minds can be seen as developing knowledge by various forms of inference. The critiques of empiricism have focussed on what can actually be learned from inductive reasoning on the basis of belief from sense experience. The earliest critique of induction was that of Hume in the mid 18th century who pointed out that knowledge of past occurrences does not necessarily lead to successful predictions of future ones using ‘induction’. He argued that inductive reasoning must, therefore be invalid and so irrational, even if widely used. Attempts to counter this critique have continued during the 20th century in three basic forms. Hume’s critique can first be denied by arguing that instead of reasoning inductively we should reason deductively and attempt to falsify: this is Popper’s ‘deductivist’ view (1959). Secondly, it can be argued that we can in fact reason validly using induction by building up confidence in our experience over time to increase our chance of correctness and verification: this is Carnap’s ‘probabilist’ view (Carnap 1950). Thirdly, Hume’s critique can also be denied by arguing that it is not in fact unreasonable to reason inductively since this approach can sometimes be valid: this is the ‘non-deductivism’ of Wittgenstein (Musgrave 1993). Note that by incorporating the critical realist model of perception (Collier 1994) in the deductive approach of Popper, the ‘critical rationalist’ (or fallibilist) approach to epistemology has been developed. Since critical rationalism accepts that both innate knowledge and experience are appropriate sources of hypotheses, this approach is a compromise between rationalism and empiricism. Another modern view is that ‘a result’ from an experiment and a general law can be combined to reconstruct the unobservable initial conditions through ‘abduction’ (Richards et al. 1998, Gahegan 2000). Epistemology also aims to give an account of causality, explanation and understanding, since they are integral to knowledge. Causality can be seen as a logical, linguistic or physical relation; according to Hume a physical relation involved ‘constant conjunction’. A causal relation of this kind requires that cause comes before effect, that the cause is spatio-temporally close to the effect and that the cause is always followed by the effect. Salmon (1998) characterised causality as a process that exhibits a conserved quantity such as momentum, energy or a charge, which has a four-dimensional spatio-temporal projection (hence objects are causal processes). A causal interaction takes place when there is an intersection of causal processes (understood in the four-dimensional sense) and an exchange of one of these conserved quantities. This connection between causal

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processes needs to be necessary and not just sufficient. In this conception it can be argued that causal connections can be discovered empirically as they are part of an external physical world, which consequently implies a materialist form of metaphysics. The key problem for this view is ‘action-at-a-distance’ where, under some conditions in quantum physics, sub-atomic particles possess information about other particles without them being in contact. Rescher (1991, 1992) gives an account of causality from the perspective of ‘conceptual’ idealism arguing that causation is part of our conceptual scheme through which we bring order to a formless world. In this conception real objects must be capable of being experienced, and being real means being causally active. The key problem for this view is breaking the circularity of reasoning involved between the conceptual scheme and the objects concerned. By contrast, explanation is a concept with a wider range of meanings encompassing science, morality and theology. Scientific explanations are causal in nature and attempt to deal with particular facts and general regularities in the world. Hempel (1965) set out the classical position: scientific explanations concern particular facts or general regularities and are based on universal or statistical laws. This yields four possible types of explanation (table 1.1): • Universal explanations of particular facts using the deductive-nomological (D-N) model, where given a set of premises the conclusion must logically follow (also known as the Covering Law model); • Universal explanations of general regularities using the D-N model involving the integration of all other appropriate D-N models; • Statistical explanations of particular facts using the inductive-statistical (I-S) model based upon statistical laws of a certain probability; • Statistical explanations of general regularities using the I-S model involving the integration of all other appropriate I-S models (the D-S model).

Table 1.1 Hempel’s four modes of scientific explanation

Universal laws

Statistical laws

Particular facts

1. Deductive-nomological (D-N)

3. Inductive-statistical (I-S)

General regularities

2. Deductive-nomological (D-N)

4. Deductive-statistical (D-S)

Each of these four forms of explanation has been challenged theoretically: the first on the grounds that deductive arguments are vulnerable to the falsity or irrelevance of the premises; the second and fourth on the grounds that the integration of explanatory models has proved very difficult and there are few good examples; and the third on the grounds that statistical laws must be epistemically relative i.e. true only by virtue of the current state of knowledge (Salmon 1998). Taking up a considered position on explanation also requires a view on determinism— the view that the universe is perfectly predictable. If the universe is deterministic (and closed) then knowing its entire state at one point in time means that theoretically, its state

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at any future time is logically entailed. Indeterminism argues that even given perfect knowledge, future states do not necessarily follow. When Newtonian mechanics was first accepted in the 18th century it was believed that only human failings prevented a proof of determinism, although Barman (1986) has since demonstrated that Newtonian mechanics is not intrinsically deterministic. By contrast, Einstein’s general theory of relativity is deterministic at the small scale of the earth but not necessarily on the larger scale of the universe, posing the problem of scale-dependency. The Heisenberg ‘uncertainty principle’ of quantum physics does not necessarily imply indeterminism: it says that either a particle’s position or momentum can be known and known deterministically, but both cannot be known with absolute precision. In other words making the measurement interferes with the phenomenon observed. Thus, quantum physics implies indeterminacy of knowledge but not indeterminism (Salmon 1998). The issue of whether human beings have free will has also been cited as a means of settling the debate on determinism. However, though determinism contradicts free will, indeterminism does not guarantee it: events will have chance causes which free will cannot alter. Therefore, in either case, free will could be an illusion. However, rationality must be incompatible with determinism as determinism implies that we will always be caused by the current state of the universe to hold the beliefs that we do. This would prevent us knowing the difference between when we are caused to be right and when we are right by virtue of a correspondence with an external world (Salmon 1998). These considerations show why a position on determinism is important to scientific explanation. If determinism is true then deductive methods using universal laws of type D-N are valid and our ability to use this approach to explain an event is only limited by a lack of information and precision about the world. If indeterminism is true then scientific explanation can still proceed using the D-S model by finding all the conditions that are relevant to the occurrence of an event and determining the probability of the event given a set of conditions. However, this view of indeterminism would imply that we could only know how the world works (at a particular level of probability up to 100%) rather than why. As the 21st century begins there are many competing approaches to the question of truth. The ‘scientific’ view that the ‘real’ external world is the ultimate standard for truth (realism sensu strictu) is opposed by the alternative view that truth is ‘constructed’ and therefore no overarching truth can be discovered (antirealism). Several roots to the antirealist view have already been mentioned, including the opposition to metaphysics in logical positivism and the arguments for conceptual schemes in idealism. However, there are further critiques of science in the antirealist account. During the late 19th and early 20th century the American ‘pragmatists’ Peirce, James and Dewey argued that truths were to be found in the stable conclusions of a community of enquirers. In this sense the world is made of texts and discourses. Dewey (1960) defined truth as ‘warranted assertion’ arguing that the context for a scientific statement should be the practices of the scientific method. Hence, facts and values are both important forms of knowledge and the external world has no privileged claims on truth. This view developed as a form of opposition to the extreme empiricism of the logical positivists. Pragmatism has been reduced to antirealism by Rorty (1979) who claimed that rationality is extrinsic: it is whatever we agree upon. Pragmatism has come to play an

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important role in the philosophy of meaning in language. Another form of antirealism, ‘relativism’, has its origins in work examining scientific method. Kuhn (1962) studied the nature of scientific progress arguing that much scientific work is actually tested not against empirical evidence but against the prevailing scientific opinion (or paradigm) in a process he termed ‘normal’ science. Kuhn further pointed out that paradigms were often incommensurable with each other making it hard to rationally justify moving from one to the other. This implied that the falsification required by Popper’s deductivist ‘critical rationalism’ (Popper 1959) was often lacking and that only truths that were consonant with the views of the scientifically powerful were incorporated into scientific knowledge. Popper’s (1970) reply to Kuhn and the other relativists claimed that ‘normal’ science was only applied science and that ‘critical science’ was the search for breakthroughs and radically new hypotheses. Despite Kuhn’s views, Popper’s ideas took on the status of the mainstream view of scientific methodology in the 1970s and 1980s. However, Sokal and Bricmont (1998) argue that Popper’s falsification approach contained some serious ambiguities, which has opened the way to a more sustained relativist critique. For example, they argue that Popper’s opposition to induction and verification under any circumstances leaves too much knowledge unnecessarily provisional. Sokal and Bricmont (1998) examine the claims of ‘epistemic relativism’ arguing that the critiques are either modern forms of scepticism (e.g. Latour 1987) or valid arguments which, however, fail to undermine rationality. For example, Feyerabend (1975) opposed rationality in the scientific method arguing that science is only one amongst several possible ideologies, but also made a penetrating critique of experimentation and measurement suggesting that theory-free observation is impossible. Another relativist, Lakatos, showed how science can constantly shift the domain of a theory’s applicability to avoid falsification (Lakatos 1976). The pragmatist philosopher Quine (1980) has argued that since falsification can be avoided in this way then this implies that science rests on practices of belief. This view can only be avoided by multiple independent falsifications (Sokal and Bricmont 1998). Quine has also argued that scientific theories are underdetermined, that is, that theories contain potentially infinite predictions while being based on only finite data. However, it can be argued that continual sets of independent experimentation can show whether the theory is sound, improving the probability of correctness with which it is associated (in the style of Carnap). Certain perspectives on cosmology have also led to antirealism. In the ‘strong anthropic principle’ of cosmology it is argued that the past and present structure of the universe is absolutely necessary for human beings to exist (Barrow 1990). This would imply that a ‘theory of everything’ might exist which physicists could discover. Such a view would make the universe dependent on us and anthropocentric in nature: this suggests an appeal to idealism. By contrast the ‘weak anthropic principle’ claims that there is a connection between our existence and the past and present structure of this universe…and that there may well be other universes which we cannot observe. If this is so then the right conditions for our existence may have come about by chance in this universe. Such a principle does not though explain human existence in itself. Anthropic principles suggest that human rationality may be linked to the nature of the universe. However, this link need not be causal as rationality could simply reflect the order we

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have discovered in the nature of things (Trigg 1993). In an alternative view to ‘justified, true belief, epistemology can also be defined as the study of procedures that give a reliable guide to truth. One view of epistemology, naturalism, argues that scientific explanations are the only kind there are, making them the only path to truth. By implication this approach denies metaphysics a role as a means to ‘ground’ science. Quine (1992) has argued that a ‘naturalised epistemology’ should be concerned not with what is ‘real’ but with what can be known, following Pragmatism. Explanation should focus on causality rather than justification in relation to an external world. This rejoins logical positivism in placing sense data at the heart of knowledge in a modern empiricism, but also opens the way to antirealism as it removes the connection between knowledge and the world. Putnam (1987) criticises the view that reality is to be identified with the discoveries of science (‘objectivism’) by linking this view with determinism, which has already been called into question. The strongest form of antirealism is the view that truth is constructed and never discovered; this is, in effect, a modern form of scepticism (Sokal and Bricmont 1998). This view has emerged from a sociological account that denies metaphysics, determinism, empiricism and pragmatism alike. In this view ‘reason, rationality and logic…reflect our acceptance of institutionalised practices’ (Woolgar 1988, p48) which are in turn socially bound. This has the effect of making truth an account of belief in its social context. It follows from this view that it is impossible to separate subject and object and that ‘representation’ is merely an ideology and not a correspondence between a concept and a part of the external world. The implication drawn by ‘social constructivists’ is that scientists produce knowledge rather than discover it. Therefore, knowledge is a social category and not an epistemological one. Hence, social constructivism brings power into the epistemological process. Trigg (1993) developed a powerful defence of (metaphysical) realism and rationality. He argued that antirealism is incoherent and ungrounded, and subject to a reflexive regress in its own assertions. If scientific knowledge is socially constructed then so are the critiques. He argues that the realist position does not imply an acceptance of determinism and empiricism but instead he argues that reality is merely determinate, as it is inherently ordered. Trigg argues that science needs metaphysics to provide an account of a reality in which claims to truth can be grounded. This view would bring science full circle back to the position before the positivism of Comte who criticised the claims of metaphysics as untestable against sense data. However, two centuries of scientific work that has produced observations of both distant stars and atomic particles as well as theories of relativity and quantum mechanics has now changed the terms of this debate making metaphysics more credible. To break up this classical dichotomy Bhaskar (1978) has offered a middle way between the extremes of realism and antirealism in his ‘critical realism’, where he argues that the ‘generative structures’ between reality and appearances should be the focus of explanation. How then can these debates be resolved? Realism argues that it has emerged from this sustained critique with its central concerns, such as rationality and an external reality, as a source for truth remaining intact. Yet antirealism argues that implicit acceptance of some elements of the critique (cf. Sokal and Bricmont 1998) must call all of science into question. Perhaps the only way to respond to these debates is to identify each position

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with their associated purpose—realism with nature and antirealism with humanity. It is also possible to characterise antirealism as reflective and realism as interventionist, as Hacking (1983) has argued. This view would imply that each view should cede a domain of applicability to the other. Collier (1994) suggests that the structuralist form of critical realism offers a solution to this enduring duality. In GISc many would agree that realist representation is an ideology associated with a desire to intervene in the world. Hence, Baudrillard (1983) argued that reality can be reflected, perverted, denied or invented in representation. The question is, can such interventions be emancipatory? This would imply that GISc must remain aware of the social dimensions of its representational ideologies and seek to work with social theory rather than attempting to dismiss it as Openshaw (1997) has done. Philosophy of mind Philosophy of mind descends from the study of special metaphysics (Loux 1998) and focuses on the nature of human knowledge of the conceptualised world. Until the 1950s positivist psychological research considered the mind to be a ‘nonobservable’ which could not be measured or studied. The dominant ‘behaviourist’ view of Watson (1919) and Skinner (1938, 1957) was that behaviours instantiated minds, and behaviour could only be studied through stimulus-response experimentation. However, the work of Chomsky (1957) on syntax in language founded a school of cognitive studies in linguistics and psychology that argued that the mind could in fact be studied through language and cognition. This raised the possibility of research on minds from a position of metaphysical realism in science. By contrast, within the idealist tradition, since the world exists purely in thought, the focus of research in this area in the 20th century concentrated on ‘being’ rather than mind. Both realism and idealism have given (largely) incommensurable accounts of mind and being. In the realist tradition the development of the ‘representational theory of mind’ (RTM) has provided a model of the nature and the functioning of the mind (Crane 1995). The RTM is based on the premise that thoughts (e.g. beliefs, desires, hopes and fears) and sensations (e.g. pains) are all mental states. Thoughts and sensations are also representational mental states if they are directed ‘at’ something, whether specifically or generally. Representational mental states that express attitudes to a situation such as conscious or unconscious thoughts like beliefs and desires (but not sensations) can be termed ‘prepositional attitudes’ after Russell (1921). The representational content of a propositional attitude is ‘what it concerns’; this formulation gives structure to the nature of thought in the philosophy of mind. Brentano (1874) argued that intentionality distinguished the mental from the physical, as physical phenomena are not directed at or ‘about’ anything by intention, while mental states are. Brentano’s intentionality thesis can also be used to form a distinction between thoughts and sensations in the way that they represent: thoughts are intentional with propositional structure, while sensations are non-propositional and only weakly intentional. Fodor (1998) argued that mental representations can exist without propositional attitudes, which can in turn exist without language. However, it is clear that intentional mental representations in the form of propositional attitudes (‘thoughts

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expressing an attitude to a situation’) are the key drivers of language and other expressions in the RTM. Once produced, language and expressions (e.g. art) represent to others using convention and resemblance through performance. A further question facing realists is how mental representations are connected with the world, the so-called ‘mind-body’ problem. There are two basic positions: in Descartes’ dualism, brains are separate from the mind, where the soul may also reside. In ‘physicalism’ minds and brains are one and the same; minds are just matter organised in a complex way. To some physicalists representation is the causal connection between the world and minds. This latter position would imply that a representation is in a causal relation with the world and that thoughts are causes (Fodor 1990). In this view a theory of representation can be found by reducing representational mental states to basic and atomistic ‘concepts’, in a view known as ‘reductionism’. Fodor (1998) argues that ‘concepts are mental particulars (which) satisfy whatever ontological conditions have to be met by things that function as mental cause and effects’ (p23). The alternative view is that concepts are ‘epistemic capacities’ (Dummett 1993); in other words concepts are truths acknowledged by communities of researchers. However, this reductionist and physicalist view has not succeeded in explaining how Brentano’s intentionality in mental representation can ever be in error (‘a thought that’s wrong’) if it is causal in nature. An alternative non-reductionist and physicalist view argues that representations form an abstract language of thought and that organisms including humans have mental states with representational content (Cummins 1989). This view suggests that representation is structured like computation without being in a causal chain with the rest of the world. A related issue concerns the way that we understand other minds. The behaviourist view has largely been supplanted by ‘common-sense psychology’, which argues that the mind constantly creates representations about the world and conjectures about ‘other minds’ and uses them in decisions about behaviour (Crane 1995). In the idealist tradition minds are equated with ‘being’, a view associated with Husserl (1913) and (especially) Heidegger (1927). This view rejects the realist account of mind arguing instead that it is impossible to separate the world and ‘being in that world’. Heidegger rejects the notion of mental representations arguing that they cannot unambiguously capture the essence of situations. Accordingly, he suggests that knowledge is invested in practices rather than entities: a key concept is that of ‘thrownness’—the kind of understanding that is effective when acting in some way. From this perspective ‘only as phenomenology, is ontology possible’ (Heidegger 1927, p60): entities emerge in the process of ‘breaking-down’ of concernful action when they become ‘present at hand’, and therefore explicit (i.e. things emerge by doing). Idealistic phenomenology gives a non-representational account of subjective qualities such as colour or smell (so-called ‘qualia’) which it is argued cannot be understood from any detached objective perspective. Philosophy of mind has developed important insights into mental states and how they are connected to the ‘world as conceptualised’ both through representation and phenomenology. In the realist tradition it has been shown that making representational models of an external world in the mind using an RTM is an activity that need not be committed to reductionism or naturalism. It has also given accounts of how concepts

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develop from representational mental states through intentionality, where realist and idealist accounts share some common ground. GISc can therefore be seen to be dealing with ‘conjectural’ representations of the world as conceptualised in the tradition of common-sense psychology. The challenge must lie in the exploration of intentionality in the development of concepts for GISc and in any possible relations with phenomenological accounts. Linguistics Linguistics is concerned with the nature of language and its role in communication and the construction of meaning. Before the 1950s behaviourist linguistics was concerned primarily with phonetics (sounds made in speech), phonology (sound variations important in context at syllable level), morphology (the structure of the language’s basic grammatical units) and syntax (the sentences and clauses). Semantics was regarded as a task of pragmatic epistemology outside linguistics by behaviourist researchers. The recognition of ‘deep syntax’ in language by Chomsky (1957) as evidence of a ‘generative’ grammar underlying language led to the development of a cognitive approach to linguistics. Chomsky suggested that a generative grammar capable of producing well-formed language is made up of rules. These rules would include: those for the generation of well-formed sentences with a noun and verb phrase structure; those for operation on phrase structure (e.g. to change from active to passive voice); and, those for pronunciation guidance. Chomsky (1965) argued that syntax can also relate language to semantics through correspondence rules, suggesting that the structure of language gives access to the nature of thought. Jackendoff (1983) argued that there is a single level of conceptual structure to representation at which all cognitive inputs (e.g. perception) and outputs (e.g. language) are compatible. This would imply that such a conceptual structure would subsume semantic structure within it, and rules of inference linking linguistic meaning to discourse (pragmatic epistemology) could operate on a conceptual structure directly. Jackendoff (1983) appeals to Kant’s conceptual schemes (cf. Putnam 1987) to provide a metaphysical underpinning to this argument and introduces a meta-language to distinguish ‘projected’ entities at the level of the conceptual structure from their equivalents in the external world. This makes the ontology of language dependent on the conceptual structure and the associated metaphysics. Pinker (1994) argued that language learning abilities demonstrated by the developmental psychology of children, studies of language impairment and comparative linguistics have together showed that language is an instinct, i.e. that it is innate. This evidence implies that the generative grammars proposed by Chomsky are built into the brain and that they instantiate language output driven by mental representations with the form of prepositional attitudes. This is a linguistic endorsement for the physicalist RTM and a rationalist epistemology, although it may suggest that mental concepts are gestalt rather than atomistic as reductionists such as Fodor argue. This view has recently been challenged by neuroscientists on the basis of experiments that show babies can recognise word boundaries from a stream of computer-generated sentences (Newport, Aslin and Saffran 1999). This may imply that children can learn language through statistical

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induction and inferential reasoning. These studies have all suggested that the structure of language is closely related to the structure of thought. Following work by Rosch (1973) challenging the classical view of linguistic categories based on natural kinds, Lakoff (1987) has argued that actual structure of categories found in language reveals a rich linguistic ontology with important implications for mental representation. Since the linguistic ontology that emerges from Lakoff’s ‘experientialism’ is embodied not abstract, metaphorical rather than symbolic, and gestalt rather than atomistic, he argues that cognitive models of thought should also be this way. In particular he argues that ‘basic-level’ linguistic categories can be identified that are intermediate in scale, maximally distinct, and that most attributes of categories are stored at this level. Similarly Johnson (1987) argued that perception is organised by kinaesthetic ‘image schemas’ based on metaphor. These views would imply that mental representations have a similar organisation to language and that experience is preconceptually structured by basic level structure (in gestalt perception, mental imagery and motor movement) and metaphoric ‘image schemas’ (e.g. part-whole, container). This approach is based on the ‘internal’ realism of Putnam (1975) which characterised realism as being concerned about objects as understood from the human perspective. Lakoff (1987) argues as a consequence that there is no universal and objective ontology in use and that meaning derives from meaningfulness in human experience. Linguistics has also been studied from the perspective of language as a communication process. Sperber and Wilson (1986) argued that the message-passing model of communication based on the semiotics of Saussure (1916) and Shannon and Weaver’s (1949) theory of communication has been unsuccessful and should be replaced by models based on inference. However, inferential models of language communication require contexts to convey meaning: hence a speaker expects a hearer to have the context necessary to recover meaning. In a model based on Grice (1957), Sperber and Wilson (1986) argue that meaning is conveyed: a) by the intention of a speaker to produce an effect in an audience; b) by the audience’s recognition of the speakers intention; and c) when the audience’s recognition is at least partly caused by the speakers intention. Focussing on the co-operation necessary to implement this approach suggests that speech should be economical, truthful, relevant and clear (Grice 1967). If the speaker obeys these principles the hearer does not need to select among alternative possible meanings as there will only be one possible interpretation. If there are any remaining ambiguities the hearer can make further inferences from the wider context (known as implicatures). Understanding the wider context of communication requires a characterisation of the ‘cognitive environment’ of both speakers and hearers. A cognitive environment is defined by Sperber and Wilson (1986) as information manifest to an individual by virtue of its effective representation in the environment. It can be argued that cognitive efficiency requires that only information that can change the representations in the cognitive environment is worth processing: this information is relevant information. Behaviour intended to change the cognitive environment of an individual is termed ‘ostension’. Sperber and Wilson’s (1986) approach to communication identified two ways to convey information about a state of affairs, firstly, direct evidence such as the language

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used (informative intention) and secondly, evidence of the intention to convey it (communicative intention). It can be argued that informative intention is behaviour intended to change the cognitive environment of an audience and that communicative intention is an attempt to make that intention ‘mutually manifest’. Sperber and Wilson (1986) argue that communication through language is focussed on identifying relevant information in a hearer’s cognitive environment so that meaning can be conveyed with the minimum of unnecessary inference. While Sperber and Wilson (1986) identified the conditions under which meaning can be communicated in an inferential process, Winograd and Flores (1986) argued that language is a form of social action with a goal of mutual orientation between speaker and hearer. Following Maturana (1978), Winograd and Flores (1986) argued that language is connotative (‘what we agree on’) rather than denotative (‘by reference to an external world’). In this conception, ‘speaking’ is a process of generating distinctions in a consensual domain; referring to ‘things’ in such language is an operational distinction and not an ontological claim. Habermas (1979, 1984) has also argued that language is a social process and that linguistic acts need to be understood as actions intended to bring about certain effects, principally agreement. In ‘communicative action’, to achieve agreement Habermas (1984) suggests that a speech act raises three validity claims, one for each of the knowledge-constitutive interests identified by Habermas (1978), which the hearer may accept or dispute: • truthfulness relative to ‘the’ world (empirical-analytic interest concerned with science); • sincerity, their motivation in terms of ‘their’ world (historical-hermeneutic interest concerned with meaning); • legitimacy, the moral, ethical and social attitude to ‘our’ world (critical interest concerned with emancipation). Winograd and Flores (1986) argue that an account of meaning can only be found by listening for these commitments in speech acts and then dealing with ‘breakdowns’ in the communicative action. The most controversial view of meaning in language can be found in the thesis of linguistic relativism advanced by Whorf (1956) when he argued that most languages have different and incommensurable conceptual systems. Whorf also argued that the nature of thought is determined by the categories in language (linguistic determinism), suggesting that each language had its own patterns of thought (and, therefore, potentially its own physics). Lakoff (1987) argues that Whorf’s relativistic incommensurability arguments have been refuted by finding various commensurable aspects of different languages. Pinker (1994) argues that the fundamental reason to reject Whorf s hypotheses is that the RTM has shown that there is a universal language of thought called ‘mentalese’ (see below). Research in linguistics has been influential in developing more sophisticated ontological models. Several quite distinct linguistic theories such as Jackendoff’s ‘conceptual structures’, Lakoff’s ‘image schemas’ and ‘basic level categories’ and Winograd and Flores’ ‘language distinctions’ suggest that ontologies are generated by cognition and language rather than received from the world. Furthermore, the work of

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Sperber and Wilson, and of Habermas have emphasised that the cognitive and social context is the key to sharing information in human communication. These accounts of language contain important pointers to GISc in its development of representations as they suggest that the objectivist view of ontology and communication provide cognitively poor drivers for representational acts. Work in linguistics also shows that the study of meaning cannot be extra-linguistic and must be grounded in language directly. There are deep implications for the development of representations intended to carry meaning that must be built into information design. Cognitive science Cognitive science is a new (inter) discipline that seeks to understand the processes of cognition, the functioning of the mind and the nature of intelligence (Simon 1980). The emergence of cognitive science in the late 1960s marked a break with the positivism of behaviourist psychology and linguistics (Machlup and Mansfield 1983). Cognitive science now focuses on the processes identified in the RTM, that is, perception, the formation of mental representations, thinking as inferencing and learning and the cognitive drivers for language. The study of cognition concerns the role of perception, that is, what we sense and how we sense it. When it is accepted that the cause of the perception is an object in the external world then this is an account based on a materialistic metaphysic. If the cause of the perception is considered to be mental in origin (requiring a commitment to idealistic metaphysics) then this is an account based on ‘phenomenalism’. There are also accounts of perception constructed on Kant’s ‘conceptual schemes’ such as Putnam (1975) that affirm the existence of an external world but argue that our access to it is experiential and not objectivist. There are two different accounts of what we perceive from the senses in the mind. The first (and oldest) account suggests that we perceive real world objects directly and immediately through ‘direct’ or ‘naïve’ realism. This account has been termed ‘sense perception’ by Dretske (1990) as it argues that we perceive objects in the mind by the way they appear to us. The alternative account suggests that we perceive objects indirectly via ‘reified’ (‘made real’) mental imagery (so-called ‘indirect’ realism). Dretske (1990) terms this ‘cognitive perception’ since we actually perceive classified mental imagery in the mind. Given the delivery of a perception, Gregory (1966) argues that we then reason about the perception to decide what it tells us—a view known as perceptual ‘constructivism’. This view is supported by the fact that perception has constancy i.e. that objects are still perceived as such from different angles and when moving, and that optical illusions can generate representations of external objects from limited geometric information. According to Gregory (1974) the sensory data used to create perceptual hypotheses about movement is derived from the relationship between the image-retina system (change in the retinal image) and the eye-head system (compensation for the scanning movement of the eyes). By contrast Gibson’s (1966) ‘direct theory of perceptual processing’ argues that the mind simply extracts from the perception, i.e. from the flow of imagery through sight and

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the acoustic environment in hearing. Gibson pointed out that change in the optical array on the retina over time (called the ‘optic flow’) generates linear perspective and motion parallax, which are directly available to the perceptual system. Such visual cues are also considered anthropologically important since ‘collision detection’ is a fundamental and important skill for human survival. Shoham (1988) suggested the inverse of this is i.e. that time invariants in a dynamic world had cognitive importance since they (in effect) highlighted that which is dynamic. Neisser (1976) synthesised the approach of Gregory and Gibson by suggesting that cognitive schema are used to guide inferences about sensory data (Gregory). Meanwhile objects unknown to the perceiver are evaluated from changes to the optical array (Gibson) and the information entered into the schema for future reference. Kosslyn (1980) studied mental imagery to attempt to falsify Pylyshyn’s (1973) view that it had a propositional structure and to establish that it had a depictive structure. He demonstrated that test subjects could scan across a remembered mental image (some experiments actually used a map) and that the time they took to do the scanning was proportional to ‘distance over the mental image’. Kosslyn argued that this result implied that the mental representation had the structure of a two dimensional representation like a picture. Pinker (1980) presented evidence to show that this result held for threedimensional objects. Shepard and Cooper (1982) showed that mental imagery of letters at arbitrary angles was rotated to the vertical at speeds equivalent to 56 revolutions per minute, before recognition. However, Pylyshyn (1984) counter-argued that the mental imagery was a mental metaphor for the represented domain, not necessarily implying deep representational structure. Pylyshyn also questioned whether the results would be applicable if the resolution of the mental imagery was to be intentionally varied. These debates remain unresolved, possibly suggesting that no definitive account can be given. Cognitive science has also given accounts of vision, given its primacy among the senses. Marr’s (1982) theory of vision suggested that the process of seeing involved two important stages. The first stage is the instantaneous mental summarisation of the scene through the identification of intensity edges and texture boundaries to create the ‘primal sketch’. By integrating the results of binocular stereo, motion prediction, shape assessment from shading, texture and colour the 2 1/2 D sketch of shape and volume would be produced in the second stage. A full object-based 3D representation can then be built on top of this by using the Gestalt psychological principles of ‘good continuation’ and ‘good figure’. The RTM argues that perception results in mental states that can become representational and also propositional. Mental representations are instantiated as cognitive ‘codes’ in the mind allowing inference to take place through computational mental operations on the codes (Pylyshyn 1984). Work in linguistics has suggested that these codes are a universal language of thought dubbed ‘mentalese’ which obey rules of compositionality (Fodor 1990). This account of mental representation suggests that the mind is an inferencing machine working on the propositional content of these (representational) codes rather than a deterministic processor of environmental stimulation as in behaviourism. In this view ‘thinking is computation’ since mental processes involve causal processes amongst mental representations, and ‘meaning is information’ since propositional content depends on their causal relations with things in

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the world (Fodor 1990). In this physicalist and reductionist account of the RTM, mental inferencing links the codes to semantics using a syntax. Pylyshyn (1984) considers this syntax as a means of giving an account of rational reasoning behaviour when thoughts are causal. However, this theory of mental inferencing has been challenged by some of the ideas of artificial intelligence, e.g. the connectionist view that the inference is dependent in some way on the functional connections in the brain rather than any syntax. Work on ‘commonsense psychology’ has also argued that while thinking may be computational and inferential it is possible for the thoughts to be indirectly causal through conjecture (Cummins 1989). An alternative account of cognitive science from biology has been given by Maturana (1978) who argues that cognition is an example of ‘autopoesis’. Autopoesis is the ‘identity of a unity of components’—in biology, the set of systems sustaining life—which must preserve their structure in order to endure and avoid breakdown. Maturana suggests that the human cognitive system exhibits structure-preserving autopoesis through a coupling to the world driven by representation. Thus cognition deals with the relevance of action to the maintenance of autopoesis. Maturana refers to interlocked cognitively driven behaviour of this kind as consensual and argues that language is the primary example. This account of language gives a powerful rationale for the importance of representation. Cognitive science has given an account of how the RTM is actually implemented in perception, cognition, language and action, and it has provided a theoretical basis for the development of artificial intelligence. A key lesson for GISc lies in the development of sophisticated models of representation which show how states of mind can be connected with the conceptualised world through perception and language. There is also evidence from cognitive science that mental representations may even have explicitly geographic properties (cf. Kosslyn’s work) making geography an ontologically basic feature of cognition. As such GISc may have an important role in developing a spatial and temporal ontology for cognitive explorations. Informatics Informatics in general is concerned with computation employing symbolic and informational representations of human knowledge. The theory of computation was made possible by the foundations of mathematics and logic established by Cantor (1873), Frege (1893), and Whitehead and Russell (1910) amongst others. Computation in the modern sense was founded by Turing’s (1936) work on theoretical computing machines, Godel’s (1930) concept of the incompleteness of axiomatic formal systems, Tarski (1937) and Carnap’s (1950) work on logic and probability and Von Neumann’s (1958) work on computational architectures. Work by Codd (1970) on relational algebra, Sutherland et al. (1974) on graphics and Knuth (1973–81) on algorithms have provided the computational basis for contemporary digital computing. Computation was characterised by Minsky (1967) as a theory of ‘effective procedures’ that are simple enough to be executed by a machine. Key aspects of computation include automata theory (leading to the construction of abstract machines), recursive functions (through the encoding of the operations of abstract machines in number theory) and

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formal languages (to define programming formalisms) (Couclelis 1998). Attempts to use computers in problem solving led to the development of the discipline of artificial intelligence (AI) which focuses on the use of computation in reasoning with symbolic representations (Simon 1969). The common factor uniting these approaches to computation is the use of symbolic representations that stand in some relation to an aspect of the conceptualised world, defined using an appropriate metaphysic. The modelling processes that identify the phenomena in the world, their inter-relationships and the operations carried out on the symbolic representations used, all depend on theories of modelling. The earliest example of a methodology for modelling is General Systems Theory whose concepts include a functioning whole (in the sense of a set or assemblage) broken into mutually interrelating elements (Von Bertalanffy 1950). Methodologies of simulation modelling using matrix arithmetic and other methods were summarised by Ziegler (1976) and those aiming to model complex systems exhibiting emergence were discussed by Casti (1989). Methods of modelling work practices that involve computers have been proposed by Rasmussen, Pejterson and Goodstein (1994) (cognitive system engineering) and by Checkland and Scholes (1990) (soft systems engineering). Methodologies of modelling and symbolic representation are discussed further in chapter 4. Informatics is also the study of information. However, many different accounts of information have been given. Machlup (1983) listed the claims that have been made for qualification as information, i.e. something that: • was either not previously known, or was less well known to the recipient (i.e. news); • affects the information held by the recipient; • consists of uninterpreted data; • is useful to the recipient; • is used to make a decision; • bears on action taken; • reduces uncertainty; • helps identify context in language; • excludes alternatives; or • changes beliefs. These accounts range across disciplines and scales of consideration suggesting that information lies behind all representation and communication. However, defining information requires a holistic perspective as its nature depends on the theoretical commitments made. For example, Winograd and Flores (1986) have argued that most notions of information are incompatible with an idealistic metaphysic, as communication has primacy. Similarly, information plays no part in epistemological theories since they are concerned with the higher level conception of knowledge. These considerations imply that information has an ontological and representational role in cognition, language and society. Within these bounds, several approaches to information have been proposed. Machlup (1983) defined information by contrasting it with data and knowledge. Hence, data is the reification or ‘making available’ of information as he argues that information is never actually extant. By contrast, knowledge is a structured, enduring and consistent

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stock while information is a fragmented, ephemeral and empirical flow. Machlup argues that true information requires an informant and a recipient: if there is no mind involved as in the genome or in a machine then he suggests that information is merely ‘metaphorical’ in nature. In sympathy with Machlup’s view Miller (1983) argues that human beings are ‘informavores’, that is ‘knowing things acting on information’ placing information in a cognitive domain. Belkin and Robertson (1976) defined information as the impact that a collection of signs organised by an informant can have on the structure of a recipient’s world-view. Information is therefore that which is capable of changing the structure of an individual’s world-view. This view poses the question, how can we know whether the individual’s world-view has changed when information is received? By contrast Brookes (1980) defined information by reference to Popper’s (1972) concept of three worlds: the first, objective and physical; the second, subjective and mental; and the third, objective and representational (that is, human artefacts of knowledge). Brookes proposes that information is that which incrementally adds to the stock of knowledge (defined as a structure of concepts linked by their relations). Hence, he identifies both objective and subjective kinds of information. A concern with the objective form of information as documents is the root of information science and the concern of libraries as institutions. Hjørland (1998) reviews the kinds of documents and their classifications that are associated with epistemological movements. He characterises empiricism as implying document clustering on similarity; rationalism as implying logical subdivision; historicism as implying arrangement by historical development; and pragmatism as implying goal-directed ordering. Dretske (1981) gives an account of information constructed on the mathematical theory of communication proposed by Shannon and Weaver (1949). He argues that signals caused by events can carry information about their origins to a receiver. This connection between a source event and a receiver implies a causal relation in the physical world; however, the correspondence between source and receiver may range from zero to perfect, due to noise. By contrast, meaning is constructed from information by the recipient from prior knowledge; it may be subjective or inter-subjective (part of the consensus implied by language). Dretske argues that if the information carried by signals to a recipient is causal (at whatever level of correspondence) then it must also carry physical or logical implications along with the information itself. The implications can be seen to be ‘nested in’ with the information according to circumstances and illustrate how there can be no one measure of the informational content of a signal. Dretske’s maxim is that knowledge is information-caused belief. Barwise and Seligman (1997) approach the definition of information from the perspective of the necessity of information flow between the spatio-temporally separated components of distributed systems (considered in the most general sense). Hence, information flow connects events outside experience to those within it in a nomological, (law-like), convention-based or logical fashion. Barwise and Seligman examine alternative accounts of how information flow might be modelled: as elimination of possibilities; as nomological connections between observables in physical systems; as legitimate inference. Their theoretical account unifies these concepts by developing a theory of information flow as tokens (‘that which is classified’) passing through channels according to regularities. The human role in information is in the definition of

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classifications in the source and target domains. Mingers (1997) defines information in terms of meaning. He argues that since the external world is a ‘continuum of difference’ rich in information, but that cognition is discrete and able to carry only limited information, then knowledge, intentions and context define what information can be converted into meaning. Mingers suggested that there are three steps involved in converting information to meaning. The first step is achieving comprehensibility of signs recognised in the flow of information. The second step is connotation—recognition of what is ‘nested in’ (c.f. Dretske 1981) with the information. The third step is concerned with intention—the recovery of any meaning intended by a speaker. Dervin (1999) has argued that understanding of information has passed through five main stages: • information describes an ordered reality; • information describes an ordered reality that is relative; • information is power through it’s domination of discourses; • information imposes order on chaos; • information is a tool to make sense of a reality that is both orderly and chaotic. Hence, information design is needed to identify cognitive gaps in communication. Fox (1984) characterised information in terms of its spatio-temporal character and its linguistic functioning. Since he argues that information is not a sentence type or token and has no duration/extent he concludes that information is best seen as the semantic content of a proposition. Raper (1999) takes a similar view arguing that ‘when properties of “states of affairs” are represented and communicated in any natural or symbolic language, then the result is information’. This allows information to be a very basic process and separates its essential ontological nature from any impact that the communication of it may have. Stonier (1991) and Frieden (1998) have gone further, arguing that information is a basic property of the universe. Finally, information has been defined as a property and a commodity. Castells (1996) recognises information processing as a form of production in what he terms the informational society. Information can be owned as an intellectual property, although most statutes refer to originality as a test, implying that it is knowledge rather than information that is being protected when in the static and material form of data (Cho 1997). The selection and signification of information will not just be a question of the channel/format through which the information is conveyed. Another key question will be what kinds of business practices, economic models and legal regulations will emerge to dictate the nature of information commodification in the digital world? The flexibility of digital information means that the next generation of information providers can reinvent information products. New strategies that have already emerged include the disaggregation of information into small units to facilitate micro-payment pricing. Such strategies will define new marketplace(s) for digital information: in many cases they will create new information ontologies by default. These accounts of information provide a background to its ontological and representational role in cognition, language and society. Geographic information, however, has subtly different characteristics, which this book explores. Goodchild (1997) has extended the information bearing object (IBO) document model of the digital library

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to the geographical information bearing object (GIBO) to define a document as ‘containing a representation of variation over some part of the earth’s surface’ (p387). The ontology and epistemology of GIBO definition could be regarded as the theoretical part of GISc; the informatics of the GIBO is the practical, work-oriented part.

THE POSSIBILITY OF GISc This chapter aimed to set out the theoretical commitments on which GISc is based by examining the fields from which these commitments must be drawn. Since there is not now and never should be a single prescriptive model of how these commitments are chosen, the reader is invited to find their own path through these issues and to redefine the issues from their own (inevitably) interested perspective. Positions will range from positions based on realism, determinism, RTM, naturalism, rationality (such as Fodor, and in GISc, Openshaw) to positions based on idealism, indeterminism, phenomenology, pragmatism and anti-rationalism (such as Rorty, and in GISc, Curry). Explicit commitments on the well-established positions of the wider debates about science and methodology will focus the debates about GISc and contextualise the positions being taken up. In this book the extremes of methodological commitment discussed above are avoided as there are other positions such as those based on realism, indeterminism and commonsense psychology, i.e. those positions accepting the world, but only as it appears to be. From this perspective, the role of social action in creating ontologies that drive representation is crucial. Following Hacking (1983, p31): ‘we represent and we intervene’. The aim here is to bring together nature and society through the role of information and representation as Wilson (1998) has proposed in ‘consilience’. Accordingly, the research agenda in GISc must be driven by the need to spatially and temporally contextualise the ontology and epistemology employed and by the need to widen the scope of representation at the informatics level. This book will argue that this is a reflexive cycle: as we develop new representations, especially three and four dimensional ones, we open up new multidimensional ways of thinking about our ontologies and our epistemologies. Such a holistic approach to GISc opens up new kinds of questions such as: • what role do concepts of space and time play in the individuation of ‘states of affairs’? • how is realism constituted by space and time? • is all geographic knowledge empirical or is some of it innate? • do maps represent an inductive argument, and if so how can they be refuted? • what are the spatio-temporal limits to the causality of ‘constant conjunction’ in GISc? • can ergodic time-for-space and space-for-time substitutions have explanatory force? • are representational or phenomenalistic accounts of cognition better for mapping? • what is geographic context in the linguistic account of relevance? • what are roles of space/time in alternative approaches to data/process modelling for computation? • what aspects of space can be ‘nested in’ with information flow?

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In chapter 2 the grounding and origins of the current two dimensional paradigm of GISc are set out to underpin current practice. In chapter 3 a further possible stage of development into a new multidimensional paradigm is laid out. Chapters 4 and 5 examine the newly available multidimensional representations that offer the scope to envision new phenomena and help rethink our ontologies and epistemologies. Part II of the book contains short case studies to set this theoretical work in context.

CHAPTER 2 Two-dimensional representations of space INTRODUCTION In the last chapter the theoretical foundations of the GISc worldview were explored and set in context. It was argued there that representation in GISc can be set consistently within a worldview that makes commitments to metaphysical realism, indeterminism, explanation, ‘common-sense psychology’ and an information ontology based on ‘states of affairs’. These commitments mark out a position in which an indeterministic external world can nonetheless be determinate, where that world is represented from diverse human perspectives, and where representations as information play a vital role in communication and social practice. Such a worldview must be concerned with the ontological, epistemological, cognitive and informational commitments that are made when we represent. This is the way that knowledge in GISc is ‘grounded’. It is clear that space and time are central to these concerns. This chapter aims to explore these representational commitments by firstly reexamining the origins and methodologies of the two-dimensional spatial representations that dominate navigation and mapping and, hence, GIS. This will help develop a contemporary view of the grounding and practices of representation and its implementation using geographical information system technologies. This chapter draws upon ideas first expressed in papers by Raper and Livingstone (1995), Raper (1996) and Raper (1999) that explored spatial representation in GIS. Chapter 3 extends this approach to multidimensional representation. The first part of this chapter explores spatial representation through the means of the worldview ‘template’ developed in chapter 1 in order to situate two-dimensional representation in a wider theoretical setting. The second part of the chapter explores the origins of two-dimensional spatial representation to examine how work in a variety of fields has contributed to the forms of representation that are used in contemporary navigation and mapping. The third part of the chapter sets out how GIS implement the concepts of two-dimensional representation developed for navigation and mapping, and develops a critique of GIS both to show the limits of this view of GISc and the potential for a new multidimensional view.

METAPHYSICS OF SPACE Metaphysics is concerned with human existence and with human knowledge of the ‘world-as-conceptualised’. To those holding idealist or naturalist views metaphysical issues can be reduced to questions of epistemology, i.e. what we know is a question of how we know it, whether at the cognitive, linguistic or social level. However, Trigg

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(1993) has argued that epistemology needs a metaphysical grounding: what we know must be limited ultimately by the properties of the world and everything in it—a view endorsed here. He argues in particular that science should take its grounding from the coherence between knowledge and the nature of the world of objects and of other minds. Successful demonstrations of such coherence are a justification of this approach. Clearly, space and time are constitutive of this coherence: any account of metaphysical grounding for multidimensional geo-representation must consider the role of space and time. In chapter 1 it was argued that there are many successful demonstrations of spatiotemporal coherence e.g. between models of contagion and incidence of disease, and that these are sufficient to establish the possibility of spatial and temporal representation. However, critiques of realist metaphysics have shown how representation can be raised to the level of an ideology and how it is sometimes used to posit coherence where no link exists. The implication is that any contemporary acceptance of metaphysics as a ‘grounding’ for representation must identify a domain of applicability for coherence defined by ontological, epistemological, cognitive and social theories. These theories set out how we know what we know. One pervasive metaphysical account argues that space in the absence of time is a property of the world that can be constitutive of knowledge in itself. Throughout the history of ideas it has been argued that space can be divided from time and considered separately: the development of Euclidean geometry in ancient Greece is the earliest example of this. This view lies behind the activity of mapping sensu lato and led to the rise of cartesian two-dimensional spatial representation during the 18th century Enlightenment in Europe. A variety of different views of the role of two-dimensional space in constituting knowledge have been advanced and are discussed here under the very wide range of headings where they have appeared. Metaphysics of space and place In a historical study of metaphysics Casey (1999) has argued that thinking on coherence between the world and knowledge has alternatively been place-oriented and spaceoriented through history. Many primitive myths such as the Babylonian Enuma Elish give accounts of cosmogony (how the world came to be) in which topogenesis (place creation) follows directly from cosmogenesis (world creation). However, the ancient Greek philosophers recognised the necessity that both space and place exist. Plato’s account of cosmogenesis in Timaeus suggests that a primal ‘receptacle’ (outside which there is nothing) is first filled with space (chora), then subdivided into regions (chorai) of ‘like sensible qualities’ and finally occupied by places containing material bodies. To Plato space is ‘infinite extension’ which defines the scope for place as ‘finite locatedness’ (Casey 1999, p 34). By contrast Aristotle argued in his ‘Physics’ that place was a more important metaphysical concept than space as it made it possible to identify motion and therefore change, although this was a definitively two-dimensional conception (Casey 1999). To Aristotle place was co-extensive with a ‘thing-in-place’, i.e. places are defined by the limits of the occupying body of matter (Couclelis 1998b). Casey (1999) notes that this Aristotelian place-oriented conception held sway until the end of the 17th century when the Newton’s space-oriented view supplanted it. In the

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Newtonian system space is sheer inert extensionality, a framework, while place is an x, y, z coordinate point in the cartesian scheme. Newton’s concept of space as a container naturally implied the possibility of empty space: Casey suggests that such a possibility shaped thinking and therefore motivations in the age of exploration. This Newtonian view of space as homogenous was constitutive of a ‘universalism’ supported by Locke, Leibniz and Kant in which the importance of place was diminished. By the early 20th century writers such as Husserl and Heidegger had reinvented place by arguing that places are constructed: places are ‘spaces for…’. Post-war phenomenological studies have yielded numerous conceptions of constructed place such as the ‘localities’ of Deleuze and Guattari (1984), the ‘heterotopia’ of Foucault (1970) and the ‘enclaves’ of Lyotard (1985). These accounts break from the past by involving time in the concept of place: for example, Deleuze and Guattari (1984) treat places as events. Metaphors for geographical thinking In a historical study of geographical thinking Buttimer (1993) reinterpreted the four ‘world hypotheses’ of Pepper (1942) as metaphors with heuristic potential for space. The first metaphor, ‘formism’, sees the world as a mosaic of forms: ‘immanent’ formism is descriptive and inductive, while ‘transcendental’ formism asserts that there are regularities of process underlying the forms, requiring deduction. Buttimer (1993) traces this worldview through history from Ptolemy through Varenius, Diderot and Kant to the 20th century geography of Hartshorne (1939) and Bunge (1962) arguing that it remains ‘[a] perennial puzzle how form relates to function, pattern to process’ (p119). In this critique (amongst other things) she is questioning the adequacy of a two dimensional account of the world. The second metaphor, ‘mechanicism’, concerns itself with causally interrelated systems: locations in time and space determine how the ‘world as machine’ functions. Buttimer traces this worldview from Lucretius through Leonardo da Vinci, Newton and Einstein to the 20th century systems theorists such as von Bertalanffy, arguing that it is ultimately limited by the role of ‘contingency’ (local circumstances) in disrupting causal chains. The metaphor of mechanicism is often reduced to two dimensions by making such representations from timeslices. The third metaphor, ‘organicism’, argues that the world must be understood in terms of wholes rather than parts, structural transformations and dialectical processes rather than rational progression. Buttimer traces this worldview from Heraclitus through Humboldt to the regional geography of Vidal de Blache and the geographical cycle of Davis. Although the organicism metaphor is explicitly multidimensional, it has usually been estranged from representation. The fourth metaphor, ‘contextualism’, sees the world as an arena for the contingent occurrence of events and, therefore, argues that space cannot be separated from time. Buttimer traced this worldview from the Sophists of ancient Greece through Voltaire to the pragmatists Peirce and James. Bergson’s thinking on space and time falls within this tradition. Defining time as the ‘continuous emergence of novelty’ (durée) from the perspective of a person moving through time implies that to represent spatially (two-dimensionally) is to freeze time and to deny the dynamism implicit in living (Adam 1990). Massey (1999) argues that this means that knowledge should be concerned with the representation of space-time rather than the spatialisation of

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the temporal. These issues will be discussed further in chapter 3. Metaphysics of geographical and spatial representation Casati, Smith and Varzi (1998) explored the metaphysics associated with spatial representation from a philosophical perspective. They identified two senses of spatial representation: firstly, representation of the environment external to the body for the organisation of perceptio00n and behaviour, and secondly, mental representation used for spatial reasoning tasks. They argued that there was no necessary connection between these senses of representation but suggested that they may be routinely dependent on each other. Their focus was explicitly on the sense of space in two dimensions. According to Casati and Varzi (1999) spatial representation sensu lato raises certain basic questions such as the relationship between objects and regions, the relationship between objects and events, the boundedness/unboundedness of objects and the ontology of space, whether absolute or relational. Theoretical tools available to work with the objects, regions and events of spatial representation include mereology (theory of part-whole relations), topology, morphology (the theory of qualitative discontinuities) and kinematics. A theory of localisation is required to deal with the relationship between an object and its region. Casati, Smith and Varzi (1998) differentiate the general case of spatial representation from the specific case of geographical representation by identifying two metaphysical questions faced distinctively in geography. The first question concerns the identity of the ‘geographic individuals’, i.e. the fundamental geographical units. These are issues raised by Harvey (1969) who suggested criteria for their selection: geographical individuals could be discrete/continuous; substantive/spatial; natural/artificial; or, singular/collective in nature. Casati, Smith and Varzi (1998) suggested two extreme positions on this question: ‘strong methodological individualism’ in which only people and substances exist, and ‘geographical realism’ in which only regions exist with no individuals. An intermediate position ‘weak methodological individualism’ is one in which regions do exist but only dependently upon individuals, which is the view taken in this book. This view is consistent with the theoretical commitments marked out at the start of the chapter. Chapman (1977) addressed the geographical individual question from the perspective of geographical entification defining first order ‘proper’ objects (structurally integrated wholes) as having properties of taxonomy, morphology, physiology, ecology, chorology, chronology and composition. Higher order objects were defined as ‘areal aggregate’ objects or ‘non-areal’ aggregate objects (intellectually constructed). From this definition he argued that places and regions cannot be objects since purely spatial criteria are not adequate enough to serve as identity criteria. This view is close to the argument presented in this book: identity criteria must be based on essences of the external world as constructed for representation in the social, economic and political setting. The second metaphysical question faced distinctively in geography according to Casati, Smith and Varzi (1998) is that of defining place. In this account place is being recognised as qualitatively different from space: place is the concern of geographical representation while spatial representation is concerned with space sensu lato. On this account geography can be seen as the study of how places are constructed and their

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relationship with space. Hence place can be defined either as a particular portion of space (absolute space ontology) or as the identity criterion for an entity, that is, the criteria by which the place is recognisably distinct (relative space ontology). In the absence of time it is argued here that this identity can only be partial. Social conceptions of geographic space Another metaphysical account of the way space constitutes knowledge is associated with the conceptions of space held to be relevant to social theory. Simonsen (1996) has suggested that three distinct conceptions of space can be recognised in social theory. The first is ‘space as material environment’ where space provides the backdrop to social action, e.g. the landscape as cultural milieu (Sauer 1925), or the built environment as fixed capital (Harvey 1982). Simonsen argues that since there cannot be social relations between people and matter, the relationship between space and society must be mediated by social practices such as the production, use and symbolisation of the material environment. The second conception suggested by Simonsen (1996) is ‘space as difference’ in which space is ‘place-oriented’. Within this tradition there is an account of ‘space as difference’ which has drawn commitments from the critical realism of Bhaskar (1978), such as the distinction between abstract and concrete domains of research (Sayer 1985). Duncan (1989) argues that social processes and causal powers operating on an abstract level connect spatial relations between objects on a concrete level. In this conception, although the social processes and causal powers are ‘necessary’ in nature, the spatial relations connect the object contingently. In other words social processes determine what happens in a place while the spatial relations constituted there determine how the processes work. By contrast, there is also a postmodernist account of ‘space as difference’ originating in the writings of Derrida (1972) whose philosophical project focussed on the impossibility of separating subject and object and on the way that texts are formed by relations among the elements of the text. Derrida’s account stresses the universality of time, contrasting with his particular sense of ‘différance’ in space and its ability to constitute heterogeneous ‘localities’. Poststructuralist analyses of spatial metaphor see identity, viewpoint and politics as sources of general social and cultural ‘difference’, which generate shifting social territories and new sites for political action. This is one account that specifically stresses the importance of two dimensions of space in the absence of time. The third conception suggested by Simonsen (1996) is ‘space as social spatiality’ in which space is seen as a dimension of social practice. In this conception the work of Lefebvre (1974) on the production of space by social practice is seminal. Lefebvre identifies three ‘moments’ of space that are simultaneously interacting: firstly, spatial practice in which space is produced by social relations that appropriate and control space; secondly, representations of space constructed by planners, architects and scientists that reproduce an instrumental discourse; and, thirdly ‘spaces of representation’ which connote lived space through the symbolism of imagined space. Thus every society produces its own space as a function of its practices at the level of the family, the workforce and the economy (e.g. neo-capitalism).

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A number of recent authors have explored the production of space following Lefebvre: Soja (1989) defined ‘spatiality’ as socially produced space; Harvey (1989a) focussed on the way capitalism has led to the annihilation of space through time by an intensification of the patterns of life; and Gregory (1994) identified and explored an embodied sensory space. Unwin (2000) has offered a critique of Lefebvre suggesting (amongst other things) that he has neglected time in his theories. Naïve geography One view of the way that space constitutes knowledge, which explicitly constitutes a two dimensional metaphysics, is the ‘naïve geography’ view advanced by Mark and Egenhofer (1995). This account builds on the ‘naïve physics’ of Hayes (1978, 1985a) where it is argued that modelling the common-sense knowledge of real people is more important than solving abstract problems designed to test research-motivated axiomatic theories. Hayes attempts to sketch out the axioms of a theory governing the properties and relations structuring the domain of human experience (though he does not restrict these to two dimensions). He breaks the predicates required to axiomatise this megatheory into sub-clusters referring to places and positions, spaces and objects, qualities and quantities, change and time, energy, effect and motion and composites and matter. For example, Hayes (1985b) argued that people have knowledge of the prototypical states of water and their behaviour in his naïve physics of liquids and that this qualitative knowledge can be (indeed, should be) captured and modelled by artificial intelligence. Smith (1989) gave an ontological account of naïve physics with metaphysical implications by showing how such a qualitative view of knowledge could be related to the quantitative view of standard physics. Smith argued (cf. Thom 1975) that naïve physical accounts usually identify salient states of physical systems such as asymptotic behaviour, stable oscillation or attractor phase states (in the sense of chaotic behaviour), where the true transience of complex physical reality is temporarily observable. Natural language has developed words for these qualitatively distinct phase states as a consequence of their very salience in the mesoscopic world of experience. Such an account finds an echo in Locke’s doctrine of primary and secondary qualities: Smith argues that while primary qualities are causal, secondary qualities are non-causal since they have emerged as qualitative aspects of the world which are merely salient in perception. Smith (1989) argues that this implies ‘the emergence not of things but of boundaries or contours’ (p232). The metaphysical implications of this approach identified by Smith (1995) are that common-sense physics cannot be causally related with the external world in the reductionist sense that Fodor (1980) suggested. Common-sense physics must be conjectural and error prone, and will always be less coherent than the external world it aims to represent. Mark and Egenhofer (1995) extended the naïve physics account by analogy, suggesting that people have naïve knowledge of geography. Their formulation included the following axioms: • naïve geographic space is two-dimensional, implying that the horizontal and vertical dimensions are decoupled and that the third dimension can be reduced to an attribute of position;

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• the earth is thought of as being flat because the shortest path on a sphere is not part of common-sense knowledge; • geographic space is better represented by a map-based configurational view of geographic space than by memories of our experiences; • geographic entities are ontologically different from enlarged table-top objects; • geographic space and time are tightly coupled, i.e. there is geographic space and there is geographic time, both of which are inherently linked to geographic concepts; • geographic information is frequently incomplete, i.e. cognitive studies have shown that people compensate for geographic uncertainty; • people use multiple conceptualisations of geographic space, switching between them at different scales; • geographic space has multiple levels of detail allowing people to change between different levels of granularity for different problems; • topological information is primary knowledge while metric information is a secondary refinement; • people have biases toward north-south and east-west directions, a result which shows up in way finding experiments; • distances are asymmetric since in everyday experience outbound and inbound journeys are often decisively different. Mark and Egenhofer (1995) suggested that these axioms be considered starting points for the construction of a new generation of GIS functions. Such new systems would operate on concepts of space closer to human cognition. Although powerful and in many cases well founded, it is argued in this book that several of these axioms (in particular the first) do not provide an adequate account of naïve human knowledge (see chapter 3).

Figure 2.1 Naïve geography and scientific geography trajectories through life

Smith (1995) put forward an ontological account of naïve physics which suggested that accounts of cognitive science should distinguish between untutored ‘natural’ cognition (governed by ‘N’-theories) and scientific ‘sophisticated’ cognition (governed by ‘S’theories). A major goal of the study of common-sense theories should be to discover the

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correspondences between ‘N’-theories and ‘S’-theories both as a function of education and of culture. As far as naïve geography is concerned it should be a goal of research to discover both how people transfer from ‘N’-geography to ‘S’-geography (figure 2.1) and what difference this makes to their cognitive behaviour and skills. Psychology of realism Psychologists have reformulated the question of how space constitutes knowledge by asking what the capacity for ‘spatial thinking’ (awareness of the sensed environment) requires. Eilan, McCarthy and Brewer (1993) identified four key requirements: • the ability to link geometric properties (volume, length) with physical behaviour (mass, velocity); • a concept of the external world, either a detached overview (allocentric) or a selfreferential personal view (egocentric); • a concept of our own relationship to the world, which links the allocentric and egocentric views; • the integration of spatial concepts of ourselves into our self consciousness. They argue that these four requirements are constitutive of a notion of a spatiotemporally extended external world inhabited by self-conscious ‘actors’. Many psychologists accept these elements of spatial thinking but then ask a further question: how do we make ‘allocentric’ map-like spatial representations in which the cognitive representations are independent of the individual’s actual location at any one time? Answers to this question either focus on the way that frames of reference help people to cognitively ‘taxonomise’ places and their relations, or they focus on the way that navigation abilities drive the definition of places and their representation in cognitive maps. By contrast philosophers often take it for granted that allocentric cognitive representations exist but ask how these representations are involved in consciousness. Campbell (1993) argues that the allocentric cognitive representation of places in the world and knowledge of the physical inter-relations between places is in itself constitutive of a detached viewpoint. Campbell argues that a cognitively detached viewpoint that incorporates an understanding of the causal relations structuring the world is, by definition, constitutive of a realist conception of the world. However, Campbell sees the allocentric cognitive representation of places as map-like, which he takes to exclude time from his analysis. Space and spaces Geographers have identified different ‘kinds’ of space with a distinct identity. For example, Sack (1981) divided space into an objective realm associated with the sciences and a subjective realm associated with the arts. He argued that these realms are ‘fused’ together in an ‘unsophisticated’ knowledge of space held by infants and adults untutored in science, but that they were fragmented and elaborated separately in the ‘sophisticated’ knowledge of space held in science. In Sack’s account the scientific ‘sophisticated fragmented’ view of space involves symbolic representations of facts in science while in

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the ‘unsophisticated fused’ view symbols are imbued with meanings taken from the social context. Couclelis and Gale (1986) developed an analytical framework to taxonomise space and characterise the properties of the different spaces identified, viz. Euclidean, physical, sensorimotor, perceptual and cognitive space. Couclelis (1992a) widened the scope of this approach to the classification of spaces by developing a four part conceptual scheme preceded by pre-conceptual (innate) space and succeeded by supra-conceptual (spiritual) space (figure 2.2). The four basic conceptual spaces can be characterised as follows:

Figure 2.2 The four conceptual spaces of Couclelis (1992a)

• physical or mathematical space—conceptions of a physical space founded on the principles of geometry established by Euclid and the coordinate framework first defined by Descartes. Such geometry can be used to measure distances and angles at the earth’s surface and has been traditionally used to make maps of geographical phenomena. However, 20th century physics has extended these concepts, creating nonEuclidean geometries, relativistic frameworks and fractals. • socio-economic space—spaces can be designed which preserve spatial relations such as a variety of economic and social spaces unlike the strictly physical space of geometry. These spaces can be used to provide a framework for travel times or accessibility constraints defined by income or status. These socio-economic spaces may be derived by transformations of physical space.

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• behavioral space—since space and spatial relations are understood by different people in different ways within and between societies, the way space is perceived is an important consideration. Hence, people’s conceptions of space can exhibit considerable variances from physical space and people often perform poorly in recalling maps. Thus, a behaviourally defined space can be identified. • experiential space—spaces that are socially defined can be considered perceptual and may be structured by sensorimotor or tactile skills. Concepts of place are established using these senses. Metaphysical implications In this survey of the metaphysics of space it has been seen that there are a number of senses in which two-dimensional space can be held to constitute knowledge of the world through its role in the coherence between minds and matter. In many cases these accounts succeed on their own terms and their analyses are useful. However, it is argued here that they all have shortcomings traceable to the lack of an embedded concept of time. The sense of place in space has been held to be important since Aristotle; yet new conceptualisations of place have begun to recognise the absence of time in these notions (Massey 1999). Attempts have been made to ‘entify’ the world two dimensionally in geographical studies; yet Chapman (1977) has shown how purely spatial identity criteria are rarely adequate. Attempts have been made to identify a naïve geography that is driven by a two dimensional spatial sense; yet Smith (1989) has shown how naïve physics demonstrates that salient physical expressions in two dimensions are derivative from the multidimensionality of the underlying physical systems. Psychologists have shown the importance of allocentric, map-like, two dimensional representations in constituting a realist view of the world; yet many others (e.g. Raper and Livingstone 1995) have shown that two dimensional space is merely a projection of the dynamic evolving of the world.

ONTOLOGY OF SPACE Ontologies are specifications of conceptualisations that are elaborated through definition, signification and ordering. Space and time have been central to most attempts to generate such conceptual specifications since attempts to constitute ontologies have generally required that they be ‘natural’, which implies a commitment to metaphysical realism (Loux 1998). Such philosophical work on the ontology of space and time has recently been augmented by a concern with ‘geographical ontology’ following the development of concepts of naïve geography (Mark and Egenhofer 1995). Geographical ontology has been concerned with geographic kinds, cognitive maps, scale and space, spatial knowledge, knowledge representation and spatial reasoning, space in language, space in representational art, the social constitution of spatial concepts, and absolute and relative views of space. Many approaches to ontology, like those reviewed above, have separated space and time when exploring conceptualisations of the world. The role of twodimensional ontological conceptualisations in constructing representations will be explored in this section.

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Geographical kinds Smith and Mark (1998) have characterised a geographical ontology as consisting of ‘mesoscopic entities, many of which are best viewed as shadows cast onto the spatial plane by human reasoning and language’ (p308). In their approach the twodimensionality of the geographic ontology is explicitly constituted and, by implication, projected from the four-dimensionality of the world. They argue that mesoscopic geographic kinds are ontologically distinct from other kinds due to the difficulty of separating ‘what’ and ‘where’ qualities, unlike the case of smaller human-sized manipulable kinds. A consideration of geographical ontology can be structured through three questions: are there geographical kinds to find; if there are, how can they be characterised; and, if we characterise them, how certain are we of their identity? Are there geographic kinds to find? Smith (1995b) argues that the set-theoretic ontological view that all of space can be modelled using sets and points is untenable in the light of Cantor’s continuum hypothesis (see chapter 3). He argues in favour of an alternate ontology constructed using the principles of mereology—the theory of parts and wholes—as this is neutral with respect to material substances. Mereological actualism is an ontological position from which it is argued that all of space can be modelled as parts and wholes, with parts having the same status as wholes. This philosophical argument suggests that parts and wholes are the fundamental ontological building blocks of the world. If the world is made of parts and wholes then an ontological project to identify kinds is possible. Smith (1996) argues that such a mereological theory should be integrated with topology to define a mereotopological ontology concerned with the parts and wholes of entities and their interiors and boundaries. Mereotopologically, an entity is closed if it includes its boundary; it is open mereotopologically if its boundary is included in its complement i.e. the exterior. This scheme can be used to explore ontological kinds and their relations. Smith and Mark (1998) argue that geographical ontologies can be explored using these tools although some geographical kinds are difficult to fit into this scheme, for example, mereotopologically open entities such as coastal bays which have hard-to-define complements such as the sea. Smith and Mark consider geographical ontology to be problematic because of the way that the identity of geographical kinds depends on their dimensionality and their shape. It is argued in this book that the act of projection from the world of four dimensions to a geographic plane is to make it impossible to fit many entities into a geographic ontology. How do we characterise geographic kinds? Starting from the position that ontological parts and wholes constitute kinds, a further question might be how kinds should be characterised, especially geographical kinds. Smith and Mark (1998) argue that such a characterisation requires a commitment to a realist position in which the ‘microphysical’ stratum of the physical world is held to be distinct from the ‘mesoscopic’ stratum of human experience. According to Smith and

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Mark (1998) within the ‘mesoscopic’ stratum it is possible to identify: • naturally delimited physical entities; • geographically constituted physical entities demarcated by individual cognitive acts; • geopolitically constituted cognitive entities demarcated by collectively held notions of space. In other words the mesoscopic world contains both ‘physical’ and ‘cognised’ entities: this is a metaphysical position termed ‘moderate’ realism by Smith (1995b) since entities are neither all real nor all in the mind, but a mixture of the two. This position recognises an ontological dependence of entities on human decisions, and things in the spatiallyextended world. Accepting this tripartite characterisation suggests that geographic ontology should be mainly concerned with the constitution of the second and the third types of entity, viz. ‘geographical’ and ‘geopolitical’ entities. In the case of the geographical entities, cognitive concepts of perception and language play a key role since the demarcation of geographical entities depends on whether an egocentric or allocentric approach is taken (Smith and Mark 1998). In the case of the geopolitical entities (termed spatial socioeconomic units in Frank, Raper and Cheylan 2000) social consensus plays the key role since the entities can be ‘produced’ as a consequence of social relations. In both geographically and geopolitically constituted entities it is clear that boundaries play a crucial role. Smith (1995c) distinguishes between ‘bona fide’ boundaries (dividing things-in-themselves) and fiat boundaries (dividing cognitive phenomena). Fiat boundaries play an important role in the definition of geographically and geopolitically constituted entities since the construction of the boundaries depends on perception, language and social consensus. Perceptual inputs to fiat decision-making are framed by the edge of the visual field and contain surfaces curving in three-dimensional space. Within the visual field there are determinate entities of attention (figures) and other indeterminate entities (the ground). Language generates ‘windows of attention’ through linguistic acts that define mereotopological boundaries around cognised entities. This process is a conjectural activity that creates fiat boundaries by analogy with bona fide boundaries—the demarcation may be a transient empirical judgement. Fiat entities may also have indeterminate boundaries e.g. the Sargasso Sea phenomenon in the Atlantic (Burrough and Frank 1996). Social consensus plays a key part in the formation of fiat entities. Raper (1998) characterised geopolitical fiat entities according to their characteristics on three scales: • their purpose, ranging from the symbolic (e.g. religious) to the instrumental (e.g. governmental); • their lifespans, ranging from transient (short lived) to the permanent (long lived); and • their spatial character ranging from the diffuse (vaguely defined) to the concrete (sharply defined). At one end of a spectrum of possible geopolitical fiat entities, communities and social groups tend to informally create symbolic entities which are transient and diffuse in nature, for example, neighbourhoods (defined by identity), favourite vistas (defined by concepts of landscape) or perceptions of ‘dangerous-places-to-be’ (defined by social

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behaviour). Smith (1997) has added to the bona fide and fiat entities the ‘force dynamic’ entity associated with the ‘force of arms’ employed in times of war. By contrast, at the other end of the spectrum governments and commerce tend to formally define instrumental entities using structured approaches that are largely permanent and concrete in nature (though not necessarily completely unchanging). Such geopolitical fiat entities are made, for example, to control access to space (defined by legal ownership), to limit the uses of space (defined by jurisdiction), to distribute resources efficiently (defined by supply and demand locations) or to characterise localities (defined by a socio-economic classification). These concepts are recognised in the legal duality of movables and immovables: the latter are entities that are the objects of legal rights. In both informally and formally defined geopolitical fiat entities the lifespans of these entities, i.e. their temporal behaviour, are key constituents of their identity. How certain are we of the identity of geographical kinds? The assumptions that we have enough knowledge to fully characterise geographical kinds and that they can be identified with complete certainty are rarely satisfied. A class of fiat entities that are neither bounded and crisp, nor emergent from unbounded spatial variation must form part of any full geographic ontology. Freksa and Barkowski (1996) characterised the identity of these uncertain entities in terms of the relationship between concepts and representation. They argued that there were three kinds of uncertainty: that due to imprecise (spatial) knowledge of the represented entity, that due to poor correspondence between the defining concepts and the represented entity; or a combination of the two. Such entities are often termed ‘fuzzy’ in nature after the fuzzy set methods developed by Zadeh (1965, 1975). Fuzzy entities can be modelled by decrisping a fiat boundary or by extracting from a field of variation. The fuzzy identity of the entity can be represented as a value in a membership function that is continuous between 0 and 1. This allows the constitution of fuzzy entities defined with overlapping classes in attribute space and represented with diffuse boundaries or a fuzzy field (Burrough 1996). Worboys (1998) approached uncertainty associated with information stored at multiple resolutions through ‘rough sets’ where the discreteness of entities is progressively improved with greater resolution. Cognitive maps The development of the ‘cognitive’ perspective in linguistics (Chomsky 1957) and psychology (Neisser 1967) led to a concern with the identification of the key elements of cognition in the late 1950s and the 1960s. From early work by Tolman (1948) on cognitive maps, by Piaget and Inhelder (1956) on the development of spatial concepts in children, and by Miller (1956) on information processing, it became clear that space was one such key element. The first cognitive models of space focussed on mental imagery of the geographic, such as images of the city (Lynch 1960) and of the environment (Lowenthal 1961). Subsequently, Gould (1966) developed the concept of ‘mental maps’ and developed a ‘surface’ representation to express their content in terms of place

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preferences (Gould and White 1974). Downs and Stea (1973) collected together early geographical work on cognitive maps including work on cognitive distance by Briggs (1973) and spatial cognition by Hart and Moore (1973). The development of behavioural geography in the 1970s provided a focus for the development of geographical and psychological research on cognitive maps of geographic space. Behavioural geography aims to find temporal sequences of goaldirected acts by human beings that have correlates in the spatial structure of the built environment and social systems (‘spatial behaviour’). It can be argued that spatial behaviour is closely related to the content of cognitive maps, which in turn can be considered to consist of taxonomies of the relative location of objects and phenomena in the environment (Golledge and Stimson 1997). This makes it important to know how cognitive maps are structured. An understanding of cognitive map structure may be one source for a general ontology of space. Most conceptualisations of the cognitive map have been two-dimensional in nature. Early studies saw the cognitive map as a warped Euclidean grid (Tobler 1976) or a metrically structured image (Kosslyn 1980). Subsequent studies have shown experimentally that cognitive maps have asymmetries (distances between points are different in different directions), that they are resolution-dependent (the greater the density of information the greater the distance between two points) and that they are alignment-dependent (distances are influenced by geographical orientation) (Tversky 1981). It has also been recognised that cognitive maps are hierarchically arranged by functional groupings of spatial information (Hirtle and Jonides 1985) into a cognitive atlas (Kuipers 1982) or a cognitive ‘collage’ (Tversky 1993). Kitchin (1994) has argued that cognitive maps are not geometric representations at all but a ‘convenient fiction’ for knowledge of the environment. The spatial ontology to emerge from studies of the cognitive map is a non-metric hierarchical ‘collage’ of spatially structured information with a two-dimensional map-like structure. Scale and space One of the features of the mesoscopic geographic stratum identified by Smith and Mark (1998) is the scale-dependency of geographic ontologies. Freundschuh and Egenhofer (1997) argue that small-scale spaces (perceivable in one go) and large-scale spaces (perceived by travelling through the space) are cognitively different. This difference raises practical issues: since large-scale spaces are made into small-scale spaces when representing geographical entities, this implies that the represented space cannot be treated in the same way as the real space. This difference also raises theoretical problems: do different scales have different ontologies, and, which scale level has ontological primacy (Montello and Golledge 1999)? Freundschuh and Egenhofer (1997) reviewed the range of approaches to scale in work on geographical ontology, characterising each type of space identified in the literature. The first group of authors only distinguish between large and small scale spaces (e.g. Kuipers 1978), while the second group also include a medium scale space for an intermediate ‘neighbourhood’ space perceivable at one time but not perceivable from one place (e.g. Gärling and Golledge 1987). A third group taxonomise scale through the

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scope of the information that can be included on a map of each scale, e.g. Muehrcke and Muehrcke (1992). A fourth group of authors relate scale to interactions between people and spaces, e.g. Zubin (1989). Zubin suggests that different concepts of space are developed for domains which are directly manipulable by human beings (e.g. within rooms) compared to those developed for domains which can be viewed but not manipulated (e.g. landscapes). On the basis of this survey Freundschuh and Egenhofer (1997) proposed an experiential classification of spatial scales dependent on whether objects in the space are manipulable, whether the space needs locomotion to perceive it, and whether the space is large or small in size. From a matrix defined by the answers to these questions Freundschuh and Egenhofer defined six spaces (five actual and one symbolic) whose characteristics are summarised in table 2.1. It can be argued that these spaces have distinct ontologies in the two-dimensional domain since each one is constitutive of different entities. Hence, it is possible to envisage multiple representations of the same world, each with a different ontology at the various scales: for example, by analogy in climbing, a pitch, a rock face, a mountain, a range, and a climber’s map. Cartographic representation has also exposed a number of scale issues as no paper map can store and display full details of all entities in a given category over a large area (Robinson et al. 1995). This is because maps must reduce real world sizes, typify entities geometrically and reduce detail as part of the representational process. These fundamental constraints make it possible to represent with high information content at large scales but make it necessary to lose information at smaller scales. Note that the cartographic sense of large scale is the opposite of that used in cognitive studies. The process of generating ‘derived’ map scales e.g. 100,000 from original large scale ‘source’ maps, e.g. 1:1000, involves the processes of ‘generalisation’ to eliminate information.

Table 2.1 A model of spaces and scales (after Freundschuh and Egenhofer 1997)

Manipulable object space

Manipulability

Locomotion needed

Size of space

Yes

Yes

No

Small Large

X

X

No

X

Non-manipulable object space

X

X

X

Environmental space

X

X

Geographic space

X

X

X

Panoramic space

X

X

X

Map space (symbolic)

X

X

X

X

Studies of the generalisation effects found when eliminating information while moving from large scale to small scale have found that there are regularities in the process that cartographers around the world have been observed to use. From a study of these empirical effects in published maps Töpfer and Pillewizer (1966) proposed a ‘principle of

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selection’ to predict how many features from a source map would be shown at a smaller, derived scale:

(2.1) where nf is the number of objects that can be shown at the smaller derived scale, na is the number of objects shown on the source map, and Mf and Ma are the scale denominators of the derived and source scales respectively. This principle offers cartographers a quantitative estimate of how much information should be eliminated as scales are reduced, although it is only applicable to a set of geometry and not to individual features on maps. João (1998) tested the predictions of the principle of selection for British and Portuguese maps finding that it underpredicted the elimination of features at large scales. A consequence of the generalisation processes used to create the features on small scale maps is that lines are longer on large scale maps, since these maps contain more detailed information. However, Richardson (1961) observed that the length of the same line on a paper map also grew ever longer when measured using dividers with a smaller and smaller aperture. This observed effect became more pronounced as the line became more complex in shape. Mandelbrot (1982) characterised the complexity in line shape (its ‘fractal’ dimension) by the rate by which the line length increased, as the measurement ‘window’ (like the divider aperture) decreased. Smooth line length changes little as window size reduces (low fractal dimension) while complex line length changes greatly (high fractal dimension). Mandelbrot (1982) suggested that the fractal dimension of a line (or area, or solid) would be self-similar across the scales despite its changing shape. While there are a class of fractal patterns such as the Koch curve (with a fractal dimension of 1.2618) which are geometrically self-similar (Gleick 1988), there are few examples of lines on maps which are statistically self-similar across scales as Goodchild (1980) and Müller (1986) have demonstrated. The falsification of the principle of selection and fractal self-similarity for maps suggests that there is a complex and non-linear relationship between scale and the information content represented by geometric shape. Exploring this relationship may reveal ontological structures: if fiat boundaries are created by analogy with bona fide boundaries then the role of scale may be important. Scale in this sense is a framing control that selects and makes salient entities and relationships at a level of information content that the perceiver can cognitively manipulate. Whereas an observer establishes a ‘viewing scale’ dynamically, digital spatial representations (e.g. for an in-car navigation system) must be drawn from a set of preconceived map scales. Inevitably, the cognitive fit with the current activity may not always be acceptable. Scale effects also appear in zonal systems of geopolitical entities where the zones defined are used to count or classify. Analysis of attributes assigned to the zones suffer from the modifiable areal unit problem (MAUP) (Openshaw 1984) in which spatial variation can be seen to differ spatially depending on the scale at which the zonal units of aggregation for observations are set. MAUP can be eliminated by moving to an analysis at the scale of the geographic individuals surveyed, however, privacy considerations rarely make this possible (Raper et al. 1999).

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Recently empirical research has been carried out on scale issues related to geographic ontology. Mark, Smith and Tversky (1999) conducted tests on non-expert subjects whose preliminary indications suggest that there are ontological differences between categorisations in the geographic and non-geographic domain, especially in the way that different types of boundaries are conceptualised. Freundschuh (1998) surveyed nonexperts on estimated travel time to various destinations, finding a scale bifurcation between the expression of short distances in geographic units and long distances in time units. This evidence of time as constitutive of ontological schemes suggests that some geographies may be scaled ergodically to time ranges over underlying spatial metrics. Spatial knowledge, knowledge representation and spatial reasoning Ontological schemes can also arise out of a cognitive analysis of spatial knowledge or by a priori representational axiomatisations that are then tested and refined during reasoning. Work in the fields of developmental psychology and behavioural geography has shown that spatial behaviour depends both on the structure of spatial knowledge and on the reasoning skills developed (Golledge and Stimson 1997). In parallel, work on axiomatised knowledge representation and reasoning has been developed to provide models of space that can be employed in image processing, architectural design, computational geometry and artificial intelligence. The classic works of Piaget (Piaget and Inhelder 1956; Piaget, Inhelder and Szeminska 1960) have strongly influenced psychological studies of childhood abilities to conceptualise and reason about space. Piaget proposed a developmental path through the following stages: • sensorimotor period of infancy up to two years, before spatial representations can be made; • pre-operational period from two to seven years, when topological representations can be made; • operational period from seven to eleven years, when Euclidean and topologic spaces are integrated; • formal period over eleven years, when systems of reference and distance metrics are integrated. These researchers argued that a child’s facility with representations of space develops from that which is egocentric, topologic and landmark-oriented in nature to that which is allocentric, fully configurational and based on linked routes by the age of seven years. This approach was modified and extended by Siegel and White (1975) who argued that the first stage in the acquisition of spatial knowledge was ‘landmark’ recognition, the second was the linking of landmarks by ‘routes’ and the third was the coordination of the knowledge into an overall ‘survey’ framework. Thorndyke and Hayes-Roth (1982) have questioned the linear developmental nature of this theory. They argued that parallel rather than sequential learning of landmark, route and survey knowledge took place. Using empirical survey results from adults arriving in a new area and learning ‘where things are’, Montello (1998) further disputed the developmental shift from non-metric to metric spatial knowledge proposed by Piaget and by Siegel and White. He argued instead that

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metric knowledge is acquired and refined concurrently with non-metric knowledge. Spelke and van der Walle (1993) studied infant perception to identify the cognitive origins of ‘landmark’ knowledge. They arrived at a set of physical principles governing the way that infants segregate a scene into units: the principle of cohesion (surfaces lie on a single object if and only if (iff) they are connected); the principle of contact (surfaces move together iff they are in contact); and the principle of continuity (an object traces exactly one connected path over space and time). These principles suggest how infants recognise and learn about objects as precursor to landmark spatial knowledge; Spelke and van der Walle argue that these methods are foundational and that they are enriched rather than replaced in later life. Blades (1991) also showed that children were able to learn routes based on landmarks and can understand correspondences between a map and a real environment much earlier (as early as three years), casting doubt on Piaget’s assertion that the development of spatial understanding parallels general cognitive development. This may indicate that spatial knowledge develops independently from general cognition, from different cognitive roots. The work of Golledge and co-workers (summarised in Golledge 1992) also challenged Piaget’s view of the development of spatial awareness. He suggested that although individuals may acquire considerable knowledge of phenomena located in space, they may not necessarily develop sophisticated representations of that knowledge due to a poverty of spatial inference abilities. This may explain why some people have only a poor understanding of spatial configurations. Golledge (1992) divided knowledge about representations of space into seven, viz. location of occurrences, spatial patterns, regionalised phenomena, hierarchies of phenomena, networks of features, spatial associations, and surfaces, noting that only the development of the first of these had been tested fully. In a series of experiments on American adults, both with and without a geographical training, Golledge (1992) showed that individuals did not perform well in tests designed to probe their understanding of spatial patterns, reinforcing his view of the importance of spatial inference rules in spatial knowledge. Spatial knowledge is also exhibited by wayfinding abilities, as it is a necessary part of the lives of people of all ages in all cultures. Gluck (1991) divided the work on wayfinding into that on competence, performance and information needs. Wayfinding competence depends on the structure of cognitive models and learning capacity and has been explored through computational modelling and through information processing linked to behaviour by action plans. Wayfinding performance depends on cognitive skills but also on task requirements and information sources. Gluck argues that way finding should also be considered as an information needs problem, e.g. the need for driving directions (McGranagan, Mark and Gould 1987). Information needs can be constitutive of spatial knowledge since the ‘recognition of what is needed’ in wayfinding will correspond to the ‘filling in’ of a spatial gap in the cognitive map, using Dervin’s (1983) ‘sense-making’ approach. Most cognitive analyses of spatial knowledge are based on empiricist principles, however, some rationalist (or nativist) researchers maintain that spatial knowledge is innate and neurologically conditioned. Bauer and Rubens (1985) found that different parts of the brain deal with the ‘spatial’ (the ‘where’ information) and the ‘visual’ (the ‘what’ information) such as shape, colour and volume. On the basis of a neurological

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study O’Keefe and Nadel (1978) argued that egocentric knowledge of space was located in the parietal lobes of the brain while allocentric knowledge was found in the hippocampus. O’Keefe and Nadel showed that location, orientation and speed were coded as vectors by neurons in the hippocampus region of the brain. Burgess, Jeffrey and O’Keefe (1999) have showed more recently that the hippocampus contains a network of place cells associated with memory functions. The place cells may be constitutive of cognitive maps. Recent work by Taube (1998) examined the functioning of the orientation cells experimentally in rats, finding that they use an arbitrary reference direction which drifts slowly over time, requiring re-calibration. O’Keefe (1993) has argued that three-dimensional Euclidean space is constructed by the brain’s neural architecture and that it constitutes the a priori space proposed by Kant. Kant required an a priori space in order for the mind to be able to understand its own role as a knowledge processing mechanism. Since these mechanisms are the basis for the comprehension of empirical objects, the mechanisms could not themselves be verified by reference to empirical objects. O’Keefe (1993) also claimed that the neurological spatial system gives place ontological primacy over objects since he argues that it is the mind that constructs the properties of space. O’Keefe accepts that non-Euclidean spaces falsify the Kantian argument that knowledge of the world must derive from our own Euclidean spatial representations. However, he argues that we use Euclidean geometry because it is simpler and more naturally congruent with the neurological structures. This view is challenged by those such as Luneberg (1947), Blank (1954), Roberts and Suppes (1967) and Heelen (1983) who have argued that vision is hyperbolic in nature therefore requiring an adaptation between the visual and configurational senses of space. Ontologies of space have also emerged from a priori axiomatisations of space for knowledge representation in image processing, computational geometry, architectural design and artificial intelligence. Spatial knowledge representations aim to model space with the maximum expressive power at the minimum computational cost. In image processing, axiomatisations of shape have been developed from boundary descriptions using chain codes (Freeman 1978), from edge detection of silhouettes (Shafer 1985) and from medial axis transforms (Blum 1967). In computational geometry Fourier and sinusoidal transforms (Pratt 1991), geometric decompositions (Keil and Sack 1985) and fractal dimensions (Mandelbrot 1982) have been used to describe shape, amongst other methods. Clementini and di Felice (1997) proposed a global framework for shape characterisation structured according to topological, projective and metric properties of two-dimensional figures, which they argued are the most significant aspects of shape in cognitive terms. In architectural design shape grammars were defined by Stiny (1976) as means of exploring possible arrangements of spatial elements in two- and threedimensions, such that they invoked a style in the sense of a compositional signature (Knight 1998). In artificial intelligence spatial knowledge representation has been driven by a need to incorporate spatial knowledge into autonomous agents’ behaviour. Kuiper’s (1978) TOUR model incorporated information on sensorimotor procedures, topological relations and metrical relations, which is learned as the agent receives information about a largescale space. By recording the attributes of ‘views’ and the ‘actions’ that change the views, the TOUR model builds up ‘place’ knowledge; by connecting places together

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‘path’ knowledge is synthesised. More recently Kuipers (1999) has extended the TOUR model in the Spatial Semantic Hierarchy (SSH) scheme. The SSH integrates four levels of spatial representation, each with its own scheme of ontology, knowledge and systems of inference, and independent of the sensors/effectors of the agent: • the control level, egocentric, sensorimotor and continuous in nature, requiring knowledge of trajectory following control laws for dynamic systems; • the causal level, egocentric and discrete in nature with an ontology of views and actions (cf. TOUR), requiring a system of logic for reasoning; • the topological level, qualitative in nature with an ontology of places, paths and regions represented as a graph, permitting exploration by brute force or heuristic search methods; • the metrical level, quantitative in nature with an ontology of one-, two- and threedimensional representations within frames of reference and integrated within ‘local’ maps aggregated to a ‘global map’. Kuipers (1999) argues that the four representations in the SSH are simultaneously active in the cognitive map. The hierarchy of representations is capable of handling a wide range of situations including those requiring inference on the basis of incomplete information. Edwards (1997) proposed a model of spatial representation called ‘geocognostics’ based on Kuipers’ ‘views and trajectories’ approach but extended it to deal explicitly with spatio-temporal behaviour. Spatial reasoning involves making inferences about spatial knowledge representations using symbolic axiomatisations of two- and three-dimensional space. These approaches make distinctions of a high level conceptual nature. Egenhofer and Herring (1990) formalised binary topological relations between arbitrary objects using the principles of algebraic pointset topology in the ‘9-intersection model’. Mark and Egenhofer (1994) tested the formalisation experimentally finding that most of the subjects grouped the same spatial relations identified by the ‘9-intersection model’. Freksa (1991) introduced the notion of qualitative spatial reasoning (QSR) following Allen’s (1984) work on temporal intervals. Cohn et al. (1997) summarised work on the Region Connection Calculus (RCC) approach to QSR based on Simon’s (1987) ontology and Clarke’s (1987) methodology, and Egenhofer, Clementini and di Felice (1994) show how the ‘9intersection model’ can be used in QSR in the case of regions with holes. For these studies to uncover ontological structure requires an assessment of their cognitive adequacy; Knauf, Rauh and Renz (1997) argue that the resolution of the RCC-8 set of relations is closer to the cognitive view of human test subjects. Studies of spatial knowledge have revealed spatial ontologies associated with cognitive development such as the principles of cohesion, contact and continuity from Spelke and van der Walle (1993). However, Golledge (1992) showed that spatial knowledge can be dependent on skill development. O’Keefe by contrast argues that space is innate to the brain’s structure. This would imply that the ontology of location is more important than the ontology of objects in the space. Work to produce expressive a priori axiomatisations of space such as the SSH scheme has suggested that spatial ontologies may be hierarchically organised around the competancies needed in different cognitive domains. However, almost all these approaches to ontology focus on two-dimensions with little

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consideration of dynamic and evolutionary spatial domains. Space in language Language plays a central role in spatial ontology as it is now widely accepted that the structure of language gives access to the nature of the cognitive system (see chapter 1). Studies of language are an important way to study spatial cognition and their diversity allows the testing of hypotheses about cultural universality. Studies of space in language have followed several themes including: the role of space in grammatical structure; the role of reference frames; the nature of locative expressions; spatial categories and metaphor; socio-spatial structuring of language; cultural universality; and, the integration of space with time in language. Studies of language have shown that there are two distinct levels of organisation within it, the lexical level (conveying conceptual content through nouns, verbs and adjectives) and the grammatical level (structural and syntactic organisation). Talmy (1983) has shown that the rich and adaptable structure at the grammatical level bridges the gap between the infinitely large perceptual and conceptual continuum and the finiteness of language in such a way that meaning can be conveyed at the speed necessary for communication. Talmy argues that space is one of the most important of the semantic domains at this grammatical level and one that further structures other linguistic domains through metaphor. In his seminal work ‘How language structures space’ Talmy argues that it is the spatial semantics in language that are responsible for structuring space in cognition rather than the properties of ‘objective’ space. Talmy (1983) shows that language structures space through schematic structure (prepositions, demonstratives and topological expressions), viewpoint (in space and in time) and distribution of attention. Schematisation involves selecting part of a reference scene with generic properties, for example, using a preposition. This schematisation uses geometric components such as locations, paths and surfaces to signify idealised, abstracted and topological elements that are marked out for secondary attention. This process involves identifying a ‘figure’ from the ‘ground’ and appears to use fuzzy Euclidean concepts e.g. any surface is reduced to a plane, which the abstraction may represent with uncertainty e.g. the plane may have no defined edges. Langacker (1983) developed a similar scheme. Viewpoint structuring of a reference scene involves the use of reference frames relative to the observer as Levinson (1996) has shown. There are ‘extrinsic’ geocentric reference systems that may use cardinal directions (e.g. ‘east of’) or other absolute environmental forms of orientation. ‘Intrinsic’ reference systems relate a figurai entity to a reference entity by projection of a reference frame from a person or entity (e.g. the station is in front of the college). The use of reference frames appears to be highly complex and scaledependent as individuals switch reference frames from intrinsic for small scale spaces to extrinsic for large scale spaces (Taylor and Tversky 1996). Individuals also switch perspective from personal (own or addressee’s) to a neutral perspective, a process that may be socially driven (Tversky 1996). Herskovits (1986) analysed locative expressions in language showing that they cannot be understood straightforwardly as prepositions expressing simple geometric relations.

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There many deviations from the ideal meanings of locative expressions based on conventions and tolerance, and these deviations of context and idiom cannot be explained by an ancillary Pragmatic account of meaning. Herskovits suggests that two levels of abstraction are required for locative expressions: the ideal account and the ‘use type’ to correspond to specific conventions associated with prepositions. She documents ‘use type’ conventions consisting of a phrase pattern around a preposition and constraints relating to the scene and the context. Lakoff (1987) has argued that structure of categories found in language reveals a rich linguistic ontology, much of which is spatial in nature. Lakoff argues that categories are organised by embodied and metaphoric ‘image schemas’. Mark and Frank (1991) developed a view of spatial conception based on the notion of the image schema as cognitive models that mediate between perception and concrete visual, tactile or haptic experiences. Since many of the image schemata identified by Johnson (1987) and Lakoff (1987) such as platform, container, path or surface are explicitly spatial, Mark (1989) argues that human understanding of space and their use of spatial language depends heavily on these ‘experiential’ concepts. Lakoff’s argument that ‘basic-level’ categories can be identified that are intermediate in scale and maximally distinct suggests that there is a way to identify spatial concepts with ontological primacy. Mark and Egenhofer (1994) attempt to study how the cognitive understanding of spatial configurations relates to geometric concepts and how it varies between the speakers of different languages. They carried out a series of experiments that asked subjects to group 40 drawings of different spatial relations between a road drawn as a line and a park drawn as an area. The results compared the groupings generated by the subjects with the grouping defined by the ‘9-intersection’ geometric model (Egenhofer and Herring 1994) and showed a broad similarity in groupings with no significant language-related differences. Studies of the role of space in social relations as revealed by language have been characterised by Broschart (1995) who argued that there were three distinct approaches. The first approach metaphorically extends space to social relations; the second approach extends the positioning of bodies in rituals to social relations; and the third approach (reversing the causal arrow) extends the social relations to the spatial domain. Broschart (1995) argues the case for the third approach from a study of Tongan directionals in language, as spatial relations derive from social setting rather than physical position of speakers and addressees. Many studies of space in language have considered two- and three-dimensional space in the absence of time. Langacker (1983) argued that space and time are differentiated in language since distinct entities (the source of nouns) are constituted by summary scanning of a scene, while change (the source of verbs) is established by sequential scanning. Tversky and Taylor (1996) suggest that space and time are handled differently in language from psychological experiments showing that place and character dominate time since they are more causally associated with events. Stolze (1992) has argued that space dominates time because the expression of motion in many languages is less basic than the expression of position as expressed by markedness conditions, and therefore as expressed grammatically. Broschart (pers. comm. 1995) argued that this does not imply that time plays a secondary conceptual role to space. Cognitively, an observer simply

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takes their own activity for granted, concentrating on what is different to ‘self’ and attempting to achieve maximal interaction at minimum effort. Givon (1979) argued that in older languages ‘semantic bleaching’ of spatial concepts has produced temporal ones, and that temporal concepts have been bleached to produce abstract ones. However, in a thought experiment Givon argued that temporal identity criteria are conceptually prior to space uniqueness. Space in representational art Representational art is another source of insights into the cognitive origins of spatial ontologies since artistic works have been independently made all over the world since prehistoric times. Using Gibson’s (1966) ‘direct theory of perceptual processing’, Hagen (1985) argues that it is possible to explore the geometric properties of representative art and to make comparisons across cultures and artistic schools. Hagen argues that this is possible since all human observers experience the same ‘natural perspective’ from light striking the retina and they all have access to its associated geometric properties such as invariance under transformation. Hence, knowledge that an object is rigid gives access to the kinds of transformations that it can undergo and its visual equivalence under projection, i.e. when it is seen from different positions. Hagen (1985) analysed the geometric styles of representational art from the perspective of station (view) point options. Most European representational art from the Renaissance to the Cubists used a style, described first by Alberti in 1436, which has a single station point in front of the picture, one or more vanishing points and central perspective (parallels converge at the vanishing point). By contrast Japanese Yamato-e style used before the 15th century used a single high station point at optical infinity with parallel perspective and an oblique angle to the ground plane. Japanese woodcut known as ‘Ukiyoe’ (pictures of the floating world) also employed parallel perspective (Smith 1988). Art from the people of the north-west coast of Canada is drawn from a multiple station point perspective and the compositions are often split into several pieces. This analysis suggests that the different geometric styles of representational art demonstrate that different representations of space can emerge from similar raw images of the world as projected onto the retina. Social constitution of spatial concepts The conceptualisation of space has been widely debated in anthropology, geography and architecture, and in each of these areas typical forms of representation can be seen to be constitutive of different ontologies. However, much consideration has been given to the question of whether these spatial ontologies are culturally universal or not. Anthropological and cultural studies have focussed on the way that culture reflects awareness of space. Tuan (1977) makes a powerful case for the development of systems of geometry in human thinking from ‘primal spatial experiences’ (p7) and suggested that ‘sensorimotor and tactile experiences lie at the root of Euclid’s theorems’ (p7). Furthermore he noted that people try to ‘embody their feelings, images and thoughts in tangible material…[t]he result is sculptural and architectural space’ (p7). In a related

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view Akhundov (1986) argues that the human sense of space and time has its roots in anthropological adaptation to the external reality of a dynamic three-dimensional world. He argues that the human development of sensory apparatus such as binocular vision and perceptual capabilities such as kinaesthesia suggest a successful adaptation to an external world rich in depth and movement. This suggests a general human ability to successfully relate perceptions of space to their surrounding environment.

Figure 2.3 How the Puluwatan navigate using the ETAK system—the reference point is an island which is lined up with a series of stars

Tuan (1977) also suggests that different cultures develop different degrees of spatial skill in navigation and the location of resources depending on the stimuli provided by their environment and the prevailing social structures, and not in relation to the sophistication of their society. He illustrates this assertion by noting the development of navigation representations such as ETAK (figure 2.3) which are learned at school and committed to memory by the widely-travelled Puluwatan islanders of the Pacific. In contrast, the sedentary Temne of Sierra Leone have a very restricted vocabulary of spatial terms and do not make representations of space. The Temne, who have highly centralised and structured communities, have (intrinsically) no need to travel since the local food supply is abundant. This may suggest a skill-oriented spatial ontology reminiscent of the

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phenomenological ‘present-at-hand’ concepts developed by Heidegger (1927). Studies of the spatial structure of human settlements have also been used to elucidate the spatial concepts involved in their creation. Hillier and co-workers have developed a methodology known as Space Syntax (Hillier and Hanson 1984) to characterise the spatial organisation of buildings and open spaces in settlements. The method of CA starts by treating built environments as ‘deformed grids’ where the deformation of the grid is expressed by changing lines of sight as streets bend, and by changes in the width of any open space. These open spaces are then divided into sub-components called ‘convex spaces’ where every point can be seen from every other. This creates a set of polygons which exhausts the open space of the study area. Hillier and Hanson (1984) note that most built environments have at least one door in each ‘convex space’ which in turn implies ownership or stewardship. Axial lines can be drawn through these ‘convex spaces’ so as to define the longest possible lines of sight (figure 2.4) generating an axial map (or grpah) of the built environment. By measuring how many lines must be traversed to go from one axial line to all others, a measure of ‘spatial depth’ or connectedness of each convex space is generated known as the integrating core.

Figure 2.4 Axial lines drawn through convex urban spaces for part of Lisbon

Studies of numerous settlements by Hillier has led him to the conclusion that the integrating core is the ‘deep structure’ of the settlement, which can be considered to be like a deformed wheel. However, Hillier (1985) suggests that this deep structure is not a designed feature of the settlement but an emergent spatial property of what he terms the

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‘morphological laws of space’ through which human social organisation is worked out. The social organisation of the settlement becomes spatial through mechanisms for generating (and restricting) contact between people which Hillier terms an ‘encounter field’ and which he has empirically tested by comparing flows of people with the ‘spatial depth’ of the different components of an ‘encounter field’. It is noted that many modern designs of urban developments break up rather than integrate ‘encounter fields’, perhaps with social consequences. This is a rare example of a spatio-temporal ontology constituted from the dynamic behaviour of individuals. A related question concerns the extent to which these socio-spatial ontologies are culturally universal. In anthropology Horton (1982) has argued that knowledge is dividable into primary and secondary forms, where the primary form is a core of beliefs common to all societies and the secondary form is concerned with beliefs that vary between societies. Key features of primary theory are: • beliefs in the role of physical objects in the spatial transmission of causes and the ordering of time; • distinctions between people and objects; • distinctions between self and others. Hence, primary theories concern beliefs about objects of perception in the mesoscopic space of human experience, i.e. they do not require apparatus to extend the reach of the body’s sensory organs. Some explanations of these cultural universals have looked to the genetic innateness of concepts in perception and language (Smith 1995a) although recent work by neuroscientists has argued in favour of learning (Newport, Aslin and Saffran 1999). Montello (1995) examined the specific case of cultural variation in spatial cognition, finding a complex situation. He identified a number of areas held to be universals: • the existence of cognitive maps; • the salience of gravity and horizon; • scale-dependence of space in language; • the hierarchical organisation of regions; • the key role of recognised visual features in memory organisation and problem-solving; • the existence of multiple frames of reference; • orthogonal-oblique differences in the accuracy of angular knowledge; • the difficulty of apprehending 3D spatial relations over the 2D ones; • use of spatial metaphors for non-spatial concepts. Blaut and Stea (1991) argued that mapping sensu lato is a widespread cultural universal; this view can be considered to be an emergent concept with respect to the universals identified above. However, Montello (1995) identified cultural variances in other areas such as: • spatial language; • pictorial perception; • home ranges and activity spaces; • measurement of space;

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• environmental cues. The view that differences in language imply differences in spatial cognition is most often known as the Whorfian hypothesis after the work summarised in Whorf (1956). Montello (1995) argues that strong Whorfianism is untenable noting Tinker’s (1994) critique on the grounds that the representational theory of the mind shows that the language of thought is mentalese (see chapter 1). However, the evidence from the Hopi, Navajo, Temne and Puluwatan still suggests that linguistic differences do exist, perhaps as forms of variation/suppression of mentalese. In summary, Montello (1995) argued that the cultural universals are much more significant than the cultural variances, which may actually reflect differences in skills rather than cognition. Absolute and relative views of space One further ontological divide is between those who regard space and time as a universal physical reference framework and those who regard them as simply a set of relations between phenomena. The ‘substantivalist’ view (absolute space and time) arises out of Newtonian physics and implies that phenomena can be defined in themselves by where and when they are found (Sklar 1974). Spatial representation simply requires the bounding or sampling of the phenomena. The ‘relationist’ view (relative space and time) was first elaborated by Leibniz and suggests that space can be defined as the set of all possible relations between phenomena. By analogy time can be defined (in Leibniz’s famous phrase) as the order of succession of phenomena (Casey 1997). Here spatial representation must be fully spatio-temporal in nature: it is the (causal) connections and dependencies between phenomena that have ontological importance and which must be identified in this scheme. These issues will be examined again in chapters 3 and 4. Ontological implications In the study of ontology there is a bifurcation between commitments to phenomenology or to realism. Smith (1995b) argues that choosing the latter option requires a mereological approach to ontology and raises questions about how to find ontological kinds in the bona fide and fiat domains. Studies of ontology have also divided into rationalist (nativist) and empiricist accounts. In the rationalist view of space ontologies develop from the architectures of the brain while in the empiricist view ontologies develop cognitively based on learning from experience. If the rationalist view is accepted (the view of the neuroscientist O’Keefe and the cognitive scientist Pinker), then it may be that the brain architectures for perception or language construct spatial ontologies. These ontologies would drive skills and aptitudes for space, force the understanding of particular representations of space and condition performance in tasks such as wayfinding. If the empiricist view is accepted (the view of the cognitive scientist Lakoff and the architect Hillier) then cognitive structures such as cognitive maps, encounter fields or linguistic categories would play the key role, defining spaces cognitively. Perhaps the key question is whether this distinction is a dualism or a duality; if it is the latter then there is a role for feedback between the two forms of ontogenesis and the relative importance of each may be constitutive of cultural variations

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in concepts of space. This debate has a parallel in the debate between substantivalism and relationalism since the former doctrine holds that the structure of space dictates ontologies while the latter holds that the cognitive ontologies generate spaces. Both debates may ultimately be derivatives of the mind-body problem. In this book it is argued that the move from a ‘timeless space’ view to a multidimensional view presents new ontological perspectives on these debates and leads to new insights.

EPISTEMOLOGIES OF SPACE There are many epistemologies of space depending on the role that space is allowed to play in knowledge. Chapter 1 gave a historical account of epistemology covering the 18th century debate between rationalism and empiricism, the 19th century and early 20th century development of positivism, and the late 20th century reaction against positivism which produced post-positivism. Each of these broad movements attributed space a different role: rationalism saw concepts of space as innate while empiricism saw them as learned; positivism sensu lato saw space as a privileged frame with causal force; while post-positivism has seen space as an arena for events. In contemporary science there are some adherents to positivism who happily commit to deductive-nomological explanation, scientism, determinism and realism in which space has a central role. However, these are neo- positivists who have accepted the critiques of relativism, the reality of indeterminism and the limits to explanation, who give space a constitutive but not privileged role. Post-positivism has developed multiple forms of analysis in which space plays various supporting roles. Each of these three schools of thought provides a focus for research in geography as well as those disciplines such as geology, architecture and anthropology where space plays a part in theories. Geography is central to these discussions because it is the only discipline to identify epistemologies of space with its own disciplinary epistemology. This section reviews the evolution of these schools of thought about the epistemological status of space and discusses the commitments of contemporary research in each of these areas, focussing particularly on spatial representation. The evolution of epistemological theories of space There are a number of threads to the evolution of epistemologies of space: the origins of the discipline of geography; the development of a scientific geography; and the various rethinkings of space. Each of these threads has influenced the epistemological whole in different ways. Metaphysical aspects of space have already been discussed above and the origin of spatial representation is discussed below, hence this section focuses on space and explanation, which is largely a 20th century concern in geography. There are many views on where the origins of the discipline of geography lie, including classical scholars like Ptolomy and Strabo, Arab astronomers like Al-Idrisi, 17th century writers such as Varenius, or 19th century authors like Humboldt and Ritter (Unwin 1994, Goodchild et al. 1999). Varenius can be regarded as the first to reconceptualise geography from the prevailing Aristotelian perspective to to the

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Cartesian/Newtonian framework (Warntz 1989). In Varenius’ (1650) Geographic Generalis, he divided general geography into the absolute (earth system science, climatic zones, oceanography, meteorology), relative (astronomy) and comparative (navigation) parts. Varenius divided his special geography into terrestrial (territory, land use), celestial (global geography) and human (population, customs, politics) parts, although he did not live to develop it fully. In the 18th century Kant argued in his ‘Critique of pure reason’ that science was concerned with time, causality and space, the latter being the concern of geography (Buttimer 1993). In his Physische Geographie (written 1757, published 1802) he divided studies of geography into morphological (form of the earth), chorological (regions) and human types. Unwin (1992) has pointed out the distinction Kant made between the sense of space and time in the Critique of pure reason and the experience of space and time in the Physische geographie. The epistemology of space was advanced in the 19th century by Humboldt’s (1845– 58) regional syntheses in his Kosmos and by Ritter’s (1817–59) teleological account in his Erdkunde. It was also at this time that the political doctrine of space as territory developed. In Europe nation-states were engaged in direct competition for territory at home and in colonisation abroad. In North America, new States growing rapidly by inmigration were literally marking out new territories (in the US using the Public Land Survey System) in a continent sparsely populated by European and Asian standards. In this era geography was concerned with space as a commodity through the exploration, demarcation and administration of new territorial possessions, overriding the sharing of land practised by the indigenous cultures (Meinig 1986, 1993). However, no systematic attempt was made to argue that space had causal force in the mesoworld of environment and society before the late 19th century through writers such as the geomorphologist W.M.Davis and the regional geographer Vidal de la Blache. In the 20th century the first major theoretical movement to advance an epistemology of space was that of environmental determinism which argued that the environment produced societies (Semple 1911, Whitehead 1933). However, environmental determinism was rejected in the possibilism of Febvre (1925) and the landscape synthesis of Sauer (1925) which then led on to the idiographic ‘regional geography’ of Hartshorne (1939). Regional geography promoted the demarcation of regions through chorology and their mapping in spatial representations. After the Second World War geographers began to stress a physical view of space: writers such as Schaefer (1953) and Bunge (1962) considered space as a container and geometry as capable of framing explanations of geographic phenomena in the deductive-nomological sense. In parallel physical geographers had begun to formulate theories of landscape behaviour based upon mechanics that explicitly used physical space: the seminal monograph by Leopold, Wolman and Miller (1964) on fluvial channel behaviour and landscape evolution is the best example. The so-called ‘Quantitative Revolution’ of the 1960s in geography as a discipline also extended the concepts of space employed in ‘spatial’ explanation to those that Couclelis (1992) termed ‘socio-economic’ by transforming physical space to develop new explanations. Thus, Tobler (1961) showed how travel times could be modelled by nonlinear functions defined by ‘work required to overcome distance’ while Hagerstrand (1953, 1968) suggested that distance away from a place was ‘experienced’ as the

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logarithm of Euclidean distance and Haggett (1965) analysed patterns in the spatial location of settlements. While the theory of industrial location deriving from Weber (1929) used a concept of isotropic space, extensions of this thinking in the 1970s (e.g. Lloyd and Dicken 1972, Keeble 1976) sought to define ‘economic spaces’ based on Euclidean distances as modified by a ‘cost of location’. Behavioural geography developed the argument that it was perception that structured space (Downs and Stea 1973, Golledge 1980), building on the pioneering work of Lynch (1960) on urban perception in Boston. Harvey (1969) considered geometry to be a language of spatial form usable in positivistic scientific explanations. Later works criticised this position: Sack (1972) argued that geometric laws cannot satisfactorily answer geographic questions since geometry is based on static axioms. Sack’s critique was among the first of many reflections on an epistemology of space in which the physical extension of space or its transformation could be regarded as causal. The 1970s saw a number of rethinkings of this position which have been documented by Johnston (1997). These new positions included humanistic geography that developed phenomenological perspectives e.g. the aesthetics of ‘place’ (Tuan 1977), radical geography which looked to structuralism and the importance of generative processes rather than the properties of space per se (Sayer 1984). The postmodern cultural turn concerned with ‘other’ spaces (Harvey 1989a) also brought new perspectives.

Figure 2.5 How rural village land can be consolidated by rebuilding houses and merging plots through land reform

In the 1980s and 1990s multiple and incommensurable epistemologies of space have

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existed side by side within geography. Hence Gatrell (1983) reasserted the importance of physical space in explanation by defining ‘relative spaces’ as relations established on sets of geographically located phenomena and used techniques such as multidimensional scaling to determine the relations between them. Gould (1997) argued that physical space and its transformations are still powerful epistemologies for epidemiology. However, other geographical work has sought to demonstrate that neither physical space nor its transformation can provide explanations for social processes—in other words that space is conceptualised experientially and merely provides an arena for social processes. For example, work by Pred (1986) shows how agricultural communities in southern Sweden were forced to change the spatial structure of their land ownership through a legislatively enforced enclosure (called an ‘enskifte’), whose origins lay in population growth and the intensification of agricultural production in the late 18th and early 19th centuries. Figure 2.5 shows how land holdings can be consolidated by rebuilding houses and merging plots of land. Here the spatial change is socio-political in nature, as it is the land reform legislation that demands consolidation of the space into larger simpler holdings. Epistemological commitments of contemporary research on space It can be argued that contemporary research in geography exhibits three distinct positions on the explanatory force of space, each of which has commitments to spatial representation. These positions are sketched out below to illustrate the way in which epistemologies of space are currently seen in different communities. Positivism There is an epistemology of space that accepts deductive-nomological explanation, scientism, determinism and realism. However, in this view space is embedded in physical laws and so is not an explanatory variable per se. Typical concerns would be the functioning of physical processes in the environment, e.g. turbulent flows in river channels. Spatial representation is seen in this view as a way to report results of analyses. Neo-positivism In this epistemological view space has explanatory power in the sense that space or its transformation is constitutive of generalities of behaviour in environment and society. Adherents to this view have accepted the critiques of relativism, the reality of indeterminism and the limits to explanation where space is regarded has a constitutive but not privileged role. In this view space is not causal but does play a role in framing, constraining or directing behaviour, whether relating to commuter flows within cities or to catchment flood discharge. Spatial representation in this view is a part of the conjectural apparatus used in developing explanation and as such their role is important. Post-positivism There is a family of (largely social) epistemologies in which space plays no special role.

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Space is an arena for social processes and so cannot play an explanatory role. In this view space is consumed and reproduced as a consequence of human actions. In these epistemological traditions spatial representations attempt to capture the ‘uncapturable’ and are doomed to failure. The issue of whether space can be used to explain is one of the most crucial issues in the development of geographical knowledge, since, attitudes to this question govern whether spatial representations are worth making. This book argues that the neo-positivist view is a tenable one since the role of space as a constitutive element in explanation is widely accepted. However, to further examine this question of ‘space as constitutive’ requires a consideration of how spatial concepts are realised as representations of space, in particular, whether currently available and used representations of space are sufficiently rich for the epistemological work they are intended to do. There are several possible directions for research: Peterman (1994) argued that it is the Newtonian model of science that has held back progress, suggesting that quantum indeterminacy offers new forms of thinking, for example, on quantum action-at-adistance (non-locality). However, in this book it is argued that the limiting factor for neopositivist explanations is the static two-dimensionality of the representations, since it is the representation that often frames the theorising. Perhaps a move beyond two dimensions to three or four will offer new possibilities.

THE ORIGINS OF TWO-DIMENSIONAL SPATIAL REPRESENTATION Two-dimensional spatial representation has evolved from roots in mathematics, physics, geometry and cartography dating back over many thousands of years. Mapping and navigation today are still based upon these representational foundations. However, premodern representation depended on, and was limited by, the paper medium with which it was associated. Modern representation need not be designed on these foundations yet many digital forms of mapping and navigation simply mimic analogue principles and processes. This section will explore the historical development of mapping and navigation from its mathematical, physical and geometric roots to show how twodimensional representation is founded, and where new multidimensional representations can be substituted. History of mathematics, physics and geometry The origins of mathematics, physics and geometry reveal much about the evolution of representations of space. While the ancient Chinese, Egyptians and Babylonians developed systems of counting (the latter using base 60), the development of mathematics and numbers is generally credited to Thales the Greek philosopher and his follower Pythagoras. The development of number systems led to a consideration of the correspondence between numbers and the external world, especially the concept of discreteness, which was required to establish the difference between numbers. The duality of continuity and discreteness is probably at the root of the Greek philosophy of

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space and seems to have led Archytas (the Pythagorean disciple quoted in Simplicius’ Commentaries) to propose a theory of space in the 5th century BC in which space had a physical existence separate from matter. This view was elaborated by Democritus and then Epicurus, who suggested that matter was made of indivisible particles (‘atoms’) which occupied space, and that bodies made of matter were separated by a void considered to be an empty (spatial) extension. This view was in contrast to Parmenides’ view that space was a continuous plenum (Jammer 1954). Plato and Aristotle (in the 4th century BC) both criticised the atomistic theory from the perspective of physics, Plato (in Timaeus) suggesting that matter cannot be isotropic due to the variable density of the elements. Aristotle argued (in ‘Physics’) that space must be finite and continuous, and not infinite and discrete (as the ‘atomists’ argued) since the discrete particles of matter would have to have ‘space’ between them. Aristotle argued that such a view implied (implausibly to him) that the ‘space between’ would have to be carried around when the matter moved. Aristotle’s own work in his ‘Physics’ defined space as ‘the sum total of all places occupied by bodies’ (Jammer 1954) and suggested that space could be considered as a field of force, thereby arguing that place exerts an influence on matter and anticipating much later work (Casey 1997). The geometry of Euclid’s ‘Elements’ (written in the 3rd century BC) was derived from this earlier work in mathematics and physics. Euclid formalised a series of laws of geometry derived from the empirical experience of ancient surveyors (for example, the Egyptians who measured and re-established field boundaries after the annual Nile floods) and the theoretical work of the early Greek philosophers (such as Pythagoreas’ theorem of right-angled triangles). These laws depend, however, on the axioms which assume a general acceptance that straight lines and circles can be defined on infinite isotropic planes. Euclid defined these geometric figures from the primitives point (‘that which has no part’) and line (‘a breadthless length’). Most of Euclid’s laws concerning geometric figures concerned two-dimensional forms on a plane (which hold very well over small regions of the earth’s surface up to a few kilometres?). Consideration of solids was limited to measurement principles and to showing the nature of the two-dimensional figures yielded by intersecting planes with solids such as cones. Eratosthenes (working in the 2nd century BC at the great Library in Alexandria) was probably the first to accurately calculate the dimensions of the globe. He was able to make these calculations when he heard that there was a well in Syrene (now Aswan) in southern Egypt whose base was only illuminated at noon on June 22nd each year. This meant that Syrene lay directly on the Tropic of Cancer, which at 23.5 degrees north is the most northerly latitude where the sun appears directly overhead on the date of the summer solstice (June 22nd). This implies that on the solstice the suns’s rays make a 90 degree intersection with the ground surface and the earth’s centre on the Tropic. Eratosthenes measured the angle of the sun above the horizon at Alexandria at 82 degrees 48 minutes on the solstice the following year, which he had measured at 5000 stadia due north of Aswan using pacers. Then Eratosthenes was able to construct a planar triangle with points at the earth’s centre, Alexandria and Aswan (see figure 2.5). From the dimensions of the triangle he was able to estimate the circumference of the earth using geometry, which, expressed in kilometres, at 46, 250km was only 15% too large. The errors lay in the distance estimation and in the fact that Aswan and Alexandria are

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actually 3 degrees apart in longitude.

Figure 2.6 How Eratosthenes calculated the earth’s circumference

From these insights it followed that position north or south of the equator (latitude) could be calculated by measuring the angle of the sun above the horizon at noon, and this became a common technique in navigation. However, measuring position around the earth’s circumference (longitude) was very difficult in classical times as there was no method to calculate relative longitudinal locations. The solution to this problem uses the fact that time is equivalent to distance in terms of the earth’s rotation: 1 hour is equivalent to 15 degrees of longitude. The calculation of longitude required navigators to find the time difference between noon at their current position with the time of noon somewhere else that had a known position. The time difference then told them the longitudinal difference, which could be converted to an angle. With latitude from the sun’s angle above the horizon at noon and longitude calculated by a time difference the navigator could fix an accurate position on the earth’s surface. This calculation first became

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possible with the construction of a clock accurate enough to maintain a fixed time while travelling in the mid-18th century. The story of the search for a method to find the longitude is very well told in Sobel (1995). Note that neither Euclid nor his predecessors used or mentioned plane coordinates despite knowledge of them in ancient Egyptian times when the hieroglyphic symbol for a district was a grid (Jammer 1954). The acceptance that the earth was spherical by the Greek philosophers did though lead to the use of coordinates of latitude and longitude. Eratosthenes in his 2nd century BC description of the ancient world used latitude and longitude to calculate the size of the earth and Ptolomy gave extensive positions in this form in his ‘Geography’ (although the original maps have been lost). Between Roman times and the Renaissance, mapping and mathematics only flourished among Arab cartographers and astronomers such as Al-Idrisi and Medieval theologians such as St Thomas Aquinas.

Figure 2.7 Conic sections

The introduction of the Hindu-Arabic system of numbers used by Arab astronomers such as Al-Khwarizmi into Europe is generally credited to Fibonacci in the 13th century. The use of the Hindu-Arabic system of numbers led to advances in counting, arithmetic and algebra by early mathematicians such as Sacrobosco, Palegrave and Recorde between the 13th and the 16th centuries (Crosby 1997). Renaissance artists and architects such as Giotto and Brunelleschi also introduced and developed linear perspective explicitly for the purpose of representational verisimilitude (Wertheim 1999). The rules of perspective were codified by Alberti of Florence in the 15th century who set out detailed rules of method. Casati (1999) argues that these artists and architects were influenced by the works of Ptolemy (who used cast shadows in his work on projection) reaching Florence around 1400 from the Arab world (Casati 1999). In parallel with developments in

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perspective, the astronomical work of Renaissance scientists such as Copernicus and Galileo between the 15th and 17th centuries established the basis of physical space and its relation to physics. In the first half of the 17th century, while investigating algebraic curves such as conic sections (see figure 2.6) and mechanical curves described by a pendulum such as the cycloids, the French mathematician Fermat studied the space within which these geometries unfolded. Fermat’s contemporary Descartes formalised the principles of plane coordinates in 1637 by defining a space to be matter extended in length, breadth and depth, thereby facilitating the assignment of numbers to these dimensions. Since he also held that space was a universal fixed framework of reference for matter, the ‘Cartesian’ coordinate system defines an ‘absolute’ (universal) representation of space. Newton used this concept of ‘absolute space’ as an ‘inertiaP frame of reference for his laws of physics published in his Principia in 1686–7. Euclidean geometry and Cartesian coordinates have been accepted as a practical framework for the description of ‘matter in space’ over small regions of the earth’s surface since the late 17th century. This acceptance has much to do with their teaching in schools and their effectiveness in making routine calculations for construction and land surveying in urban societies. However, Kant also suggested in his Critique of pure reason published in 1781 that ‘Euclidean geometry formulates the structure of the form of our external intuition’ (Nagel 1964, p 195)—in other words that geometry is in some sense innate to the human sense of space. Kant made this argument in the context of his classification of knowledge into statements which are analytic (true by virtue of the meanings of the words they contain) or synthetic (true, otherwise), and gathered from a priori (mental) or a posteriori (experience) sources. To Kant and the rationalists mathematics in general and Euclidean geometry in particular was ‘synthetic, a priori’ knowledge. However, non-Euclidean geometries destroyed the most important argument for rationalism. Early 19th-century European mathematicians such as Lobachevski and Bolyai discovered non-Euclidean geometries by examining Euclid’s axiom defining parallel lines and questioning whether it was necessarily true that parallel lines could never meet or cross. By assuming that a space could have constant negative curvature Lobachevski and Bolyai defined hyperbolic spaces (more than one parallel line is possible), while Riemann and Klein defined elliptic spaces (no parallel lines are possible) where space had a constant positive curvature. These discoveries showed that Euclidean geometry could not be a priori as there were other kinds to be discovered. Einstein commented, ‘as far as the laws of geometry apply to reality they are not certain, and as far as they are certain they do not apply to reality’ (Einstein 1921, p 28). However, despite these discoveries showing that Euclidean geometry had no privileged status it was still clear that it played an important part in perception. Hence, Musgrave (1993) argued that ‘Kant was wrong to say that we must (logically must) structure our science on Euclidean principles—he was right to say that we always will’ (p234). Poincaré (1900) argued that we use Euclidean geometry because of its simplicity, pointing out that if science used hyperbolic geometry, science would be complex! This illustrated a duality between possible and physical spaces: hence it can be argued that mathematics reveals the possible spaces while physics decides which of them corresponds to physical space (Reichenbach 1964). Perhaps geometry is analytic a priori

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and deals not with reality but with proving theories from axioms. This position is the foundation of 20th century studies of space, which have concerned themselves with the linkages between space and time (see chapter 3). History of cartographic representation The evolution of spatial representation in mathematics, physics and geometry has paralleled the development of maps and cartography since earliest times. The oldest maps with an identifiable geometric form which still survive are the 4000-year-old Bedolina petrograph in Italy and the 3500-year-old clay tablet with a large scale city plan of the Nippur district of Mesopotamia (Thrower 1996). Only fragmentary maps are preserved from the ancient world on sarcophagi, coins and tablets. At large scales these maps reflect their use, for example, water management in Egypt, while at small scales their purpose was normally symbolic. In China maps have survived from the 2nd century BC (Hsu 1978) when Chang Heng developed a plane square grid outline. Later, a manual of cartographic principles covering distance, elevation and scale was written by Phei Hsiu in the 2nd century AD. The earliest mention of the magnetic compass dates from the 3rd century AD in China, although compass bearings may not have been used for mapmaking until the llth century. The 6th century Korean Buddhist priest Gyogi-Bosatu also pioneered map-making in the ancient eastern world through his direction of civil engineering projects in Japan (Thrower 1996). One of the earliest Chinese regional maps is the ‘Map of the footsteps of Yü the Great’ dating from 1137 which was carved on rock with a constant scale over a grid and shows largely geographically correct river courses as lines. The first printed map was published in 1155 in China, and Chu Ssu Pen produced the first atlas of China in the early 14th century. Printed maps of the late Indian Moghul empire were also produced in accurate but pictorial style. In the western world ancient Greek work on astronomy by Aristotle had established that the earth was a sphere by observing the curved shape of the earth in eclipses of the moon (although he suggested that the sun and planets orbited the earth). Mapping seems to have been practised by the Greeks as Eratosthanes and Hipparcos (2nd century BC) discussed the principles of cartography such as the methods for finding latitude (angle of the sun above the horizon at noon) and longitude (finding the different times of eclipses at different places). Ptolomy (2nd century AD) later tabulated latitude and longitude positions for a wide range of places in his Geography. However, only fragments of maps from this time have survived in their original form such as the Dura Europa shield map from 260 AD. Roman cadastral mapping used rectilinear surveys subdivided into hundreds in a process known as ‘centuriation’ that was widespread through the Roman Empire, as indicated by the Corpus Agrimensorum published around 500 AD (Thrower 1996). In the years following Ptolomy’s work in the 2nd century AD little evidence of mapping remains although the 4th century Peutinger map of the Roman Empire showed itineraries and country outlines in diagrammatic form. Maps of the European Middle Ages were mainly of the ‘orbis terrarum’ (T-O) type, which took the form of a circle divided into three continents (Europe, Africa and Asia) by a T in which the

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Mediterranean formed the upright of the T (east was at the top). Although St Augustine may have described a ‘T-O’ map of the ancient world in his De Civitate Dei published in the early 5th century (Wright 1965), the Hereford Mappamundi of the 13th century is the archetype and one of the few of its type to survive. Ptolomy’s world map (extending from the Indian Ocean to the British Isles) was lost and had to be reconstructed in the 15th century from his geographical descriptions as preserved by Arabic scholars in Syria, Babylon and Persia in the 7th and 8th centuries AD (Qadir 1988). More elaborate world maps showing the approximate courses of rivers and mountains were produced by the Spanish Benedictine monk Beatus in the 8th century (although only copies such as the St Sever map of 1050 survive). The Arab cartographer Al-Idrisi at the court of Roger of Sicily in 1161 also made a celebrated world map from the accounts of travellers. While these maps of the Middle Ages are diagrammatic in form with significant distortions due to ignorance or a desire to portray important areas of the time, such as Palestine, in greater detail, they do use symbols and show features to scale using point and line geometric primitives. Other maps such as those of Britain derived from a matrix of itineraries by the monk Matthew Paris in 1240 are annotated and symbolised to show land cover e.g. marsh, forest and mountain. Early observations of latitude and longitude were made by Arabic astronomers such as Al-Khwarizmi in the 9th century and compiled into tables, for example, those produced by Raymond of Marseilles in 1140. Latitude was determined from observations of the sun’s elevation at noon while longitude was determined by comparing the times of eclipses recorded by different astronomers at different locations. However, these observations were not used to make maps before 1250: according to Wright (1964) ‘their influence on the cartography of the age was absolutely nil’. However, the arrival of the magnetic compass in Europe the 13th century led to a decisive step forward in mapping—the creation of planimetrically correct nautical maps known as ‘portolan charts’ made from accurate positional information collected by navigators. An example is the Catalan atlas of 1375 described by Campbell (1993). The period of the Renaissance from the 14th to the 16th centuries saw rapid advances in astronomy, geographic knowledge and cartographic technique. In 1514 Copernicus proposed that the planets (including the earth) orbited the sun and not the earth itself, overturning the view of Aristotle. The observations of the moons of Jupiter by Galileo in 1609 showed that a non-geocentric universe was possible as their orbits did not pass around the earth (Burtt 1932). European exploration was completed eastwards (Marco Polo’s travels overland to China in 1271–5) and westwards (Columbus’ voyage to the West Indies in 1492). Early sea voyages of exploration to Africa and Asia were organised by Henry the Navigator of Portugal whose ships reached the Cape Verde Islands by 1460. Before the end of the 15th century the Portuguese reached the Cape of Good Hope under Bartolomeu Bias and India under Vasco da Gama. The first circumnavigations of the globe were achieved by Magellan’s expedition (1519–22) and by Drake (1577–80). These expeditions resolved the last unknowns regarding the positions of the continents and permitted the creation of the first longitudinally correct projected world maps by Contarini (1506), Waldseemüller (1507), and Rosselli (1508) (Thrower 1996). Mercator’s world map of 1568 projected the sphere onto a plane using the conformai cylindrical transformation later known as the Mercator projection. In 1570 Ortelius published the

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first comprehensive atlas, the Theatrum orbis terrarum consisting of a bound set of planimetrically accurate maps. This process of ‘projecting’ the three-dimensional globe onto a two-dimensional plane for mapping purposes began a convention of spatial representation which is now deeply embedded in (western) thinking, education and practice. Publication of paper maps and atlases became common in the 16th century, with the focus shifting from world to regional maps. These included works such as the Saxton atlas of England and Wales published in 1579, city plans such as the Civitates Orbis Terrarum atlas of European cities by Braun and Hogenberg in 1572, and marine charts such as the Spiegel der Zeevaerdt by Waghenaer in 1584–5. Maps of this time represented rivers by stylised ribbons, elevation by vague shading and settlements by symbols or pictures of various kinds. By the late 17th century surveyors began to use triangulation techniques for mapping (the first triangulation of France was complete by 1740), leading to the creation of much more accurate maps which could be used to measure distances between places. Perhaps as a consequence of the greater overall planimetric accuracy, early 18th century maps based on triangulation such as the English county maps by Warburton (published in the 1720s) marked roads and rivers in the correct locations and showed the extent of settlements by symbolisation. The 18th and 19th centuries saw further technical development in map making with the accurate measurement of the shape of the earth, permitting the development of models of the spheroid. Metric units were defined in 1791 by the Paris Académie des Sciences and a number of new projections were developed by Lambert and Gauss. Hydrographie mapping began at this time with work on tides by Halley (1702) and bathymetrie mapping of the English Channel by Buache (1737). Geological mapping also began in the 18th century with surveys of rock types and mineral outcrops in Saxony by Gläser in 1775 and of the palaeontology of Wessex by Smith around 1800 (Oldroyd 1996). The clockmaker Harrison developed a chronometer in the mid 18th century capable of determining longitude accurately (using differences of sun’s zenith time from that at standard meridians (Sobel 1995). The designation of the Greenwich meridian as the globe’s Prime meridian or 0° line of longitude in 1884 and the introduction of the International Time Zone system were important acts of standardisation with far reaching consequences for geographical knowledge. The first nationally consistent ‘official’ map series were surveyed and published in the 18th century in Austro-Hungary, France and Britain at scales of around 1:50,000. These ‘topographic’ maps were originally made by the state for military purposes, notably during the Balkan wars between the Austro-Hungarian Empire and the Turks, and during the Napoleonic wars between France and Britain. Accordingly topographic maps were designed to express geographic knowledge useful to the military such as relief, rivers, coastlines, land use, boundaries and the names of settlements. This knowledge was invaluable to field commanders: in the early 1800s Peninsular campaign of the Napoleonic wars the British General Wellington commented on the advantages of fighting a battle in ‘a country of which I had an excellent map and topographic accounts’ (Hodson 1993). The requirements for geographic knowledge established by these early military campaigns have had a profound impact on the development of topographic maps. Many

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national surveys when established were primarily set up for military reasons and staffed by army surveyors. Hence, many early topographic map series contained the knowledge required by the military and omitted much else, for example the type of housing or water distribution methods. The design of these early maps employed geometric primitives for representation of the mapped features of the landscape. Hence, field boundaries and woodland were represented as polygons, roads, rivers and boundaries were represented as lines and settlements were represented by symbols whose size and shape may or may not have corresponded to the actual buildings. While these maps vary somewhat with the landscape surveyed (e.g. Swiss maps developed sophisticated relief representations, American maps depict whether river channels are perennial or not), the overall design of the topographic map was propagated in a remarkably similar manner across 19th century western Europe and North America. Maps made for the recording of land ownership and taxation developed from early models in Sweden, Piedmont (Italy) and Savoy (France). The record or ‘cadastre’ of all land parcels began to be based on maps in the 18th century, the Savoy Cadastre carried out between 1728 and 1738 being an early example (Kain 1993). Such maps were functional and used line geometry to represent the edges of land parcels and symbolisation or lettering to show their ownership. In this sense these maps implemented a sense of space in which it is possible to delineate sharp boundaries between properties (usually represented by a wall or fence) that were ‘owned’ by a named individual. These maps often contained (and still contain) very little other information although privately commissioned estate maps often showed additional information. Such cadastral maps were usually drawn at large scales, for example the Savoy Cadastre was made at 1:2372 and the first survey of Ireland (created for taxation purposes) was made at 1:10560 from 1824 onwards. Topographic and cadastral maps have developed over the last 200 years in close association with the governance of (western) states. This followed from the realisation that only states had the money and power to accomplish universal mapping at that time, and that it was in the interests of the state to inventory and control resources, especially land. As such the scale and content of maps has tended to serve specific government policy objectives which have sometimes been internally conflicting. For example, the development of mapping policy in the British Isles involved what Harley (1975) refers to as the ‘Battle of the scales’ between 1850 and 1858 in which various interest groups in Parliament sought to influence the designated base scales used in different parts of the country. As well as within governments, the content of maps has also been a matter of contest between governments and external users of mapping. Hence, map specifications have periodically been revised to permit the inclusion of new features and take account of policy changes such as the introduction of comprehensive planning laws, which have become common in the 20th century.

MAPS AS REPRESENTATIONS OF SPACE Mapping can be considered in the narrow or in the broad sense. Mapping in the narrow sense concerns maps as sign systems and representational devices. In the broad sense

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mapping concerns the ‘interested acts’ carried out by the cartographer to communicate a message and to highlight some things and to hide others (Harley 1989, 1990). Both perspectives shed light on the nature of maps as representation. Maps and mapping The content of maps for a particular scale, the correspondences between world and map, and the symbolisation of the map have been progressively refined by national surveys during the 20th century. The implementation of these issues is often described post hoc in manuals of current practice (Australian Survey 1992). However, the deeper issues of what model of the world that the ensemble of mapped features represent in topographic/cadastral maps has rarely been examined. Mark (1989, p555) comments that ‘it is unlikely that the features and feature classes shown on topographic maps correspond exactly with the concepts of topographic features held in the minds of users’ noting that often map features generalise or summarise the real world entities in undocumented ways. He examined the Digital Line Graph-Extended (DLG-E) specification for US Geological Survey, National Mapping Division topographic mapping which divided ‘geographic reality’ into cover (land cover and use), division (administrative areas), ecosystem, geoposition and morphology (landscape and built form). He notes the restricted nature of this model, e.g. shoreline features include ‘bar, beach, cape, foreshore, island, isthmus’ but not spit or fjord. Mark (1989) argues that topographic mapping signs should be built on image schemata, which are cognitively relevant to users and not the views of cartographers. Smith (1979), then head of the Ordnance Survey in the UK, carried out one of a very few de novo studies of the goals and implementation of topographic mapping for the Serpell Enquiry. He divided the goals of topographic mapping into two, viz. first, ensuring order—security, protection of life and property, and administration; and second, encouraging progress—educational, economic and social. From these goals he derived priorities (figure 2.8) for the inclusion of a range of ‘features’ on maps extending from a geodetic base (essential for all scales) through boundaries, roads and rivers (essential for most scales) to features such as tourist information and antiquities (only desirable on some maps). This work by Smith (1979) opened up a series of questions about topographic/cadastral mapping such as whether the state was still the only body that could carry it out given the need to protect individual rights; whether it should be spatially consistent across national territory; and, whether the economies of scale which the state could derive justified its involvement in the process (Rhind 1991). It also anticipated later debates between users and producers of mapping as to what ‘features’ should be included (Rhind and Coppock 1991). McHaffie (1995, p114) comments that ‘the social investment in the creation of large scale “general purpose” mapping systems has become an essential element in the systematic public provision of infrastructure’. In this sense topographic mapping has become both a reflection of public policy and a powerful influence on perceptions of space (Dorling and Fairbairn 1997). The symbology of topographic mapping is taught in schools and the terminology of the map is employed in law and professional practice.

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Where complete and mandatory cadastral systems are in place, as in the Netherlands, the map is a legal instrument and its depictions implement title to land. Maps and communication about space in the narrow sense From this cartographic history and the review of topographic/cadastral mapping it can be seen how much professional geographic knowledge has become linked to concepts of Euclidean space implemented using geometry and coordinate systems in two dimensions. Hence Euclidean space and representations of it have come to be defined by those concerned with the logistics of battle, the delineation of land ownership, and, in the 20th century, by civil engineers responsible for road, canal, railway and property construction. In all these cases physical distance is the key characteristic of space: the distance soldiers have to march, the extent of property and the line of the constructed transport infrastructure. The primacy of distance in the Euclidean space of topographic mapping and the coordinate geometry required to implement it are though not the only concepts of space expressed in mapping.

Figure 2.8 Topographie features required by map users (from Rhind 1991, after Smith 1979)

Thematic mapping has developed alongside topographic mapping since the early 18th century—Robinson et al. (1978) identify a map of magnetic variation over the Atlantic by Halley in 1701 as one of the earliest examples. Thematic maps portray spatial variation, flows, patterns and inter-relationships among and between phenomena. They often use topographic map features such as boundaries as a base for representation although many thematic maps also transform ‘physical space’ to portray other spaces. For

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example, Hagerstrand’s map of perceived distance from Asby (Hagerstrand 1953) shows how distance in physical space can be logarithmically transformed to a ‘behavioural space’ which approximates people’s perception of how ‘far away’ places seem. Gould and White (1974) also studied perceptions of space and ‘mapped’ the results as cartograms. Even ‘experiential’ spaces have been rendered in concrete form (Tuan 1977). Hence, mapping has developed as a method of representation and visualisation of phenomena using several different concepts of space. Maps are made, therefore, as a form of communication about space between those gathering the spatial knowledge portrayed and those using the map to be informed. The definition of the map in the ‘History of Cartography’ is that ‘maps are graphic representations that facilitate a spatial understanding of things, concepts, conditions, processes or events in the human world’ (Harley and Woodward 1987, pxvi). This process of ‘facilitating understanding’ has been analysed extensively by cartographers from the perspective of communication theory, semiology (sign systems) and psychology (visual understanding). Early views of cartographic communication were based on the theory of communication (Shannon and Weaver 1949), i.e. a source is encoded, transmitted through a channel (which has some associated noise) and decoded by a receiver. However, this model concentrated on the transmission process rather than representation and understanding (Woodward 1992). Guelke (1976) asked a key question: is the information communicated by the sender meaningful to the recipient? This depends on the context of the transfer, in other words the transmitted data must be contextualised to give it meaning. To this question must be added another: what motivated the sender to communicate the information? As can be seen above, topographic maps were often motivated as particular kinds of inventories—to ensure order and encourage progress according to Smith (1979). However, in thematic mapping, as Monmonier (1991, p 1) argues, ‘not only is it easy to lie with maps, it is essential’. Monmonier (1991, p 1) goes on to document ‘the map’s power as a tool of deliberate falsification or subtle propaganda’ in war, advertising and urban development, while Gould (1993) mapped the spread of disease. The mapping process has also been examined from the perspective of semiology—the study of sign systems (Eco 1976). Schlichtmann (1985) summarised the principles of semiology as they applied to cartography. Thus, he argues that signs (on maps) are composed of a content (a meaning) and an expression (a graphical form), which are linked by a code (a set of rules or conventions). Note, however, that maps cannot be truly propositional languages as they have no negation sign. By analogy with natural language he argued that minimal signs (geometric symbols) are ‘words’ while ‘macrosigns’ (a located and attributed symbol) are ‘sentences’ which can be considered the minimum unit of communication. The ‘code’ linking the content and the expression of the sign can be by motivation (content reflected in expression), through singular transcription (conventional associations such as those developed by Bertin 1983) or through gradual distinction (variations in content reflect variations in meaning such as a graduated symbol). Wood and Fels (1986) extended the concept of the code linking content and expression, dividing it into ‘intrasignification’ (signs, lettering, time and the their presentation and syntax on the map) and ‘extrasignification’ (the context and

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understanding of the map in culture, politics, history, locality and use). Yet all such communication is limited to those who are able to read the code. Cartographic communication has also been viewed from a psychological perspective. In this work the role of the ‘map reader’ in holding and using the ‘codes’ linking the content and expression of maps is examined, hence, Head (1984, p 10) comments that ‘what we look for is at least as important as what is there’. Head (1984) adapts the ‘Human Associative Memory’ model of Anderson and Bowers in which a proposition is made up of subject, predicate and context in order to understand how a map reader searches a map for information. Blades (1991) has demonstrated in experiments that even three-year-old children can ‘read’ a map and establish correspondences with a real environment, although they perform much better at an age when the map and environment are mutually aligned. Studies of the human visual system and short-term memory as they constrain the perceptual process have also been used to understand mapping. Edwards (1991) suggested that when an image or map is examined the reader uses what he terms a ‘trilevel structure’ to process the image or map. Firstly the reader examines the frame (the field of view), secondly, they look for the major regularities or structures within the frame (object identification), and thirdly, they compare these structures with each other (characterising texture) before choosing one of the structures to be a new frame. This process continues until the simplest units or those that can be characterised by a metaphor are found. Similarly, the neuro-psychological work of Bauer and Rubens (1985) showed that different parts of the brain treat spatial (positional) and visual (shape, volume, colour) information. Papadias and Sellis (1992, p 154) argued that ‘spatial representations can be considered as indexes that spatially connect visual representations to create a scene’. This examination of concepts of space, their expression as representations and the process of communicating them to ‘readers’ has revealed how closely spatial representations are adapted to spatial concepts. Indeed maps play such an important role in the manipulation of spatial knowledge that human spatial reasoning processes are often re-formulated in terms of map concepts. The marking of sharply delineated features which are fuzzy in reality or the static treatment of dynamic phenomena on maps are examples of representational compromises that maps often require human users to make. These compromises often lead map users to make mistakes, which, on the coast or in the mountains can have fatal consequences. The delicate balance between the limitations of maps and the value of the frame of reference that they provide remains a crucial debate. By perverting their purported accuracy, maps can be used for propaganda purposes (Monmonier 1991) or to intentionally mislead in war (Board 1993). Yet they can also be used to hold governments to promises over land development or to protect individuals from encroachment by their neighbours. Maps also provide a means to debate over the nature of ‘spaces’ experienced by peoples: spaces of exclusion and poverty (Shepherd 1993) or spaces of amenity and conservation (Board 1993). In each of these maps the nature of the conveyed message may however be defective by nature of the representational compromises: maps of sea level rise threats seldom convey the essence of magnitude and frequency in coastal flooding. Maps, therefore, are recognised as flawed but durable methods for the

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representation and communication of spatial knowledge (Monmonier 1998). In the most part education, dialogue and professional practice have limited the disutility of these compromises, but many dynamic processes still cannot be communicated this way. The cartography of the 1990s has begun to recognise the limitations of traditional cartographic communication. For example, McEachren (1992) has begun to reformulate cartography within ‘Geographic Visualisation’ (GVIS) while Unwin (1994) described the development of spatial applications of cartographic visualisation (VISC). These developments have sought to create new modes of cartographic communication: hence, McEachren (1992) defined GVIS as ‘the use of concrete visual representations…to make spatial contexts and problems visible, so as to engage the most powerful human information-processing abilities, those associated with vision’ (p130). In this, GVIS and VISC are associated with the development of Exploratory Data Analysis (Tukey 1977), which DiBiase (1990) and Kraak (1994) have reformulated for spatial exploration in two and three dimensions respectively (see chapter 5). Mapping as representation in the broad sense Historically, cartography has journeyed from the fictional maps of the Middle Ages to the science of late 20th century topographic mapping. However, the scientific inventory of territory as conducted by contemporary mapping agencies around the world (Rhind 1997) should not and cannot be regarded as socially, culturally and politically neutral. In the sense that much mapping is still in the hands of the state and business then cartography can be identified with the ‘scientific-technical’ interest of Habermas (1978). Thus, mapping as representation in the broad sense remains a contested activity shaped by the objectives of the sponsors of the cartography. Harley (1989) attempted to deconstruct the map through an analysis of cartographic rules as a form of discourse. His deconstruction focussed on the use of a ‘value-free’ scientific epistemology in mapping and on the sense of an ‘instrumental space’ being projected by the map, for example in the underlying essentialism that considers that the duty of cartography is to catalogue what is already ‘naturally there’. Harley (1989) argues that maps should instead be examined through metaphor and rhetoric to see how power is exercised through them. Harley (1990) went further in arguing that the lack of a social dimension in cartographic theory had brought cartography to a ‘crisis of representation’. Paraphrasing Marshall McLuhan, he also suggested that the technology of geographical information systems (GIS) was becoming the message, and not just a new form of the medium. It is argued in this book that the geographical information science that has emerged alongside the GIS have greatly expanded the scope and self-awareness of mapping as representation. Harley’s penetrating analysis of the cartographic enterprise began a debate on the aims of mapping, and in particular its truth claims. Thus, Monmonier (1991, 1998) demonstrated ‘how to lie with maps’ by exploring visual seduction, maps as propaganda, cartographic disinformation and the ecological fallacy of the chorpleth map. MacEachren (1995) reconceptualised mapping as GVIS and explored truth in the sense of reliability and error and observing that these representations are not true or false as such but similar or dissimilar to what is represented. Dorling and Fairbairn (1997) attempted to produce

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maps that explored ‘other’ geographies such as ecomapping, humanist cartography and the cartography of war experiences such as the genocide of the Second World War Holocaust. Cosgrove (1999) presents a collection of works on the power in mapping and their social context and comments that ‘[a]ny map may thus be regarded as a hinge around which pivot whole systems of meaning, both prior and subsequent to its technical and mechanical production’ (p9).

THE DEVELOPMENT OF GEOGRAPHICAL INFORMATION SYSTEMS The development of geographical information systems (GIS) in the 1980s initiated a revolution in spatial representation on several levels. On one level GIS have made it much easier to produce maps and spatial models by digital methods. This has led to a restructuring of the topographic mapping process and has widened the range of organisations making maps (e.g. environmental campaigners), thereby expanding the perspectives served by spatial representation. On another level, GIS have made it possible to query and analyse spatial representations in new ways enabling the monitoring of the mapping process through error assessment. Finally, GIS have made it possible to develop entirely new representations that implement concepts of space previously not constructed, for example using multimedia and virtual reality techniques. These developments have motivated the development of geographical information science (Goodchild 1992) which has developed an interdisciplinary dialogue on concepts of space with philosophy, cognitive science, psychology, computer science and linguistics. To put these developments in context, the development and representational basis of GIS as software will be summarised here. GIS were originally developed as methods to automate cartography and map production (Rhind and Coppock 1991): the earliest experimenters were map producers such as mapping agencies, governments and planning departments. The explicit aims of many early experiments in ‘computer-assisted cartography’ (Tobler 1959) were the improvement in the efficiency and scope of mapping through digital methods (Rhind 1971). Early experiments in the 1970s could not deliver these benefits due to the low computing power available and the formidable technical challenges of extending contemporary computer graphics to handle cartographic data and spatial models. These benefits were not realised until a software integration took place in the mid-1980s to create packaged GIS capable of offering digital mapping functionality on the more powerful computers then becoming available. The initial functionality of the GIS products available in 1985 was highly tuned to mapping functions and the biggest early customers were often mapping agencies in the military and government sectors. This initial phase of GIS development (Ottens 1991) was succeeded by a spurt of growth in the late 1980s which was strongly demand-led by utility companies who, under pressures of regulation, competition or privatisation were being driven to improve the efficiency of their fixed capital use. As major owners of plant, above or below the ground, utilities found it desirable to make the business case for investment in this new technology in order to better manage their assets and reduce their fixed costs. Mapping

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and cadastral agencies around the world have also made major investments in GIS, initially to automate mapping functions. In order to serve these major new customers GIS developers directed their representational base and functional scope towards the requirements of automated mapping/facility management (AM/FM). This inheritance remains in the commercially available GIS today as can be seen in contemporary analyses of functionality (Albrecht 1995). In parallel with the development of GIS software, surveying and data capture technology has also been revolutionalised in the 1980s and 1990s. Surveying instruments have been enhanced by the addition of electronic distance measuring and computer logging of observations facilitating the direct capture of field data by a much wider range of organisations than previously. Position fixing by satellite navigation such as the Global Positioning System (GPS) has also made it possible to obtain positions and elevations anywhere on the earth’s surface rapidly and inexpensively. Satellite imagery is now available in a variety of wavebands for most of the earth’s surface at high resolution, some images such as weather data being updated in real time. Finally, the development of the World Wide Web has facilitated the implementation of a client-server approach to GIS in which maps are served to web browsers across the Internet. The representational basis of most GIS is based upon a set of conventions, some drawn directly from surveying and mapping and some newly developed in GIS research and development. The key conventions are briefly outlined below along with pointers to more definitive accounts. Surveying conventions In the main GIS are optimised to handle data originating from ground or air survey. Ground survey operates within a set of conventions established by the surveying profession (Brinker and Minnick 1987) and each branch of surveying uses its own formal professional language for space (Raper and Bundock 1993). Although conventions differ in detail around the world, all approaches depend on the definition of boundaries or lines between different parcels of land, sea bed, mining prospect and so on. These are drawn as fixed width geometric lines in the survey, and do not usually represent the actual dimensions of the linear feature. In reality lines between parcels vary between chain-link fences of trivial width to tracks or lines of trees. They may also be notional lines as in the case of mean tidal level (which is not usually a line but a zone on low slopes with high tidal ranges) or lines which have no surface expression and cannot be seen on the ground such as the boundaries between some countries. In order to decide where to establish a point or line a surveyor must also have a definition of what it is they are identifying. Surveying practice involves the definition of ‘features’, which imply a clear and consistent identity for the delineation process. These features are often codified in a professional language: some examples from land and mining surveying are given in table 2.2. The specification of a surveying operation usually formalises this definition as a catalogue, often assigning labels to the ‘permitted’ features. Most national surveys publish definitions of their feature catalogue, in some cases with detailed rules about how they are to be identified. For example the Australian Survey publishes a handbook its practice (Australian Survey 1992) which offers some

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indication of the resolution of the surveying at different scales.

Table 2.2 Some examples of user language for space with regard to land and mining surveying practice

Application terminology Geometric data Description Land surveying Monument

Point

Fixed point located by physical mark

Centroid

Point

Centre point to which reference code is linked

Metes

Line

Parcel edges defined by distance and direction

Bounds

Line

Boundaries of adjoining land parcels

Strip

Line

Corridor of fixed width along a centreline

Abuttal

Line

Boundary of a parcel on an adjoining parcel

Easement

Line/polygon

Corridor or land parcel set aside for access

Parcel

Polygon

Unit of land ownership

Aliquot

Polygon

Subdivision of parcel

Tract

Polygon

Land segregated by re-survey

Face

Line

Section of mine boundary used for excavation

Entry

Line/polygon

Centreline of tunnel forming access to face

Cross-cut

Line/polygon

Centreline of tunnel at right angle to entries

Pillar

Polygon

Area of unexcavated material within mine

Room

Polygon

Section of tunnel ending in a face

Mine Surveying

Air survey involves air photo interpretation usually by a skilled operator who is familiar with the terrain. Practising air photo interpretation involves identifying ‘features’ from the imagery, although this can be difficult if there are shadows, the image was acquired during an inappropriate season or the imagery is too small a scale to allow feature identification. As in ground survey the operator usually defines points and lines often involving considerable compromises in interpretation. In summary, the output of the surveying process is a set of geometric primitives derived by simplifying reality, which identify a range of features in a catalogue. This process provides data for the cartographer to make maps. Cartographic conventions Many GIS are primarily populated from cartographic sources and hence carry certain conventions drawn from maps. A closer look at this process is essential to understand

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how maps have changed and been changed by GIS. Maps are drawn up to provide a definitive version of (often) multiple surveying sources for the same area and to regularise the surveys on the same geodetic base (Harley 1975). To achieve this integration it is necessary to adopt conventions of equivalence between different sources, to transform into a common referencing system and to ensure that the map is positionally coincident with other maps (João 1994). This process of integration is greatly simplified if the map is assumed to have a uniform provenance corresponding to a single point in time. Accordingly most maps have a single release date and individual features are not usually given a distinct date of origin. Exceptions to this rule are marine charts where extensive provenance information is usually given. The gathering of multiple maps into a GIS therefore implies the aggregation of a highly temporally heterogeneous set of features into a single representation. Rarely if ever are these differences stored as a form of data quality leading the user to make the unchallenged assumption without further research that the features are a uniform temporal sample. Such rules have not always carried over to GIS where the focus of functionality development has often lain more in data processing than cartographic communication. The result has been the excising of the many signs, shading devices and marginalia used on some maps to convey dynamic behaviour or variation in quality. Digital mapping conventions From the above discussion it is clear that GIS have often only implemented limited aspects of the map’s representational scope. Representation has been further changed in GIS since, unlike paper maps, digital representations are often not interpreted by human visual and cognitive systems but processed and then interpreted by computation. This transformation into the digital domain has led to the creation of a further series of representational devices to accommodate the nature of these digital spatial representations. Digital spatial representations adopted for GIS draw from a variety of other fields including computational geometry, computer graphics, image processing, database management systems, processor design and ergonomics amongst others. General treatments are given in Longley et al. (1999), Laurini and Thompson (1992) and Burrough and McDonnell (1998). The critique of GIS from social theory A number of geographers developed a critique of GIS methodology in the mid-1990s as the GIS industry grew rapidly, even though GIS research and GIS development retained separate agendas. Harvey (1990) equated GIS with ‘the static rationality of the Ptolomaic system’ suggesting that in GIS ‘if it can be mapped, then it is geography’ (p432). Gregory (1994) argued against seeing the world as ‘exhibition’ where external form that can be mapped is considered as intrinsically important as internal meaning. The most direct challenge to GIS came in a work edited by Pickles (1995a) entitled Ground Truth, which contained a trenchant critique of GIS. Pickles (1995b) set out the themes of the critique, firstly, the role of GIS in ‘the transformation of data handling and mapping

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capabilities…and the impact they have had on the discipline of geography’; second ‘the constellation of ideas, ideologies and social practices that have emerged with the development of new forms of data handling and spatial representation’; and, thirdly, the characterisation of GIS as ‘a tool and an approach to geographic information within the wider transformations of capitalism in the late 20th century’ (pviii). The early chapters of Ground Truth presented generalised critiques of GIS in various forms. Pickles (1995c) referred to GIS as belonging to the ‘new information and imaging technologies [that are] a revolution—almost Maoist in form’ (p4) and stated that GIS exhibits ‘technocratic myopia’ (p16) in the way that they form representations of the world. He charged that GIS fail to acknowledge their technologic and empiricist nature as when he stated that ‘the spatiality of GIS [is] a virtual space of data manipulation and representation whose nominal ties to the earth [are] infinitely manipulatable and malleable’ (p7). Taylor and Johnson (1995) argued that ‘GIS practitioners are…applied quantitative geographers’ (p54) who ignore the earlier critique of quantitative methods. They characterise GIS-based analyses as attempts to explain by reference to empirically determined relations between unproblematic datasets which originate from the state or large capitalistic enterprises. Curry (1995) asked three sets of rhetorical questions: whether it is possible to locate objects in space and if it is important to do so (answer, no and no); whether GIS aim to amass information rather than engage in a discourse of knowledge (answer, the former not the latter); and, whether or not there is something called rationality, and, if so, whether it can be adequately modelled in GIS (answer, no and no). He explored these questions further in Curry (1998) where he also asked who owned geographic information and what ethical responsibilities they have. The response to these charges involved drawing a distinction between GIS and GISc. Hence, Flowerdew (1998) argues that GISc is not merely empirical but has also provided theoretical insights. Clark (1998) argued that it was possible to see some GISc research as post-positivist in nature with a focus on contingency and perspective in social representations. Dorling (1998) showed that a GISc-driven ‘human cartography’ using GIS could generate emancipatory representations to highlight injustice, poverty and environmental degradation. Only Openshaw (1997) rejected the critique outright in a detailed series of rebuttals, arguing that it is inconsistent of the critics to accept Newtonian mechanics when travelling by air but to reject positivistic approaches elsewhere! Raper (1996) presented a deconstruction of the Ground Truth book itself, arguing that many of the contributors had consumed marketing information about GIS software development rather than dealing with the underlying research of GISc. The longer term outcome of this debate has been a series of considered engagements between geographical information scientists and social theorists via a series of research initiatives (Sheppard et al. 1999). Thus, Aitken and Michel (1995) argue that GIS could allow communities affected by planning decisions to speak for themselves if a GIS could be embedded in a hypermedia environment and made more user-friendly. Wiener et al. (1995) show how a GIS can be used to capture forms of local knowledge in a process of social transformations in post-Apartheid South Africa, and Obermeyer (1998) surveys the evolution of public participation GIS. Pickles (1999a) identified the key outcomes of the Ground Truth debates as the growth of a critical reflection on GIS, the new concern of GIS social impacts of technology, and the realisation that GIS activities need to be

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contextualised within the political economy of informatics and the practices of geography. Pickles (1999b) moved the agenda onto the issues of the role of GIS technology in the ‘digital transition’.

THE CURRENT AND FUTURE SCOPE OF GIS AND GISc This brief review of conventions used in the conversion of geographic knowledge into digital ‘geo-representations’ shows how the information content is transformed and standardised within the parameters of surveying, mapping and GIS practices and processes. While current GIS have proved to be valuable to a wide range of professions as tools for inventory, map production, querying and spatial modelling, GIS have limitations as a means for spatio-temporal representation. These limitations can be divided into internal limitations, i.e. those which reflect technical constraints on the scope of geometric representations, and external limitations, i.e. those which reflect the overall grounding of the representation. Thus the themes of this book emerge. The key structural limitation of current GIS is that they are restricted in representational terms to two dimensions and alphanumeric data types. It is axiomatic that few geo-phenomena can be holistically represented after such sweeping simplifications. As such, many phenomena of geographic interest cannot be meaningfully represented in the current two-dimensional GIS. Such geo-phenomena often go unstudied when they go unrepresented. However, in the past few years a whole range of new multidimensional systems has developed to expand the scope of representation: the theory, implementation and application of these new multidimensional representations is the main subject of this book. Yet the concept of geo-representation also needs a richer grounding to give a methodological context to the representation, as the Ground Truth debate has shown. The whole representational undertaking should be a reflexive cycle of thinking about the way the world appears to be, its reproduction digitally or otherwise and reflection on the process and its outcome. This methodological approach places the representation in a central role in the development of geographic knowledge. For this approach to be sustainable the representational process must be rich, self-aware and reconfigurable. It is argued in this book that these twin structural and methodological representational limitations must be addressed together. The methodological limitation can be tackled through a new approach to theory and practice based on an explicit and well-grounded worldview. The structural limitation can be addressed by developing new representational scope in GISc. The major structural limitation in contemporary GIS is the widespread use of ‘timeless space’ concepts. This chapter has shown a range of challenges to these concepts: • coherence between representations and the world requires a temporal dimension; • many geographic phenomena require time to establish their criterion of identity; • many phenomena are salient in perception because of their spatio-temporal nature; • scale in space is inseparable from time in the representational process; • allocentric concepts of space develop from egocentric concepts which have a strong time structure;

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• the use of verbs in language to describe changes in phenomena is foundational in some sense; • spatial behaviour such as that seen in ‘encounter fields’ creates spaces from spatiotemporal acts. Each of these challenges is enough to warrant a concern with spatio-temporal representation on its own; taken together they demand a programme of action. The next chapter explores the grounding for the integration of space and time in a multidimensional geographic information science and develops an agenda for further development.

CHAPTER 3 Multidimensional representations of space and time INTRODUCTION It was argued in the previous chapter that geo-representation faces a number of profound challenges to methodologies based on two-dimensional ‘timeless space’ concepts, and that the solutions may lie in a richer multidimensional approach. This chapter will explore the conceptual foundations of three- and four-dimensional representation by reviewing the history, philosophy, physics, mathematics, psychology, anthropology and social theory of ‘space integrated with time’. This will provide a foundation upon which new multidimensional approaches to digital geo-representation can be built. However, GISc is only one locus of a wide interdisciplinary debate that is currently reexamining and reinventing space and time and their representations. This debate spans scales of consideration from cosmology and astronomy (macro-) through geography, social theory, cognitive science and psychology (meso-), to biology and quantum physics (micro-scale). While each scale of consideration has its specific concerns there are many generic issues of universal concern. This chapter aims to situate GISc in this universe of discourse.

FOUNDATIONS OF THEORY ON SPACE AND TIME A wide body of theory on multidimensional representation has developed from antiquity through to the present. The following review of the foundations of theory on space and time is intended to illustrate the wide range of multidimensional representational concepts available, and to attempt to draw out common themes between fields. This will furnish a methodological platform on which to build the next generation of (digital) georepresentations. Ancient thinking on space and time It is clear from anthropological studies of prehistoric human societies that the linking of sensory apparatus such as binocular vision with sensorimotor skills, for example when engaged in hunting, must have promoted an integrated and multidimensional concept of space and time (Akhundov 1986). However, Indo-European science and culture has developed in largely sedentary communities and so has tended to see spatial and temporal concepts employed in human reasoning about the world as interdependent but distinct. This duality is evident in the earliest known literary works such as Homer’s 10th century

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BC Odyssey where space and time are each categories (Hellwig 1964). Consequently, ancient thinking on the nature of the world usually recognises space and time as separate domains that are subject to separate processes of reasoning. The temporal domain was probably first codified in human societies through the development of speech. Since speech elements are recognised by their pitch, their duration and their rhythm, time is a key organising principle of language. Yet temporal concepts in the earliest known languages such as Middle Egyptian at 2000BC only used verb tenses for repetition rather than temporal relations (Whitrow 1988). The earliest language to support verb tenses discriminating between past, present and future seems to have been archaic Greek in which the time of some event is related to the time the speaker experiences. The evolution of a human sense of time was probably also related to the development of counting systems and arithmetic, by virtue of the link between a number sequence and the ‘flow’ of time. The development of counting systems was required by, and facilitated by, the recording of time’s passing and the formation of calendars. Hence, the Chaldean people of ancient Babylon developed the sexagismal system of numbers underlying the modern division of minutes and hours into 60 for astronomic reasons. The ancient Egyptians developed the first known calendar by averaging the annual rising and falling of the waters of the river Nile to create 12 months of 30 days with 5 additional days, making 365 in all (Neugebauer 1957). Although the origins of this ‘civil’ calendar are not known, the more precise ‘Sothic’ calendar of 365.25 days based on astronomic observations has been calculated to have been introduced in 2773BC (Winlock 1940). The Sothic calendar divided the months into 3 decans of 10 days each and divided the day into 12 hours of day and night (whatever the season), characteristics which were taken up by the Greeks, then incorporated in the Julian calendar of the Romans and ultimately incorporated into the Christian Gregorian calendar. The ancient Chinese began written chronicles of events in 2200BC and developed a calendar based on star observations and sundials (in use by 1500BC) (Aveni 1989). Independently, the ancient Mayas of central America began written records in the form of a day count beginning on 10th August 3113BC and developed a sophisticated calendar based on astronomy, which was one day per 1000 years more accurate than the Gregorian calendar (Whittrow 1975). By contrast, the Babylonians developed a calendar based on 12 lunar months adding a 13th month every 19 years in recognition of the moon’s 18.6 year cycle. They also developed the division of the sky into the 12 signs of the Zodiac, each sign divided into 30 parts: the sum of these parts is 360 and led to the practice of dividing the circle into 360 degrees. All these early systems of time were cyclical: the Chinese and Mayas organised society around the ‘natural’ cycles of the day/year and longer ‘historical’ cycles which had a mythical origin. Since temporal cycles had such an important role in organising society, the interest in time led to the study of natural cycles such as the tides, the phases of the moon and the movement of the star constellations. Hence, the ancient Chinese Emperors were patrons of astronomy, since by knowing how natural cycles progressed they were able to ‘predict’ the future (Aveni 1989). While the ancient civilisations of the Egyptians, Babylonians, Chinese and Mayas all developed sophisticated calendars based upon astronomy, the ancient Greeks developed the first philosophies of space and time. The earliest work to develop an explicit

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conception of space and time may have been Hesiod’s mythological and philosophical treatise ‘Theogony’ dating from the 7th century BC. In ‘Theogony’ the world emerges from a state of ‘chaos’ (a timeless and spaceless state) into ‘chronos’ (ordered time) when ‘gaia’ (the earth) appears. Akhundov (1986) has suggested that chaos is associated with a ‘higher’ linear time while chronos is associated with ‘cyclic’ time. Nunes (1991) and Casey (1997) review a wide range of mythical and historical accounts of the origins of space, time and place. A more complete philosophy of space and time was provided by Heraclitus writing about 500BC. To Heraclitus the world was perpetually changing, driven by the eternal conflict of opposites. He defined time as being the order of things and pointed out that ‘you cannot step into the same river twice’. Heraclitus’ view that space and time were not separate but completely integrated was the exception among the ancient Greek philosophers. Pythagoras’ philosophy of the 6th century BC was based on the importance of numbers and their correspondence with external spatial and temporal reality (Jammer 1954). To Pythagoras space and time were distinct: space was represented by geometric figures whose configuration may though be temporally dependent, as, for example, in the movement of the shadow on a sundial. Pythagoras considered that time itself was the soul of the universe. Later Greek philosophers perpetuated the Pythagorean view that space and time are distinct in origin and meaning. The philosopher Zeno underlined this separation in his five famous paradoxes concerning space, time and motion published in 460BC. The tortoise paradox refers to a race between a tortoise and Achilles: if the tortoise is allowed to start first, once Achilles starts he must first reach the point the tortoise was at when he started; however, once Achilles reaches there, the tortoise has moved ahead to a new point. Achilles must now reach this new point, but once again, when Achilles reaches that point the tortoise has moved further ahead. Although each time the distance between Achilles and the tortoise gets smaller, Achilles is doomed always to be behind. In this and the other paradoxes Zeno shows that if motion is evaluated using (discrete) units then the results will not match observed (continuous) reality, i.e. that Achilles (running faster) soon catches and overtakes the tortoise! In reality the distance Achilles runs is finite, while there are an infinity of numbers that could be used to represent that distance. Modern treatments of Zeno’s tortoise paradox use the mathematics of infinitesimals tending to limits in order to calculate and compare the ‘instantaneous’ velocity of both tortoise and Achilles when they are in the same vicinity (Ray 1991). The paradoxes marked out by Zeno led the later Greek philosophers to debate whether matter should be treated as discrete or continuous, or to treat space and time as distinct but interdependent. Hence, Plato in ‘Timaeus’ considers space to be made up of matter reduced from chaos to order by reason, and time to be a characteristic of the motion of the universe, i.e. that time is produced by the universe. Aristotle criticised Plato’s notion of time denying that time can be defined by motion since motion itself is partly defined by time. Aristotle in his ‘Physics’ suggested that time be seen as the order of events: much of his work focussed on spatial configurations that were ordered according to time. Note also that Aristotle’s 10 categories of logic (ways in which the subject of a proposition may relate to its predicate) included place and time. The interdependence of space and time were also noted by Aristotle in his work ‘On

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the heavens’ where he observes that the north star is lower in the sky as you move south and higher as you move north (Hawking 1988). These observations and the disc-like shadow of the earth on the moon during a lunar eclipse led him to conclude that the earth was a sphere. In 150BC Hipparcus realised that it was possible to calculate position ‘around’ the earth’s circumference by recording the times of a lunar eclipse since the times that the eclipses take place differ by longitude. Ptolomy actually used the various recorded determinations of the time of the sun’s eclipse on the day of the battle of Arbela in 330BC to establish the lines of longitude on his map of the world. Commenting on these observations Lippincott (1994) noted that ‘space first created time and later time created space’. Her observation succinctly summarises the way that Ptolomy’s awareness of differences in the position and movement of the sun and stars over geographic space created a sense of a universal and externally determined time, while later the 19th century negotiations over the International Time Zone system helped formalise the spatial subdivision of the earth’s surface. The ancient Greek philosophy of space and time was also embedded in a general notion that time (chronos) was cyclic in nature and that the future was predestined by the progress of the cycle. Whitrow (1988) argued that the key advance in thinking about time after the Greek philosophers was the introduction of the notion of linear time by historians such as Polybius (2nd century BC) and the development of religions holding teleological beliefs such as Judaism and Christianity. Both of these religions are characterised by their belief in significant past events on a historical continuum and that prophesised events will occur in the future to make life different. This change in perspective on the nature of time from cyclical to linear opened the way to quite different forms of thinking about time. Hence, Plotinius (3rd century AD) in a commentary on Plato suggested that time can only exist if a mind exists to measure it. St Augustine (4th century AD) explicitly rejected cyclical time (in City of God) and suggested that time had no existence in itself (in Confessions), simply providing a frame for the passing of events (Smart 1964). He also noted that the past can only be measured by the extent of something currently in memory. However, St Augustine regarded time as a theological problem and considered it only within this frame. Several important reforms in the calendar were accomplished in the Roman era with implications for the recording and measurement of time. Firstly, Julius Caesar introduced a new universal calendar in 45BC (later known as the Julian Calendar) to apply throughout the Roman Empire in which: the first day of the year was 1st January; the number of days in each month was regularised; and an extra day was added to February in leap years. Secondly, the monk Dionysius Exiguus when preparing tables for the date of Easter for the Pope in 525AD suggested that the years should be reckoned from the Incarnation of Christ (using BC and AD) rather than the founding of Rome in 753BC. Dates in ‘AD’ form were then used by the Venerable Bede in England in his work ‘On the reckoning of time’ published in 725 and reintroduced to Rome in the 10th century. Scientific studies of time in the Middle Ages were largely carried out in a religious context. Hence, while Bede’s measurement of time was originally carried out to forecast the date of Easter it also facilitated the first study of the relationship between the phases of the moon and the times of high tides at a given locality. In the Islamic world astronomic observations were carried out to calculate the times of prayer and the

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direction of Mecca. Astronomy flourished during the 8th and 9th century rule of Harun al-Rashid and Al-Mamun in Baghdad who patronised scholars such as Qusta ibn Luqu who tabulated the ‘fixed’ stars and the movement of the planets as well as translating ancient Greek philosophical texts (Qadir 1988). Islamic concepts of time seems to have been atomistic as seen in the 12th century work of Maimonides who stated that periods of time could be divided until fundamental unit were obtained. These works were later translated to Latin (for example by Adelard of Bath in the 12th century), making their insights available to European scholars. St Thomas Aquinas developed a theory of time in the 13th century in which three types of time existed: that of eternity, belonging to God; so-called ‘aevum’, time with a start but no end such the time of ideas; and time on earth which he characterised as the succession of phenomena in a view similar to St Augustine. The restriction of the spatial dimensions to two rather than three has always been a pragmatic one: Plato in his ‘Republic’ (4th century BC) speaking through the dialogue character of Socrates notes that ‘for while the next thing in order is the study of the third dimension or solids, I passed it over because of our absurd neglect to investigate it’ (Jammer 1954). Plato, however, was aware of the properties of the five regular polyhedra which have faces that are equal regular polygons and angles that are equal at the corners. These polyhedra are now known as Platonic solids (figure 3.1): the cube (8 corners, six squares), the octahedron (6 corners, 8 triangles), the icosahedron (12 corners, 20 triangles), the tetrahedron (4 corners, 4 triangles) and dodecahedron (20 corners and 12 pentagons). In Plato’s philosophy matter was made of the elements of earth, air, fire and water which he represented (respectively) by a cube, octahedron, icosahedron and tetrahedron. Barrow (1991) notes that Plato’s position was that ‘the elements are just these solid geometric shapes, not simply that they possess geometric shapes as one of their properties’ (p176). This meant that the elements could change into one another by the merging and splitting of triangles into which all the Platonic solids could be broken. This scheme indicates how Plato used geometry to describe the underlying structure of the world, which he believed to be ultimately mathematical in nature. Euclid in the ‘Elements’ deals with solids in much less detail than with figures in the plane. In book 11 he covers measurement in three dimensions (‘stereometry’), while in book 12 he covers the determination of volumes and, in book 13 he proposes a limited theory of regular bodies. Following Euclid there was only limited work on solid geometry such as the theory of conies and higher curves by Apollonius in 200BC (figure 2.6); the spherical trigonometry of Hipparcos in 150BC (Gray 1989); and some remarks on solid modelling by Ptolomy (2nd century AD) in an essay called ‘On extension’ mentioned by Simplicius but now missing. Hence the art of the Middle Ages used planar twodimensional representations with no perspective. In fact drawing and painting using perspective with vanishing points for parallel lines was not developed until the Renaissance by artists such as Giotto, Brunelleschi and Uccello (Hagen 1985, Wertheim 1999).

Multidimensional representations of space and time

Figure 3.1 Platonic solids

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Thinking on space and time between the Renaissance and the 20th century While the scholars of the Middle Ages such as the Venerable Bede in England or Omar Khayyam in Persia extended knowledge by measurement and synthesis, they tended to rely on the fundamental ideas of the ancient Greek philosophers, in so fer as their writings were still extant. The strong influence of patronage and the influence over secular law of all churches in that era placed constraints on thinking outside this framework, which was dominated by philological compilation of sources. However, the Renaissance of the 14th to 16th centuries began a process of discovery (in the widest sense of the word) which progressively challenged the church-supported ‘orthodoxy’ of the ancient philosophers whose works had long since been integrated with theology in Europe and the Middle East. Notable advances were made in the fields of technology and in exploration which enabled a resurgence of thinking on space and time. Amongst the most important of the technological developments was the development of accurate timekeeping devices. Before 1300 most of the clocks used in both China and Europe were water clocks, which measured time through the steady flow of water into vessels (Whitrow 1988). Although some of these devices were highly elaborate such as the Chinese water clock designed by the Mandarin Su Sung in 1088, they were very poor performers compared with the ‘verge-and-foliot’ mechanical clocks developed in Europe in the 14th century. The advent of mechanical clocks on public buildings and churches in the 13th century (such as the Strasbourg Cathedral clock erected in 1350) was influential in the decision to move from timekeeping based on 12 hours of the day and night depending on the season to one of 24 equal hours of the solar day. The practice began in England in 1380 and formalised the practice of timekeeping by using regular subdivisions of time. Recognition of the need to regularise the measurement of time lay behind the move by the Vatican to introduce a new calendar in 1582. By the late 16th century the Spring equinox of the calendar was falling 10 days behind the actual solar equinox since the Julian calendar had drifted over the 1600 years since its introduction. Accordingly, Pope Gregory XIII approved the introduction of a new calendar based upon a more accurate estimate of the mean tropical year in which the day after 4th October became 15th October 1582. Although it took some time to be accepted outside Catholic Europe (Nb. Britain finally approved it legally by an Act of 1750), it has ultimately become the world’s first universal standard for the measurement of time. There were also important Renaissance explorational discoveries, which considerably advanced the understanding of space and time. In astronomy, Copernicus proposed in 1514 that all the planets including the earth orbited the sun and not the earth itself; he then calculated tables of lunar and planetary movement on this basis. Copernicus’ views (which he initially kept secret due to fear of the Inquisition) radically altered the basic conceptions of time and founded a new cosmology of heliocentrism. Copernicus was the first to note the need for a ‘mean day’ which would be a standard against which planetary motion could be measured. Copernicus was followed by Kepler who set out laws of planetary motion in 1609 which were based on the mathematics of conies (figure 2.6) and elementary dynamics. However, Kepler considered that the beauty, regularity and simplicity of geometry indicated its creation by God (Akhundov 1986).

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The 17th-century astronomy, mathematics and physics saw the development of some of the foundations of modern theories of space and time. In his Dialogue concerning the two Great Systems of the World (1632), Galileo evaluated the Aristotlean system of dynamics where the speed of falling bodies is supposedly inversely proportional to the density of the environment. This implies that the speed of bodies is infinite in a vacuum, making the vacuum impossible. His own assertion was that that the speed of falling bodies is finite for all environments. This led him to formulate the principle of inertia that predicts the perpetual continuance of an object at rest or in uniform motion in a straight line until interrupted by external forces. The principle of inertia suggested that empty space (a ‘vacuum’) outside the earth could exist and that some frame of reference such as the surface of the earth was required to measure the motion of an object (Burtt 1932). That ‘empty space’ was meaningful, was partly the heritage of Galileo’s invention of the telescope in 1609, which had revealed to him the full complexity of the solar system, including the motion of Jupiter’s moons. Another astronomer of the period, Roemer, first measured the speed of light in 1676; the implications of this discovery for the dimensions of the universe were profound. By contrast Descartes in his Principia of 1644 defined space as the extension of matter, hence space by definition could not be empty. Descartes was also the first to define extension by three perpendicular axes of length, breadth and depth. He distinguished between the ‘space’ occupied by an object and its ‘place’. Place for an object is defined as ‘occupying a position relative to other objects’ (Jammer 1954). Descartes distinguished between ‘eternity’ (which is divine) and the ‘duration of motions’ which are referenced to an external reference duration known as ‘time’. This conception equates time to a mode of thinking or a sense of objective reality (Akhundov 1986). Descartes and other mathematicians such as Fermat and Pascal of the mid 17th century also explored the characteristics of the algebraic space curves (conies and polynomials), the transcendental space curves (sines, exponentials and logarithmics) and their associated calculi. The work of Galileo and Descartes and other 17th-century mathematicians were essential precursors to the formulation by Newton of his four laws of inertia, motion, action/reaction and gravitation in the 1687 Principia. However, Newton’s laws were dependent on the definitions of such concepts as ‘perpetual movement along a straight line’. Newton took Euclidean geometry and Cartesian extension as given in his laws (Nagel 1961) but introduced a universal frame of reference for motion known as a ‘privileged’ or ‘inertial’ frame. Newton introduced this frame to account for inertial forces experienced during the accelerations of entities, which he regarded as accelerated relative to space itself (which is defined by a universal frame of reference). In the Principia he defined absolute space as ‘without relation to anything external, [it] remains always similar and immovable’ and says that absolute time ‘flows equably without reference to anything external’. These statements have been taken as the definitions of absolute space and time (‘substantivalism’) and introduced a metaphysical framework for his empirical statements (Barman 1989). The implications of Newton’s theories of space and time were far reaching. Absolute space implied that motion arises out of a causal relationship between space and matter, while absolute time implied that the universe had a single universal clock capable of

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determining that two occurrences were simultaneous. Such notions suggest that space and time have an existence independent of matter, and that while there can be space but no matter, there cannot be matter but no space (Barman 1989). Although Newton’s laws were criticised by Euler in the 18th century (challenging the universality of the inversesquare law of gravitation) (Barrow 1991), and by Mach in the 19th century (challenging the validity of ‘privileged’ frames) (Nagel 1961), they were not replaced as the foundations of physics until Einstein’s theories of relativity. Newton’s contemporary Leibniz took a quite different view of space and time, considering them to be forms of existence of material entities i.e. systems of relations, not fixed frames of reference. Leibniz defined space in his correspondence with Clarke in 1715–16 as ‘an order of things existing at the same time’ while time was defined as ‘the order of succession of phenomena’. In Leibniz (1714) he argues that nothing is truly separate as entities cohere. Leibniz also puts forward his ‘principle of the indiscernibility of individuals’ to underline that there must always be qualitative differences between individuals and that position alone is not a sufficient means of distinction between entities. He considers space to be the set of all possible relations between entities, hence, where there is no matter there is no space. By analogy, Leibniz considered two events to be simultaneous if they form a particular state of the universe. This relative space and time view became characterised as ‘relationalism’ in the 20th century (Barman 1989). It was Lagrange (1788) who formulated mechanics so that time was presented as a fourth dimension, which then made it possible to envisage how some of Leibniz’s ideas could work. Geographic exploration also led to discoveries of great importance to thinking on space and time. Firstly, in geographic terms Columbus’ voyage to the West Indies in 1492 and Magellan’s circumnavigation of the earth between 1519–22 resolved many of the unknowns about the distribution of the continents and the shape of the earth. Secondly, in navigational terms such voyages required the accurate estimation of longitude to fix geographic positions at sea. Also a number of treaties such as the Treaty of Tordesillas dividing the Spanish and Portuguese ‘spheres of influence’ were defined along lines of longitude. One method of finding the longitude involves observing the relative movements of a planet such as the moon and the ‘fixed’ stars (the ‘lunar distance’ method as proposed by Werner in 1514). The other standard measurement of a ‘differential time’ between some defined meridian and the unknown location (as proposed by Frisius in 1530, Howse 1980). Consequently, the importance of knowing the longitude for position fixing inspired the offering of prizes for a successful method by Phillip II of Spain in 1567, the foundation of the Paris and Greenwich Observatories in 1667 and 1675 respectively, and the passing of the Longitude Act of 1714 in England (following a sea disaster in 1707) which offered a prize of £20,000 for a solution. The ‘differential time’ technique attracted much attention during the late 17th and early 18th centuries following the development of Huygens’ pendulum clock in 1657. Harrison’s H1 chronometer was tested on a voyage to Lisbon in 1736 and his H4 ‘watch’ was tested on a voyage to the West Indies in 1762, succeeding within the terms of accuracy laid down in the Longitude Act (Howse 1980). A replica of H4 was used by Cook in his exploration and charting of the South Seas in the 1770s. In 1755 Mayer successfully submitted his tables of the moon’s movement based on Euler’s calculations

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for an award under the Longitude Act making the ‘lunar distance’ method a practical alternative and check on the ‘differential time’ method. Whitrow (1988) charted the progress in timekeeping technologies in terms of errors in seconds/day, noting that the key improvements were between the mid 17th century and the mid 18th century (figure 3.2).

Figure 3.2 Improvements in timekeeping (from Whitrow 1988)

Technological advancement in time measurement devices also required progress in its standardisation. An early step was the adoption of mean time adjusted for the sun’s motion in the ecliptic throughout the year. This was accepted in Geneva in 1780, London in 1792, Berlin in 1810 and Paris in 1816. Another step was the development of standard

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times for territories replacing the plethora of ‘local times’ observed in each city (Thrift 1981). This was first required with the development of faster transportation systems such as mail coaches and railways. In Britain the first passenger railway service began in 1825. By 1847 the British railway companies had agreed to implement the mean time of the Greenwich Observatory in SE London (later named Greenwich Mean Time or GMT). While the British Appeal Court ruled in 1858 that local time was the legal time, the de facto standardisation of time by the railways made the 1880 Statutes (Definition of Time) Act inevitable. Similarly, in Germany local times were brought together into one time zone by law in 1891. In North America, the railroad companies coordinated the standardisation of local times into four time zones in 1883 using central meridians 5, 6, 7 and 8 hours west of GMT, although the US Congress did not legalise this until 1918. Adam (1990, 1995) has explored the implications of this standardisation on the social life and work of the period. Standard times and fixed relations between them were also required by the growth of instantaneous communication between places (Howse 1980). This was facilitated by Wheatstone’s Electric telegraph developed in 1836 and the laying of cables over long distances, notably the first Transatlantic cable which was laid in 1858. The first step in standardising time zones was the agreement at the International Meridian Conference in 1884 to adopt the Greenwich meridian as the Prime Meridian of the globe. This was followed by an agreement to construct an International Time Zone system with 24 time zones centred on meridians 15° apart, starting at the Prime Meridian (making the zones each 15° wide). Over the following 40 years countries gradually aligned their national time zones to this system: the last large country to do so was the USSR in 1924, and France merely amended their statute to redefine GMT as an offset of Paris time. In 1928 the International Astronomical Union formally adopted GMT under the name Universal Time (UT). The later 18th and early 19th centuries saw the integration of insights gained in astronomic and geographic discoveries with the new developments in cosmology and physics. This led to the development of new cosmologies and histories of the earth based upon unified scientific views of space and time. The first of these was Kant’s Universal Natural History and Theory of the Heavens published in 1755. This work hypothesised that the solar system originated by the condensation of matter under gravity and was produced by applying Newton’s laws and his absolute concept of space and time. Herschel extended this idea when he suggested in 1814 that the formation of galaxies could be used as a cosmological chronometer. The age of the earth was also subjected to scientific analysis by Hutton’s 1788 ‘Theory of the Earth’ in which he used evidence of geological deposition to illustrate that the earth must be very old, a conclusion expressed in his maxim ‘we find no vestige of a beginning, no prospect of an end’ (Oldroyd 1996). Darwin’s 1859 ‘Origin of Species’ also established the logical necessity of long periods of time for species diversity to develop under natural selection. Research on optics and electromagnetism also opened up new perspectives on space and time. Maxwell’s 1865 theory suggested that electromagnetic fields were propagated as waves travelling at fixed speeds through space and experiments soon confirmed this hypothesis. However, since Newtonian space is an empty frame, it was suggested that outside the earth space was filled with a substance called ‘ether’ in order to provide a

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medium for electromagnetic waves to travel through. However, the Michelson-Morley experiments of 1887 failed to confirm the existence of ether when they showed no difference in the speed of light reaching the earth either in the direction of or against the direction of the earth’s orbit. This negative result played a critical part in the formulation of Einstein’s Theory of Relativity.

Figure 3.3 Tissot’s Indicatrix and graticule for the orthographic projection (from the Projector program by J.Wood)

This period also saw major developments in mathematics and geometry, for the first time extending these fields beyond the work of Euclid, Archimedes and Apollonius in Classical times. Hence, in 1775 Euler extended Newton’s dynamics by formulating the laws of conservation in mathematical terms, i.e. expressing the laws of motion as invariances with respect to orientation and position in space and time (Barrow 1991). Lagrange extended this thinking in his ‘Analytical Mechanics’ of 1811–15 showing that the laws of conservation are specifically determined by the symmetry of space and time (Akhundov 1986). In 1772 Lambert introduced his analytic treatment of projections; later Tissot (1881) developed the ‘indicatrix’ to show the distortion properties of different

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geometric projections. Also in the late 19th century Cantor defined mathematical infinity and distinguished different ‘levels’ of infinity such as the set of all natural numbers {1,2,3…} and the set of all rational fractions. Cantor (1874) showed that the set of real numbers was of a higher cardinality than the set of all natural numbers since the real numbers cannot be counted using the natural numbers (proved by the existence of ‘diagonal’ numbers). Although three-dimensional solid representation was mentioned by Plato and Euclid, little further progress was made until Descartes formalised solid geometry in terms of angle and face relationships in 1639. Euler re-formulated solid geometry in 1758 by specifying that polyhedra were made of zero- (vertex), one- (edge) and two- (face) dimensional components. This enabled him to state that for convex and simply-connected polyhedra the number of vertices plus the number of faces minus the number of edges was always equal to two (which has become known as Euler’s Theorem). The Euler Theorem was refined by mathematicians such as Cauchy who showed that it applied to polyhedra where only two faces met at any edge and where no path within the polyhedron was forced to pass through a vertex. Euler’s Theorem also holds only when the faces are polygons whose edges have no points in common except the vertices, where only two edges meet at any vertex and where the edges are straight lines. These definitions are required to avoid the various counter-examples known as ‘monster’ polyhedra suggested by mathematicians such as Lhuilier and Poinsot (Lakatos 1976). Möbius (1865) extended the theory of solid geometry by showing how to calculate the volume of a polyhedron from the set of interior pyramids based on the interior faces, the apex of each being the same arbitrary point within the polyhedron. These pyramids are formed for all the faces and their respective volumes totalised. It is possible to ensure that all faces are visited by using Möbius’ law of edge traversal for polyhedra: all faces are visited if all edges are traversed twice, once in each direction. Möbius (1865) also showed that there are some polyhedra which do not obey these laws, notably the halftwisted rectangular band with both ends touching now known as the Möbius Strip. The Möbius Strip is ‘non-orientable’ since a path starting at any point can reach the same point on the other side of the surface without passing through a hole. Other mathematicians such as Hilbert and Klein studied the topological properties of threedimensional solids including the sphere, the heptahedron and the torus. Crucial steps towards modern concepts of space and time were taken in the 19th century by mathematicians examining the axioms of Euclidean geometry, especially the ‘parallel postulate’ which (put in the terms used by Playfair) states that a line on a plane can have exactly one parallel passing through a given point. Working independently Lobachevsky in 1829 (in Russia) and Bolyai in 1832 (in Hungary) proved that more than one parallel line can exist when the surface is curved, thereby proving that non-Euclidean geometries can exist. Gauss’ geometry of spherical surfaces also showed that Euclid’s geometry was limited to the plane since no parallel lines can be drawn on a sphere (Reichenbach 1928). Riemann formalised the mathematics of geometry in 1854 by using the concept of the curvature of space. Euclidean space has constant zero curvature, i.e. it is a plane and has one and only one parallel to a line passing through a given point; the hyperbolic space of Bolyai/ Lobachevsky has constant negative curvature and so more than one such parallel can exist; the elliptic space of Riemann has constant positive

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curvature and so no such parallel can exist. Klein showed how the concepts of Euclidean and non-Euclidean geometry corresponded, demonstrating the mathematical consistency of the two systems. Riemann (1873) later speculated that space may be Euclidean in some places in the universe and non-Euclidean elsewhere. The 19th century also saw the birth of psychology as a distinct discipline. Much early work in this field was experimental and focussed on the physiological basis of vision and other senses. For example, Lotze (1851) showed how eye fixations and muscle actions were related to the structure of retinal images; Fechner (1860) studied the relationship between the magnitude of a stimulus and the associated sensation; Helmholtz (1856–66) studied the speed of nervous impulses, pitch in hearing and colour vision; and Ferrier (1876) studied the functions of the brain. Wundt was responsible for establishing a methodology for experimental psychology in the 1870s, for example, classifying sensations into modes (e.g. visual, auditory) and assigning dimensions of variation (e.g. duration, intensity) to them. Wundt’s methodology involved breaking down conscious thought and perception into its constituent parts by observing mental processes through a processof introspection under controlled conditions (Gross 1992). J.S.Mill (1843) was among the first to examine the mechanisms of perception, suggesting that the disparate forms of energy received by the human sensory apparatus were synthesised so as to create the impression of an object in the mind. Likewise Helmholtz (1856–66) suggested that sensory signals are learned and meaning assigned to them empirically. These studies of space and time in physics, mathematics, astronomy and physiology after the 16th century were also instrumental in the development of new theories of knowledge, replacing the methods of the ancient Greek philosophers. At the beginning of the 17th century Bacon was the first philosopher to reject the Aristotelian method of ‘deduction tested by an appeal to intuition’ as a basis for explanation. He proposed that observation should be used to formulate hypotheses that should be tested against experience to see if they were correct. Bacon’s method of induction founded a school of (mostly British) empiricist epistemology continued by Locke (late 17th century), Berkeley (at the beginning of the 18th century) and Hume (in the mid 18th century). These views challenged and ultimately undermined the rationalist epistemology of Descartes with the discovery of non-Euclidean geometries. Research on space and time in the 20th century Before the 20th century, most writers dealt with space and time as separate and distinct domains. This view was common in mathematics, geometry and philosophy at the turn of the century as a remark by Klein (1908) when introducing his ‘Geometry’ indicates: ‘the concept of motion is consistently avoided…the fact that this arrangement was preferred in ancient times, as it frequently still is, was due, in part, to philosophical considerations. It was feared that motion would bring into geometry an element foreign to it, namely, the notion of time.’ Einstein’s paper on the Special Theory of Relativity (published in 1905) revolutionised thinking on space and time making it clear that in some circumstances it was necessary to think of a unified space-time. This was stated by Minkowski in a lecture in the same year

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as Klein’s remark above was published: ‘Henceforth space by itself and time by itself, are doomed to fade away into mere shadows, and only a kind of union between the two will preserve an independent reality’ The influence of relativity subsequently spread far beyond physics and had a widespread influence in 20th century science (Ray 1991). As well as being subject to such changes in the underlying paradigm of physics many fields of science have been revolutionised by technological change: for example, cosmology by astronomy, mathematics by computer science and geometry by visualisation. Physics of space and time and space-time Before the 20th century classical (primarily Newtonian) mechanics held that space and time were absolute and that they could be distinguished from each other. This formulation had certain key implications: firstly, consistency with the conservation laws required that space be isotropic; secondly, absolute time implies that dynamics take the form of constraints on simultaneous values of quantities, i.e they only express behaviour at single points in time (Shoham 1988). This implied that the universe was constructed from a series of temporal states that could be associated with an infinite series such as the set of real numbers. Classical mechanics also assumed universal simultaneity—a single clock for the universe—which in turn implied that forces acted over space simultaneously i.e. action took place at a distance. At that time space was thought to be filled with ether as a medium for light transmission. However, electromagnetics proved impossible to reconcile with classical mechanics following the Michelson-Morley experiment to establish the speed of the earth through space using the properties of the supposed ether. This led Einstein and Poincaré (separately) to suggest alternative concepts of integrated space-time which quickly replaced classical Newtonian mechanics. Einstein’s formulation of his principles of relativity proceeded in two steps. Firstly, in the Special Theory of Relativity (STR) (Einstein 1905), he showed that the speed of light (approximately 300,000km/second) is a fundamental constant, which all observers agree on: in this theory no physical effect can travel faster than this. However, all observers measure their own ‘local’ time i.e. two observers at relative rest measure the same time for an event, while two observers in relative motion will not. This is so because the moving observer is in motion relative to the propagation of light from the event and therefore the light must take a different period of time to arrive at the moving observer. Hence the moving observer must measure a different time of occurrence for the event than the observer at rest: the difference in times can be predicted by the Lorenz transformation. The implication of this is that there is no absolute, universally ‘correct’ time: in this Einstein asserts that the metric of time is an aspect of the universe and is not independent of it. Although Einstein supported a relative space and time view, he accepted the existence of space unlike Leibniz who had suggested that space did not exist, and whose place was taken by relations between things.

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The second step in formulating the principles of relativity came in 1915 and involved introducing the effect of gravitation. In the General Theory of Relativity (GTR) Einstein suggested that space-time is curved or warped by the presence of mass and energy within it. Gravity can then be interpreted not as a force as such but as an acceleration relative to the prevailing gravitational field created by the variable mass and energy of the universe. Hence, the earth moves relative to the sun since the sun’s mass curves space so as to create an acceleration in a mass. This acceleration defines the earth’s orbit around the sun as a ‘geodesic’ in four dimensions i.e. the shortest path between two points in space-time. The implication of the GTR is that space and time are dynamic quantities such that when a body moves it affects the curvature of space and time, and vice versa (Hawking 1988). The GTR was formulated by Einstein in terms of a four-dimensional geometric spacetime manifold, a field of matter, a local reference metric and field equations which predict the movement of matter in the local metric (Ray 1991). The properties of a fourdimensional space-time include a definition of distances (the metric), the affine structure defining force-free motion (the four-dimensional straight line or geodesic), the conformai structure (defining angles) and the topological structure (defining the topological nature of the continuum). Minkowski (1908) proposed that this space-time manifold could be represented using a four-dimensional continuum with x, y, z and time axes. The Minkowski continuum or ‘world’ can be considered analogous to a four-dimensional Euclidean space if the time coordinate is scaled by the velocity of light (Einstein 1952). This formulation means that the Lorentz transformation relating the time experienced by different observers in relative motion would be equivalent to a ‘rotation’ of the Minkowski continuum in four dimensions. The Minkowski scheme also allows spacetime to be visualised at any point as a four-dimensional light-cone (Hawking 1988). Within this light cone ‘world lines’ connect places at times. Hence, the classical threedimensional dynamics of Kepler and Newton become four-dimensional geometry in space-time, and, ‘space’ and ‘time’ alone become (respectively) three- and onedimensional projections of the four-dimensional ‘world’ (Akhundov 1986). Despite the specific critique of Newton’s absolutism in Einstein’s work some have argued that GTR does not necessarily falsify absolute space and time. In Einstein’s GTR as set out in 1918 matter is a ‘filler’ for space-time which itself is finite and bounded. However, Newton-Smith (1986) points out that Einstein’s field equations can be solved without the presence of matter or energy, thereby indicating that empty space-times can exist. This finding would favour the substantivalist hypothesis of absolute space and time since relationism claims that where there is no matter there can be no space. Grünbaum (1957) also pointed out that the boundedness of Einstein’s GTR implies an absolute frame defined by boundary conditions at infinity. He notes that ‘although matter provides the epistemological basis for the metric field, this fact must not be held to confer ontological primacy on matter over the field: matter is merely part of the field rather than its source’ (p315). This debate has raised a question about the physical nature of the field defined in GTR. To substantivalists the field is an infinite set of space-time points definable anywhere; association with a unique space-time point is the identity criterion of absolute space and time. To relationalists the space-time manifold is made up not of points but of events and their relations; identity is constituted by the structural roles played by event individuals in

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the current world. Therefore, fields can be seen both as qualities of absolute space-time or as physical events in relative space-time (Rynasiewicz 1996). Hence, the ‘fields’ of the GTR could be interpreted as consistent with both substantivalist and relational theories of space and time. Earman (1989) argues that the relational view of space-time entities can always be reduced to the substantivalist view through the unique ordering power of the absolute space-time field.

Figure 3.4 Light cones and world lines

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The theoretical apparatus of Einstein’s GTR enabled physicists (notably Friedmann 1983) to postulate new cosmological models. In the early 1920s Friedmann used Einstein’s Field Equations to construct and characterise models of the universe which are isotropic and homogenous. These models were extended to cope with an expanding universe following the astronomical observations of Hubble in the 1920s, which showed that the universe is made of galaxies that are moving apart from each other at a constant rate. These models have been progressively refined and extended during the 20th century to encompass the ‘big bang’ hypothesis for the origin of the universe and the physics of black holes (Hawking 1988). In the light of Relativity and 20th century cosmological models there have been several attempts in physics to characterise the direction of time formally. Reichenbach (1928) argued that time is reducible to causal order and that it can be defined by irreversible physical processes. Eddington (1928) suggested that time be defined by the Second Law of Thermodynamics (in a closed system, entropy increases with time). Hawking (1988) showed that time’s direction can be measured in terms of cosmology i.e. the direction in time that the universe is expanding. The study of sub-atomic particles in physics by Planck and Heisenberg has also revealed directional asymmetries in time which arise through quantum uncertainty (opening the possibility that the microscopic and macroscopic worlds may differ in nature). Quantum physics also helped unify the discrete (particle) and continuous (wave) views of physics through Bohr’s principle of complementarity. Philosophy of space and time Space and time have remained of central importance to 20th century philosophy and have been studied from many different points of view. Philosophers have examined the assumptions and implications of the relativistic physics and cosmology of space-time; considered the role of space and time in metaphysics; examined how views of space and time have influenced the development of epistemology; studied the assumptions of temporal and spatial logics and evaluated the meaning of concepts of continuity and discreteness with respect to space and time. Akhundov (1986) has characterised 20th century philosophy of space and time as being concerned with on the one hand theoretical structures (‘T-Structures’) providing concepts and heuristics, and on the other hand empirical structures providing representations (‘E-Structures’). If the ‘macroworld’ theories of General Relativity by Einstein and his successors can be considered as providing the key T-Structures then Minkowski’s four-dimensional coordinates can provide the E-Structure. In the ‘microworld’ of Quantum mechanics the T-structures are multidimensional Hilbert spaces. Hence, Heisenberg (1952) observed that ‘the mathematical expressions suitable for the representation of experimental reality are wave functions in multidimensional configuration spaces’ (p15). However, Akhundov considers that these microworld TStructures are not commensurable with the macroworld space-time of relativity and that while the E-Structures employed in quantum physics are those of macroscopic space and time, these may yet prove to be inappropriate. Superstring theory may yet be able to bring these perspectives together (Greene 1999).

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Philosophical consideration of the macroscopic T-Structures of space and time have been strongly influenced by Mach’s 1883 Science of Mechanics. Mach argued that physical processes should not employ any theoretical frame of reference (as Newton did) but should use a material framework capable of being tested experimentally. In the ‘Science of Mechanics’ Mach argued that this framework should be the ‘fixed’ stars. Einstein described this as ‘Mach’s principle’ and suggested that it was a ‘litmus’ test for a non-absolute or ‘relational’ theory of space-time. The argument that space-time is relational can be summarised in the statement that ‘all spatio-temporal elements involved in motion are wholly reducible to material terms’ (Ray 1991, p138). According to Ray it has not been shown satisfactorily that models of the General Theory of Relativity meet this requirement due to limitations in its topological determination. Characterisations of the E-Structures of space and time from a philosophical point of view have tended to use the Minkowskian four-dimensional coordinate system. Hence Carnap (1958) characterises ‘spatial and temporal extents of events’ as ‘things’: ‘a thing occupies a region in the four-dimensional space-time continuum. A given thing at a given instant of time is…a cross-section of the whole space-time region occupied by the thing. It is called a slice of the thing (or a thing-moment)’ (p158). Heller (1990) argued that every filled four-dimensional region of space-time is exactly filled by a hunk of matter in a view known as Perdurantism. This hunk of matter has its actual configuration and location in every world in which it exists. This is in contrast to the view that threedimensional objects exist in multiple worlds having different configurations and locations in each world, which forms a position known as Endurantism (Loux 1998). When defining concepts of ‘Naïve Physics’, Hayes (1984) proposed a terminology for describing physical scenarios that he termed ‘histories’. A history is a defined portion of space-time within which the behaviour of the phenomenon is qualitatively the same. Hayes gives examples of the potential behaviours for an amount of liquid (such as falling free, being held in a container and so on), each of which is characterised as a ‘historytype’. It is then possible to reason that no two histories may overlap in space-time and that a history may be projected onto a point in space-time. This formulation can then be used to consider how space-time histories interact. From the perpective of metaphysics the existence of space and time can be either denied or affirmed. Bunge (1973) suggested that physical theories relied on formal premises (requiring logic and mathematics), philosophical premises (requiring metaphysical statements) and ‘protophysics’ (concepts of space and time). However, since protophysics are in fact ‘undefinable’ according to Bunge the only practical methodological approach is to axiomatise physics using any suitable (perhaps ‘fuzzy’) ontology of space and time which is then improved by testing. Akhundov (1986) has criticised this approach noting that the axioms in such an approach are often highly variegated and have no conceptual integrity. By contrast, Friedman (1983) sees the very purpose of space and time to be the provision of a unifying background for the physics of gravity and electromagnetism. Barrow (1991) has argued that such a view presupposes that the universe is, in fact, algorithmically compressible, and has questioned the need for a ‘theory of everything’. The discovery of non-Euclidean geometries led 20th-century philosophers to debate the status of geometry. Poincaré suggested that ‘no geometry is true or false’ (1900, 73)

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and that the methods for defining congruence (length equalities for different bodies) involve a circularity in the abstract. Distance can only be established by measurement, but measurement requires use of an instrument itself calibrated by distance (Grünbaum 1963). This view was known as ‘conventionalism’ since it held that no construction of geometry was any more valid than any other. However, the logical empiricist philosophers such as Reichenbach (1928) and Carnap (1939) argued that since geometric knowledge cannot be a priori knowledge (i.e. innate) as the rationalists had thought, then it must be entirely empirical in nature (Ray 1991). To accommodate the axiomatic method of mathematics in the empirical view, geometry was divided into a ‘pure’ form (which aims to derive new theories from geometric axioms) and an ‘applied’ form (which aims to relate theories of geometry to sense experience) (Musgrave 1993). Einstein (1921) noted an asymmetry in the status of knowledge in these two forms of geometry, commenting that ‘as far as the laws of [geometry] refer to reality, they are not certain; as far as they are certain they do not refer to reality’ (p28). Husserl (1913) constructed a phenomenological account of the human subjective experience in which each individual can shift their ‘standpoint’ around in space and time bringing ‘objects of intention’ into focus at will (Collinson 1987). However, Husserl (1939) suggested that the very fact that the concepts of geometry have been handed down through many generations with their meaning unchanged indicates that the experience of geometry may be a priori in nature. Grünbaum (1963) provided a critique of Husserl whose views he characterised as neo-Kantian, and therefore partly rationalist in nature. The claims of critical rationalism have also been examined by considering the nature of observations as evidence for testing a theory. Feyerabend (1975) argued that theory-free observation is impossible, while van Fraassen (1980) makes a distinction between that which we could observe given appropriate resources and what is believed to exist by virtue of indirect evidence. Hacking (1983) distinguished between knowledge of existence and knowledge of behaviour arguing that the former must be observable in the strict sense. This raises the question of whether space and time can be observed, and, if not, whether the indirect evidence of their effects is strong enough to accept their existence. This question of how we get information about space if it is causal goes back to the work of Locke (Nerlich 1994). Philosophical studies of temporal reasoning have focussed on the nature of time. Grünbaum (1963) suggests that theories of time must distinguish between ‘closed time’ in which time has a beginning and end, and ‘open time’ which is infinite. If ‘open time’ is preferred then questions of order arise as temporal order can be defined in several ways. Carnap (1958) follows Hume and Einstein in suggesting that time can be reduced to causal chains; Eddington (1928) suggested that time be measured by entropy increase; Reichenbach (1928) suggested that time can be defined by the nature of irreversible processes. However, Grünbaum (1963) has criticised: Carnap on the grounds that quantum physics has cast doubt on causal chains; Eddington because time is defined by entropy and entropy is defined by time, implying a circularity; and Reichenbach because irreversibility involves time in its definition. Grünbaum (1963) therefore suggests the use of ‘betweenness’ to order time; this still leaves the problem of the directionality of time, i.e. which event is later, which Carnap (1963) raised in reply to Grünbaum. Grünbaum (1963) suggests that ‘asymmetry of inferability arises on the macro level in the absence

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of knowledge of the microscopic state of the total [closed] system at a given time’ (p663). In the mesoscopic world it is extremely difficult to determine entropy levels in physical systems, partly because of the role of ‘branch systems’ which separate from and rejoin global systems. Research into temporal logic has attempted to formalise the concepts of time in order to reason about events in the world. Reflecting philosophical considerations already mentioned various temporal ontologies are possible: time can be bounded or unbounded; linear or branching; and be represented either by points (McCarthy and Hayes 1981), points defining intervals (Shoham 1988) or intervals (Allen 1984). Representations involving points and intervals are discrete, reflecting the need to reason about events perceived to be crisply defined (although Zadeh (1975) introduced fuzzy logic). However, notions of ‘discreteness’ require a definition of whether the represented time is dense or not dense i.e. is there is a point between every other point? According to Suppes (1970) events are associated with points in an unbounded linear time. The prima facie causes of an event are the set of candidate events that preceded it. It is then necessary to choose the genuine cause from amongst these and to decide whether it is direct or indirect. By contrast Lewis (1973) employs the concept of causation in defining time’s direction by reducing the concept to that of the similarity between possible ‘worlds’, i.e. an effect has a cause because the effect was the closest world to the cause. Note that this does not prohibit time reversals such as those potentially occurring in quantum experiments. McTaggart (1908) introduced definitions of time based on tense. His ‘A’ series are positions in time (earlier than, later than) ordered from the perspective of an observer moving through time. By contrast his ‘B’ series are time positions ordered by a universal external reference. McTaggart argued that the ‘A’ series of time is necessary to register change, and therefore that the ‘A’ series in itself is a necessary condition for time. McTaggart argued that there clearly could not be a ‘B’ series unless there was also an ‘A’ series. In contrast Russell (1915) argued that since the ‘A’ series can be analysed in terms of the ‘B’ series expressions then the ‘A’ series is ontologically dependent on the ‘B’ series (Le Poidevin 1998). McTaggart (1927) also introduced a generic non-temporal concept of linear ordering he called the ‘C’ series. Detailed philosophical consideration has been given in the 20th century to the concepts of discreteness and continuity in space and time. Zeno’s paradoxes of motion were a starting point for Russell (1897, 1922) who showed that they were based on the assumption that finite spaces and times consist of a finite number of points and instants. Russell argues that the paradoxes can be escaped in three ways, either: by recognising that the number of points and instants in any finite interval is infinite; or by denying that space and time do consist of points and instants; or by accepting Cantor’s infinite numbers (the approach that he prefers). This allows him to argue that the series of instants from ‘any earlier one to any later one’ is infinite, though the period of time is bounded. This clearly requires the continuity of time, and by implication, space. Grünbaum (1964) followed Riemann in considering space and time to be continuous by observing the failure of the continuum of physical space to possess an intrinsic metric. This is so since measurement of length does not proceed by determining the ‘amount’ of space or time between two markers, but by determining the ratio between the measured

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length and an external standard. Since ‘length’ is an extrinsic property of space and time, they must, therefore, both be continuous. Many physical theories are developed using spatially and temporally continuous concepts such as mathematical functions. However, the evaluation of these theories almost always requires the existence of entities which are spatially and temporally discrete. The framework called ‘modelling’ by Casti (1989) is based on the notion that there are an infinite set of ‘states’ of natural systems in the real world and that ‘models’ can represent a finite subset of these named ‘abstract states’. Casti defines the concept of an ‘observable’ as a rule for associating a real number with each ‘abstract state’ defined by the ‘modeller’. Such ‘abstract states’ are, by definition, discrete but can either be derived from theory expressed in continuous terms—for example by identifying the local minima and maxima or derivatives of mathematical functions, or by observation—by the identification of sharply changing gradients or patterns in sampled data points. Mathematics, space and time Mathematicians have also made a major impact on the study of space and time by virtue of the symbiotic relationship between mathematics, physics and philosophy. Barrow (1991) points out that Riemann’s tensor methods were essential mathematical apparatus for Einstein’s General Theory of Relativity and Hilbert’s multidimensional spaces provided a crucial tool for the formulation of quantum theory. Physics has influenced mathematics by posing new theoretical problems such as the characterisation of the ‘superstring’ theory of matter, while philosophy has provided mathematics with an epistemological context. In the 20th century, further mathematical discoveries led to the development of new concepts of space and time. Since axioms play such a crucial part in mathematics in general and geometry in particular, 20th century mathematics has focussed on axiomatisation. Hilbert (1899) formalised the axiomatisation of Euclidean geometry around the belonging, betweeness and congruence relations holding for point, line and plane primitives. He reorganised the Euclidean axioms into five groups including 8 incidence axioms, 4 order axioms, 5 congruence axioms, 2 continuity axioms and 1 axiom of the parallels (Vaisman 1980). Formal analysis of systems of axiomatisation led Gödel to theorise in 1930 that no finite logical system can prove all the true facts about the infinite set of natural numbers. This conclusion arises from the observation that no deductions proved from a set of axioms can contain more information than the axioms themselves—and further raises the question of whether any set of axioms are independent of each other. Mathematicians from Archimedes to Gauss examined the axioms of Euclidean geometry for over 2000 years before the independence of the parallel postulate from the other axioms was discovered and non-Euclidean geometry developed (Gray 1989). Investigations of the axioms of set theory led Cantor to study the properties of infinite sets such as the natural numbers and the rational fractions. He was able to show that the rational fractions was necessarily a larger set than the natural numbers and suggested that further infinite sets could be found which were intermediate between the two. This is known as the ‘continuum hypothesis’, which if true suggests that an infinity of infinities can exist. If mathematics can be said to describe the objective universe (mathematical

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Platonism) then the ‘continuum hypothesis’ can be used as further evidence that the universe is objectively continuous. Cohen (1963) later showed that if the ‘continuum hypothesis’ was treated as an axiom of set theory then it is independent of the other axioms. Hence, to add the ‘continuum hypothesis’ to the other axioms implies the creation of a new and extended set theory incorporating the concept of continuity. Mathematicians (notably Hilbert) have also studied the properties of multidimensional ‘phase spaces’ to represent knowledge of the multiple characteristics of an object. Such ‘phase spaces’ can have as many dimensions as there are independent attributes of the object, since this form of representation is not limited by the four-dimensional character of space-time as defined by the theories of relativity. Such multidimensional ‘phase spaces’ can be used to represent the form of complex phenomena such as superstrings on the micro scale or the state of complex systems on the macro scale. 20th century mathematics has also extended the analysis and use of space curves. Hence cubic and quartic polynomial curves were used by Thom (1975) in the development of Catastrophe Theory to explain abrupt change in dynamic systems which continuously tend towards some minimum or maximum equilibrium state. By using higher order polynomial functions to define a surface in n-dimensions, phase spaces with ‘folds’ or ‘cusps’ can be defined. If the minimisation or maximisation process traces out a path in such a ‘folded’ n-dimensional space then the system can exhibit abrupt changes in characteristics. These include ‘jumps’ from one point on the surface to another (say across a fold), trajectory ‘hysteresis’ (where reversing a path involves taking a different route) or trajectory ‘bifurcation’ at topological singularity (paths dividing in the core of a fold or cusp). A further mathematical development that has proved important in understanding the behaviour of dynamic systems is chaos theory. Phillips (1992) defines deterministic chaos as ‘complex, random-like behaviour arising from the dynamics of deterministic nonlinear systems’ (p365). Chaotic systems exhibit a sensitive dependence on initial system conditions so that with alternative starting points the system may develop in radically different ways. The significance of chaos in natural systems is that apparently random spatio-temporal patterns may result from the behaviour of chaotic systems. Culling (1987) suggested that the existence of chaotic behaviour may make equifinality (where initially different forms converge towards a single final form) unlikely. An analysis of chaotic behaviour shows how patterns and trajectories within an ndimensional system phase space may be attracted towards certain configurations (‘strange attractors’). Searching for chaotic behaviour by looking for system divergence from a common start point is a widely used technique in a range of fields (Gleick 1988). The foundations of modern three-dimensional Euclidean geometry also lie in mathematics (Rucker 1987). The work of Boole, Frege and Peano on logical statements and notation in the late 19th century led to the writing of the Principia Mathematica of Russell and Whitehead (1910–13) (which put mathematics in a standard logical form) and the development of Hilbert’s (1926) concept of mathematics as a formal system (which brought together mathematical axioms and the rules of logic). Such mathematical tools were used by Jordan (1893), Russell (1897) and Klein (1908) to formalise the principles of two- and three-dimensional Euclidean geometry in the early years of the 20th century. It was also noted at this time that three-dimensional space has distinctive

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topological properties from two-dimensional space. Hence, three-dimensional objects which are mirror-images of each other cannot be transformed from one to the other by continuous rigid motion as can two dimensional ones. Poincaré (1900) used such discoveries to argue that although multidimensional spaces are possible mathematically, both causality and sense experience require that physical space be considered three dimensional. Mathematical study of three-dimensional Euclidean space has focussed on the characteristics of 3-manifolds. Such three-dimensional geometric manifolds can take a wide variety of forms ranging from regular polyhedra (such as a tetrahedron) through solids defined by polynomial surfaces (such as a paraboloid) to figures defined by closed curved paths defining non-planar topological discs (such as a ‘handlebody’). Only the first two of these types of manifold have generally been used in geometric modelling of real objects while the latter have been studied for their topological and combinatoric properties (Johannson 1991). Mortenson (1985) has summarised the requirements for geometric modelling of an object and the subset of points defining its surface: the object must be bounded (definable in a finite space) and connected (all points in interior joined by a path without leaving the interior); the surfaces must be closed, orientable, non-self intersecting, bounding and connected. Requicha and Völcker (1983) also specified requirements for modelling consisting of rigidity, homogenous three dimensionality (no isolated line segments), closure under rigid motions and Boolean operations (i.e. such operations also produce valid solids), finite describability and boundary determinism. The derivation of these requirements from Euler’s Theorem was illustrated allegorically by Lakatos (1976). Given such constraints six methods of geometric modelling have been developed: primitive instancing; cell decomposition; sweeping; Constructive Solid Geometry (CSG); Boundary Representation (BR); and wireframes (see chapter 4). The psychology of space and time The foundations of 20th century psychology lie in a critique of the prevailing late 19th century approach of Wundt which was based on the use of introspection to study the processes of perception and thought. Watson (1919) dismissed introspection as ‘subjective’ and argued that the workings of the mind should be studied by ‘objectively’ monitoring human actions, founding a school of thought known as behaviourism. Behaviourists argued that human behaviour is the product of conditioned responses to external stimuli. Behaviourists can be divided into two groups. Firstly, those who considered that behaviour is ‘respondent’ or reflex such as Pavlov and Watson, i.e. dependent automatically on a stimulus. Secondly, those who considered that it is ‘operant’ or voluntary such as Skinner, i.e. behaviour is shaped and maintained by its consequences. Behaviourists argued that learning takes place through conditioning. ‘Classical’ conditioning occurs when a new stimulus comes to produce a particular response during learning by being paired with an existing stimulus already producing that response. ‘Operant’ conditioning occurs through the action of reinforcing factors, i.e. the likelihood of a particular response is related to the past consequences of such behaviour (Skinner 1938). Gestalt theory developed in the 1920s as an alternative critique of 19th century

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introspection and in opposition to behaviourism (Koffka 1935). Unlike behaviourists who believed in the importance of trial and error in learning (through its role in reinforcement), Gestalt psychologists considered that much learning took place through insight. Insights could occur when earlier episodes of learning had established forms of knowledge, which could be connected to generate new knowledge. Gestalt theory therefore emphasised the role of cognitive processes rather than conditioning. The importance of cognitive processes in learning was also demonstrated when Tolman andHonzik (1930) showed by experiments using rats in a maze that learning could take place, but need not be demonstrated until later. In other words a cognitive model of the maze was constructed but was not demonstrated until reinforcement was applied. Such ‘cognitive maps’ were later demonstrated to develop in human subjects (Tolman 1948). Hence the development of Cognitive Psychology recognised the importance of the cognitive mediation of behaviour (Craik 1943). Gestalt psychologists (e.g. Koffka 1935) advanced a non-empirical, rationalist explanation for perception based on raw sensory data (direct realism), although it was also influenced by phenomenology (the study of the essence of perception). In this view, perception of an object involves synthesis of disparate sensory data into an organised whole. The whole will always be the simplest and most stable shape, or that requiring the minimum information to generate. The Gestalt theory of perception consists of a series of simple rules: objects are perceived as one if they have proximity in space and time, closure, continuity and symmetry and similarity; sensory data can also be divided into figure (some part that stands out) and ground (background); and, the whole is greater then the sum of its parts. Although the Gestalt principles have proved valid for twodimensional isolated objects, they break down to some extent for three-dimensional objects, and when the objects are part of a scene (Gregory 1984). Most recently perception has been approached from a computational perspective, i.e. how precisely is information extracted from the sensory data and how could the procedure be achieved theoretically, algorithmically and in ‘hardware’? Marr (1982) has argued that for vision the primary activity of perception is recovering shape and that this is achieved in four stages: firstly, recovering the raw image; secondly, making a ‘primal sketch’ from the image to identify edges and objects independent of wider knowledge of the world; thirdly, a ‘2 1/2 dimensional sketch’ (a partial sketch) giving depth to the components in the scene; and, fourthly, a three-dimensional model representation in which the perceiver creates a symbolic solid model of the perceived world by comparison with stored primitives. However, it has still proved difficult to build systems that actually perform well at automated visual recognition. Studies of time in psychology have focussed on the nature of temporal experiences such as the sense of time, the way time passes, and notions of the past, present and future (Friedman 1990). Physiological studies of the sense of time in chronobiology have revealed that although most organisms simulate time’s passing through circadian clocks, the process needs to be continually recalibrated by reference to the sun and is not very accurate (for example circadian clocks are temperature dependent). No evidence has been found that any form of internal timer is effective (Church 1984). In fact, human beings tend to estimate time by reference to the ‘mental content’ of periods of time (Frankenhaeuser 1959). Studies of memory by Freud stress that the unconscious mind

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retains a continuous record of events although the conscious mind may not have functioning mechanisms to recall the information. Time is usually seen as ‘flowing’ or ‘passing’ in psychological studies: Hawking (1988) says that the psychological and thermodynamic arrow of time go in the same direction because the brain is, in fact, a computer. A wide range of mental representations of time that involve the spatial arrangement of symbols to signify temporal relations have been recorded (Friedman 1990). Early work by Galton (1880) and Guilford (1926) suggested that concepts of time were organised by ‘spatial images’ ranging from visualised numerals to graphs showing temporal progress as an upward sloping line. Schroeder (1980) found experimentally the people also use linear, circular and matrix representations. However, Friedman points out that verbal coding of temporal order and orientation through rhymes, weekends, seasons and holidays is also important. Such concepts are known to develop cognitively during childhood: Piaget (1954) studied children’s development of temporal concepts finding that before/after relations are perceived by 8 months, the order of causality by 18 months and relationships between durations and orders of happening by 5 years. Children appear not to be able to manipulate representations of time (of whatever sort) until about 8 years, although later work (see chapter two) has challenged several of these findings. Anthropological concepts of space and time The spatial and temporal structure of the physical world, the experience of space and time in perception and the embedding of spatial and temporal concepts in language are, collectively, powerful influences on the organisation of human societies. Anthropological studies have attempted to record and understand the nature of the spatial and temporal concepts which different societies have developed and by which they have been organised (Aldenderfer and Maschner 1996). Turton and Ruggles (1978) studied the time concepts used by the Mursi people in an arid part of SW Ethiopia noting that they record the number of lunar cycles to chart the progress of the growing seasons and the setting times of certain stars to measure the length of the flooding of the river Omo. However, to the Mursi these measures of time’s passing are secondary to a sense of social consensus about the ‘right’ time to plant their crops or to migrate with their livestock. Hallowell (1937) studied the temporal concepts of the Saultaux of central Canada noting that they did not reckon years, merely winters and lunar months. This meant that individuals had no concept of absolute age and only classified themselves by socially-constructed notions of life-stage. Studies of native cultures, before influence by western societies, have also yielded important insights into how representations of space develop and relate to environment. Turnbull (1961) studied the settlements and language of the Pygmies of the Congo rainforest showing how the environment of the dense rainforest constrains their thinking about space and time. Since the Pygmies rarely see the sky, cannot see great distances and do not experience a seasonal rhythm, Turnbull found their spatial and temporal sense to be shallow and restricted. By contrast, studies by Whorf (1956) on the language of the Hopi who live on a semiarid plateau in the south west United States which offers wide perspectives over the

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landscape showed that they used advanced spatial concepts. The Hopi conceived of a ‘manifested’ realm—everything that is or has been accessible to the senses, and an ‘unmanifested’ realm—covering things that are expected or desired. According to Whorf their language has no tenses but does have different expressions for the two realms as well as an expression for characteristic occurrences. The ‘manifested’ realm is associated with an objective space employing concepts of distance and direction associated with the rising and setting of the sun, while the ‘unmanifested’ realm is associated with an axis joining the underworld and upperworld, and which is wrapped around the manifested realm. The Hopi do not interlink space and time since what occurs simultaneously ‘elsewhere’ cannot be known ‘here’ until later (Tuan 1977). Work by Kluckhohn and Leighton (1948) on Navaho concepts of time shows yet different principles again, notably a focus on the type of activity with respect to time, i.e. whether the activity is repetitive, iterative, momentary, transitional and so on. Von Bertalanffy (1955) suggested that the distinctions between the Hopi concern with ‘validity’, the Navaho concern with ‘type of activity’ and the Indo-European concern with ‘time as a smooth flowing continuum’ is rooted in language and not any universal law of physics. Von Bertalanffy notes that Indo-European languages separate entities from their properties and behaviour, relating them together in sentence structures. He considers this linguistic structure to be derived from the basic categories of western thinking (Rosch 1973) and suggests that the separated space and time of Newtonian physics is merely an expression of the Indo-European linguistic duality of the entity (space) and its behaviour (time). In this respect, according to the Whorfian hypothesis, Hopi, Navaho and Indo-European languages generate different space and time concepts (Sack 1980, Hopgood 1993). Pincker (1995) has refuted these views on the basis that the language of thought—mentalese—is universal. These results may indicate that other social factors are at work in space and time conceptualisation. Social construction of space and time 20th century geographers and sociologists have examined the role of space and time in human social behaviour and organisation on scales ranging from individuals to societies. Many of the studies by geographers carried out before 1970 were based on the principles of positivism, i.e. that observable facts are the only possible forms of knowledge. Positivism is generally considered to have developed, firstly, from Comte’s (1842) view that the methods of the physical sciences could be applied to human behaviour and organisation; and, secondly fromMach’s (1883) view that observational confirmation is the key characteristic of scientific statements and that metaphysical statements have no meaning (Ray 1991). Logical positivist philosopers such as Carnap and Ayer developed the methods of positivism in the early decades of the 20th century emphasising empiricist methods based on verifiability from a realist perspective on perception. Geographers of the 1950s and 1960s largely accepted the claims of positivism, i.e. that relevant spatial processes could be observed and explanatory laws could be formulated, although many adopted the methodology of critical rationalism which involved falsification rather than verification (Johnson 1997). Three distinct groups of theories of space have been developed using positivist

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methodologies based on a rationalist scientific method. Firstly, there are theories that aim to explain spatial organisation of land use. For example, in the early years of this century Christaller’s Central Place Theory proposed that settlements were located at the centres of zones of influence which themselves were spatially and hiererarchically ordered by settlement interactions. Von Thunen’s theory predicted spatial zonation of land use in and around cities according to the cost of land and transportation of products to markets. Weber’s theories suggested that spatial variations of resources governed spatial zonation of land use. These rather simple theories were elaborated in the 1950s and 1960s by adding ‘realistic’ conditions such as the spatial distribution of demand, ‘economy of scale’ effects, cumulative development, and agglomeration processes in order to explain observed spatial patterns (Lloyd and Dicken 1977). In a later stage of development in the 1970s these theories were modified by adding ‘uncertain’ or probabilistic decisionmaking as a factor in so-called behaviourist studies. Secondly, ‘positivist’ theories of space were also developed to explain the evolution of regions. Notable examples include the ‘geographical matrix’ of Berry (1964) in which geography is represented as a matrix of places and characteristics at a series of specific times; the study of the ‘spatial structure’ generated by interaction between regions in developed societies developed by Haggett (1965); and, the use of system theory to model the behaviour of a regional economy (Chorley and Kennedy 1971) and agricultural economics (Chapman 1977). Thirdly, a number of attempts have been made since the 1970s to formally define ‘zone design’ methodologies arising out of ‘Broadbent’s rule’ (Broadbent 1970), which governs the relation between the length of trips made by individuals and the radius of the neighbourhoods from which the trips originate. This rule is based on the axiom that an ‘interaction’ takes place in a spatial system if a trip crosses a zone boundary. As a ‘ruleof-thumb’ for the design of such zone systems, 90% of interactions should cross a zonal boundary (Masser and Brown 1978). Trips were usually defined as straight-line distances, although distances through road networks were sometimes used. The problem with these approaches is that they only defined the appropriate size of zones, or ways in which they could be aggregated hierarchically. Reis and Raper (1994) examined the possible approaches to the larger problem of actually constructing zones from basic geometry since many parts of the world still have no zones defined for socio-economic purposes. Wood et al. (1996) suggested that zones could be derived from the second derivatives of a smooth function representing population density and illustrated their approach using London as an example. However, spatial organisation, regional evolution and zone formation theories share certain ‘positivist’ assumptions: that space is treated as isotropic physical space; that time can be held constant over space; that ‘places’ such as communities, neighbourhoods or cities could be delineated with precision; that the characteristics of places could be represented using quantitative indicators; that spatial processes such as commuting or diffusion of disease can be represented mathematically; that ‘geographic individuals’ (whether persons, communities or socio-economic classes) behave rationally and reproducibly; and that the creators of zones hold ‘universally’ supported values. Positivist theories of space have also normally adopted the methodology of critical rationalism (from Popper) which involved falsification rather than verification as an

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approach to theorising. However, the many falsifications of the positivist theories of space have often been met with extensions to the theories or by exclusion of any ‘falsifying’ circumstances from the scope of the theory. In the period after 1970 there have been a wide range of reactions to the use of positivistic methodologies in the social sciences in general. In the social sciences one critique of positivism was provided by Foucault (1980) who questioned whether science could be equated with truth, and suggesting instead that truth is defined by the systems of power which create and sustain it. Foucault (1972) took a historical approach arguing that truth is always situated within the worldviews (or ‘epistemes’) that are created by a society in a particular period. By contrast, Habermas (1978) sought to show that human ‘interests’ structure knowledge and that different epistemologies are appropriate for each. Hence, positivist scientific method supplies a methodology for the study of the ‘technical’ interest expressed through work, hermeneutics (the study of meanings) provides a methodology for the ‘practical’ interest expressed through language and communication, and ‘critical’ social theory provides a methodology for the ‘emancipatory’ interest expressed through power. The development of critical social theory is based upon the belief that positivism (explanation of appearances) and hermeneutics (understanding meanings) fail to provide any framework for the individual to develop the knowledge of how to act given contemporary structures of power in society. Habermas argues that the identification of knowledge with science is false and that positivistic science can only function through the ‘technical’ interest, which cannot reflect a concern with values or impressions (Unwin 1992). One reaction to the critique of positivism in geography was a reworking of the general assumptions of positivistic theories of space and attempts to improve them through ‘behavioural approaches’. Examples include the attempt to aggregate the ‘geographic perceptions’ of individual decision makers by creating ‘mental maps’ rather than assuming perfect knowledge of an isotropic physical space (Gould and White 1974), and the experimental study of human mobility by Golledge (1980). Behaviourists, however, do not specifically account for the nature of the surrounding society in which individuals act (Smith 1979). The post-positivist critique generally does not accept that behaviourist modifications of positivistic theories are adequate. Reactions to positivistic theories of the role of space in human social behaviour also took the form of new humanistic theories of space. Hence, the application of idealism to geographical decision-making focussed on the thinking and actions of individuals over space, for example, in route planning. Since in idealism no ‘real world’ can be said to exist, such decisions must be determined by individuals’ own models of the real world (Guelke 1974). Tuan (1977) sought to develop a new approach to the study of ‘place’ through the methods of phenomenology. In this fashion the sense of place defined by a ‘landscape’ or a ‘neighbourhood’ can be defined by the aggregate of human appraisals of such environments. However, individuals do not have complete freedom to act through simple self-awareness and are socially constrained (Johnson 1997), implying that some form of ‘external’ social structure may exist. A variety of more radical alternatives to positivistic theories in geography and social science were proposed that were based on structuralist approaches (Levi-Strauss 1963). Structuralism argues that appearances and the underlying are not the same in a social

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context and that three levels of experience can be identified: the level of appearances (the ‘superstructure’), processes (the ‘infrastructure’) and imperatives (‘deep structure’). Gregory (1978) argued that, as far as the role of space in human behaviour is concerned, the superstructure could be equated with external spatial patterns while the underlying infrastructure was responsible for spatial structured processes. Marxist analyses of society and space, for example concerning the commodification of land in capitalism (Harvey 1982), are also developed using structuralism. Structuralists argue that the ‘spatial’ superstructure can only be understood through the processes of the underlying ‘spatial’ infrastructure: from a Marxist perspective the superstructure is largely irrelevant and analyses of it simply perpetuate the social relations which it reflects. However, the socio-spatial processes of the spatial infrastructure are deterministic, leaving little room for the autonomy of individuals (Duncan and Ley 1982). Giddens (1979, 1981) developed the theory of structuration to integrate social structures and human agency in an explicitly spatial formulation. In structuration, social structures link the interaction amongst autonomous individuals with the reproduction of social systems across time and space. Hence, social systems are place- and time-bound: Giddens (1984) defined a ‘locale’ as a ‘setting for interactions’ which can be an institution with spatial and/or temporal identity. Gregory and Urry (1985) argued that a spatial structure is a medium through which social relations can be produced and reproduced. Hence, the spatial organisation of a society reflects a continuous sociospatial dialectic referred to as the process of ‘spatiality’ by Soja (1985). Pred (1986) summarised this process in the maxim ‘the spatial becomes the social, and the social becomes the spatial’ (p198). Harvey (1989b) suggested that control over space played a key role in the reproduction of power in social relations. Another critique of positivist views of space has been based on ‘transcendental realism’ (Bhaskar 1978) which seeks to re-examine a basic ontological question: what are the ‘proper objects of knowledge’? Bhaskar argues that real structures exist outside human knowledge and experience that can generate phenomena. In critical realism it is the interaction of such generative structures that should be studied as causal mechanisms for events and objects. Sayer (1984) characterises realist research programmes as ‘intensive’ since they attempt to discover the causes of events as perceived on a case by case basis. Positivist empirical research programmes by contrast are ‘extensive’ involving descriptive generalisations, which cancel out individualistic behaviour. However, according to Sayer neither the causal mechanisms themselves nor the relationships between the mechanisms and the conditions are invariant in social science. This implies that social science is an open system and, therefore, that the results of research are not generalisable. Realists, therefore, believe it is a mistake to discriminate spatial zones since the generative structures in social processes have ontological primacy over spatial objects such as zones. In the 1990s these critiques of positivism have themselves been critically examined through the (re)thinking of the postmodernist movement. Postmodernism rejects theory and order and aims to examine the hetereogeneity and diversity of social spaces at scales ranging from the individual to the settlement. For example, Soja (1989) argues that the very concept of a geographical region or zone is now dead since there are often greater intra-regional differences than there are inter-regional differences. Highly heterogeneous

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cityscapes are simply reproduced everywhere in the same way. Friedland and Boden (1994) argue that the technologies of ‘distanciation’ (ability to act at a distance) such as telephone, fax and television has destroyed ‘place’ as a meaningful concept. Distanciation also means that capital (in the form of money) has a huge ‘spatial elasticity’ whereas labour cannot move as fast since it must physically move. Although postmodernist thought can be rejected as merely deconstructionist, it is implicit that zones are rejected as ‘modern’ (ordered, regular) and not ‘postmodern’ (diverse, irregular). Geographers and sociologists have also studied the role of time in human social behaviour, although to a lesser extent. Early work was dominated by the ‘time geography’ of Hägerstrand (1968) in which time and space were seen as constraints on action by individuals or processes such as diffusion. Such constraints can be represented by time-space prisms (figure 4.13), which can be interpreted as a two-dimensional projection of a ‘light cone’ in social form (c.f. Minkowski 1908). Individuals could be seen as following a path through time and space (a world line of Minkowski) with a granularity of hours (e.g. shopping), days (e.g. holidays), or years (e.g. careers). In this scheme, places can be seen as the intersections of many individuals’ time-space paths. Time geography was also explicitly incorporated into structuration theory by Giddens (1984). Giddens argued that social systems recognised three timescales: the immediate; the contingency of life; and long term reproduction of institutions. Hence structuration adopts a relative concept of time and space by focussing on the spatio-temporal nature of social relations. Parkes and Thrift (1980) extended time geography to create a new form of analysis termed ‘chronogeography’ concerned with the change of societies through time and space. Thrift (1981) also noted that the nature of time experienced by individuals had changed dialectically both through history and through space (in a case study of England from 1300 to 1900). In pre-industrial society the only time of experience was local solar time which governed all activities through the need to use daylight efficiently. Industrial societies, however, progressively harmonised local solar times into ‘mean times’ such as Greenwich Mean Time (GMT) which were enforced over whole states or regions regardless of the disparities between the clock and the sun’s position. Industrialisation also introduced time governed by machine requiring shift work and defining a social distinction between work time and ‘spare’ time.

CONCEPTS OF MULTIDIMENSIONAL GEO-REPRESENTATION The wide-ranging review presented above has been assembled to illustrate the rich and diverse nature of thinking about an integrated view of space and time. Acceptance of space and time integration implies that the world can be regarded as consisting of fourdimensional ‘geo-phenomena’ and their inter-relations. This section explores the implications of such a theoretical position in the mesoscopic domain of geography. Representation of a four-dimensional mesoscopic world has traditionally been conducted by projection from a four-dimensional space-time to a two-dimensional space. While ‘timeless space’ concepts will continue to be useful, it will be argued in this

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section that new representational scope can be found in the development of multidimensional geo-representations. A framework for multidimensional concepts in the mesoscopic domain Acceptance of a multidimensional framework for the mesoscopic world necessitates theoretical commitments in several different areas, including physics, ontology, epistemology, cognitive science, linguistics and social theory. Each of these areas is discussed in turn to evaluate their role in a multidimensional synthesis. Physics Concepts of space and time have influenced the nature of physical theories of the world from the ancient Greeks through classical dynamics to modern physics. In ancient Greece physical theories adopted a separation of space and time through the study of geometry in isolation from change. Classical dynamics of the 16th century developed theories of motion but considered it to be taking place with reference to absolute spatial and temporal frames. Modern physics has unified space and time through relativity and quantum theory and has stimulated the development of new cosmologies. To physics, space and time are part of the structure of the universe: they are continuous in nature, having no intrinsic metric; they unify gravity and electromagnetic forces; and they provide a way to bring phenomena into existence. Yet physics applies across all the scales from micro to macro and some of its insights are only demonstrable outside the mesoscopic domain. As such the arguments of physics may be necessary but not sufficient to support a multidimensional framework in the mesoscopic domain. Ontology Space and time are part of most ontological schemes since they appear to be foundational in a wide range of classifications of phenomena. This implies that space and time are constitutive of identity in the mesoscopic world. In a multidimensional framework, identity is four-dimensional: phenomena describe a three-dimensional path through time. Any geo-phenomenon with a one-, two-or three-dimensional identity is, therefore, a projection from the four-dimensional world. This raises questions of the role that concepts of space and time play in the individuation of ‘states of affairs’ and their propositional properties. As phenomena can be created from propositions originating in human thinking, the embedding in the world depends on whether an objectivist or phenomenological perspective is adopted. Either perspective is consistent with a multidimensional framework. Epistemology It can be argued that epistemological realism is constituted by space and time through its relationship with causality. From Hume’s famous formulation that ‘cause is spatiotemporally close to the effect and that the cause is always followed by the effect’, it can

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be argued that the world must have a spatio-temporal structure. Thus, there are spatiotemporal limits in the mesoscopic world to causes and effects. These limits are ‘event horizons’ for causes and are in some sense foundational for explanation as they imply a regionalisation of space and time. By contrast antirealism cedes space and time no privileged status in knowledge although space and time may play a role in bring phenomena into focus. Cognitive science A functional view of cognition might take the form of a reflexive cycle of information processing joining the world and the individual social actor. At a high level of abstraction the actor absorbs sensory inputs of information, processes it in the mind by reasoning, and forms propositional attitudes (‘thoughts expressing an attitude to a situation’) to represent outputs such as language, art and work. Such outputs can become the inputs to the minds of other actors in a continuously and socially mediated dialectic. The extended result of such a repetitive and reflexive process is the progressive formation of mindcreated representations of the world, which are persistent within certain social contexts. At a lower level of abstraction, the sensory data recovered from (or emitted by) the world is structured and constrained by psychological controls on perception. In early life, this sensory data is evaluated from visual perspective and motion parallax until experience populates mental models of the external world. It is clear that such models must be explicitly multidimensional in nature given the perceptual primacy of motion and perspective. Space and time are a factor in the multidimensional character of image schemata (the fundamental organising structures of mental models). Thus, the fabric of space and time define qualitative aspects of the world which are salient in perception Many forms of human representation and expression also echo spatio-temporal patterns of the world such as diurnal and seasonal cycles and transformations of phenomena in motion. Artistic expression in painting and sculpture employ colour and texture to reproduce motion; the staging of theatre employs sequence and movement on the stage; and, architectural design seeks to construct spaces which order interaction and reproduce a variety of real world environments. In other words, the multidimensional fabric and structure of many forms of human expression is reinforced by the fundamental spatio-temporal nature of cognitive models. Linguistics Modern physics has developed a cosmology that is hard to reconcile with the structures of (Indo-European) languages where space is associated with entities and time is associated with behaviour. However, such distinct concepts of space and time could simply be seen as ways in which it used to be convenient to axiomatise both naïve and ‘sophisticated’ physics. Such distinctions may also be culturally relative if the Whorfian hypothesis (that languages can be shown to generate different space and time concepts) is accepted. Language can also be regarded as a form of projection from the fourdimensional to a lower dimensional form.

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Social theory It is clear that representation is also socially mediated and constructed. Social processes are constrained by the access and mobility available to the individual, thereby spatially structuring their activities. The control that individuals have over their daily schedules through work or domestic life also acts as a constraint on social process. Taken together, space and time constraints define profound structures that are interwoven with social power to form important generative structures for social process. Such socio-spatial processes may be constitutive of representation, which must be multidimensional by nature. Synthesis Certain conclusions can be drawn from this synthesis. The first is that the conventional mapping ‘paradigm’ is no longer an adequate form of representation for the forms of multidimensional knowledge which emerge from modern geography and geosciences. In physical terms, the two-dimensional mapping paradigm is a restricted projection of a four-dimensional world; in terms of social theory, the mutual constitution of entities and relations cannot be captured in this way. A second conclusion is that the ‘boundarydrawing’ approach to entification embodied in mapping is conceptually and operationally limited. It was argued in chapter two of this book that the act of projection from the world of four dimensions to a geographic plane is to make it impossible to fit many entities into a geographic ontology. Such a limitation must call the whole enterprise into question. Although phenomena and their representation are accepted by workers ranging from phenomenologists to realists it is clear that their identity must be established through a richer and more explicit process of spatial and temporal reasoning. In the physical world, certain landforms can sometimes be seen only to exist in a minority of spatial and temporal contexts yet they may have ontological primacy. In society, policy or administrative zones may be delineated and function as resource distribution units yet the socio-spatial processes may revolve around quite different transient aggregations or nonspatial networks. The challenge of spatial and temporal reasoning about the world’s social and environmental fabric can be approached through the production of multidimensional georepresentations. Representations can be created to exemplify or visualise the phenomena, relationships and processes of the external world and to project them in terms of information onto symbolic ‘facsimile’ entities, associations and transformations. This view of representation argues for the representation of space-time and not the spatialisation of the temporal to use the methods of Raper and Livingstone (1995) and the language of Massey (1999). It is a realist approach unlike that of Thrift (1996) who gives an alternative phenomenological account of representation. Development of multidimensional geo-representations It is argued in this book that new representational scope can be found in the development of multidimensional geo-representations. The value in this approach is both in the process

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of multidimensional conceptualisation and in the attempt to represent multidimensionally. Each of these undertakings changes the other, which it can be hoped will offer new strategies for some intractable research problems. The process of multidimensional conceptualisation of phenomena demands a consideration of the spatio-temporal fabric that we find in the conceptualised world. Ontological studies have attempted to provide possible structures and heuristics. Specific challenges are posed by: • functional roles for processes; • identity criteria for dynamic phenomena under motion; • part-whole mereotopology or the possibility of discreteness among continuity; • scale issues—spatio-temporal processes often generate their own scales of effectiveness; • qualitative temporal structures—e.g. cycles, chaos are constitutive of multidimensional behaviour. The challenges for the implementation of multidimensional geo-representation fall into two areas: • modelling complex and dynamic geo-phenomena; • spatio-temporal exploration of multimedia and virtual reality geographic data. These issues will be explored in chapters 4 and 5 to give the background to the case studies found in part II of this book.

CHAPTER 4 Multidimensional geo-representations for modelling INTRODUCTION In chapter three the case for multidimensional geo-representation was made on the grounds that it can provide a means by which spatial and temporal reasoning about dynamic geo-phenomena in the world can be explored. Geo-representations provide the crucial link between the conceptualised world and models (Raper 1999). Modelling with multidimensional geo-representations is an epistemological procedure that geographic information science uses in the development of knowledge in geography and the geosciences. Multidimensional geo-representations encompass the development of threedimensional models capturing behaviour states, and four-dimensional models capturing process behaviour. This chapter will focus on the scope, procedures and implementation of multidimensional geo-representations in their symbolic and computable form. This chapter develops arguments that were first sketched out in Raper (1996a) and Raper (1999).

SPATIAL AND TEMPORAL REASONING ABOUT PROCESSES AND GEO-PHENOMENA The process of spatial and temporal reasoning, the representation of multidimensional geo-phenomena and the formation of models is a reflexive cycle of activity which has been carried out for several centuries. However, in the late 1980s a new generation of representational tools for multidimensional geo-phenomena became available as a result of rapid technological change in computing (Raper 1989a). In the 1990s, these representational tools made it possible to begin to represent and visualise geo-phenomena that were previously intractably difficult to explore and understand. Yet even more fundamental shifts have taken place in the processes of conceptualisation that have been stimulated by these new representational environments. This first part of the chapter will discuss the theoretical spatio-temporal considerations lying behind multidimensional conceptualisation in order to set in context the data structures and computational procedures that are outlined later. Multidimensional conceptualisation of geo-phenomena In giving a theoretical account of how geo-phenomena are conceptualised it is clear that

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the key notion is identity. The identity of phenomena, that is, the position that human beings individuate and understand phenomena, is widely accepted from many theoretical positions. From the perspective of metaphysics and ontology, identity is concerned with the discovery of ‘particulars’ (entities) and their attributes. In the cognitive science tradition, phenomena are recovered through the perceptual apparatus. In phenomenology, identity emerges from social action, contingently. Hence, the identity of phenomena can be (at least) discovered, recovered and/or be emergent. The argument that identity is discovered comes from ontology, which is (mostly) committed to realism about phenomena (see chapter one). In this approach geophenomena can be argued to come into existence through immanent (that is, eternal) ‘causal processes’ that exhibit a conserved quantity such as momentum, energy or a charge (Salmon 1998). Metaphysical realists give an account of identity that is either based on: • bundles of attributes; • ‘bare’ substrata conferring identity; • ‘essences’. If identity is based on essences then Aristotelian essentialists argue that there are ‘natural kinds’ that confer identity upon phenomena. In geographic information science, Smith and Mark (1998) have argued that geographic kinds can be defined from a mereological actualist position (see chapter two). Rhoads and Thorn (1996) have put the case for natural kinds in geomorphology arguing that geomorphological kinds when defined must be fuzzy and continuous. However, Wilkerson (1988) argued that natural kinds are found at lower physical levels than landforms, for example the chemical elements. Whichever form of ontological identity is endorsed, these approaches all argue that phenomena are discovered among the structures existent in the external world. The argument that the identity of phenomena is recovered perceptually has been developed in the philosophy of mind and cognitive science. In this account individuals develop intentional mental representations in the form of propositional attitudes (‘thoughts expressing an attitude to a situation’) which lead to the individuation of phenomena. Smith (1995c) argued that phenomena are recovered in this way due to their ‘salient’ identity in the visual field. While Gibson (1966) argued that the mind simply extracts from the flow of imagery through sight and the acoustic environment in hearing, Gregory (1966) argued that reasoning about the perception took place to generate phenomena. The argument that the identity of phenomena is emergent from social practices was first proposed by the phenomenologist Heidegger (1927) who suggested that phenomena emerge in the process of the ‘breaking-down’ of concernful action when they become ‘present at hand’. Lefebvre (1974) also showed how the identity of social phenomena could emerge from the production and reproduction of social space. Hillier (1996) showed that non-planned settlements had a ‘deep structure’ which was not a designed feature but an emergent spatial property resulting from the patterns of interaction amongst the inhabitants. These accounts of identity are surely all commensurable. The identity of phenomena, therefore, emerges through the interaction of socially driven cognitive acts with the

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heterogeneous structure of the world (figure 4.1). However, the constitutive role in this interaction may well be played by space and time, through their role as a framework for places and events (Massey 1999). From the perspective of ontology the importance of space-time in the identity of phenomena lies in the concept of intrinsic difference. If space-time is relational then phenomena are different by virtue of their nature, whereas if space-time is absolute phenomena can be different by virtue of their spatio-temporal locality.

Figure 4.1 Conceptualising identity

A relational space-time is preferred here since a dynamic set of spatio-temporal relations between causal processes and the contingent aspects of the environment is a potential generator of identity criteria for phenomena. In other words, it is the interaction between the physically determined behaviour of processes and the historically determined configurations of form, which drives particular expressions of identity. Raper and Livingstone (1995) showed how different sets of environmental phenomena such as coastal landforms could be ‘emerged’ from a set of attributes sampled at a spatiotemporal location, if different sets of attributes were selected. Note that this conception of identity allows the spatio-temporal interpenetration of the different phenomena. Another argument for the constitutive nature of space-time in the identity of phenomena comes from the methodological realism of Harré (1970) and Bhaskar (1978).

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In this account the immanent (eternal) causal mechanisms interact with the contingent (local) spatio-temporal configurations to produce phenomena by a process of mutual feedback. Richards et al. (1998) showed how such spatio-temporally extended generative mechanisms can produce landforms with a limited, process-dependent existence whose identity is not a function of the conditions of the process study in itself. In this approach, the identity of phenomena can be seen to be constituted by the spatio-temporal relations between the contingent conditions. This would have the implication that equifinality (where similar outcomes result from different processes) might be so common as to make reconstruction of process from form almost impossible in geomorphology, and perhaps elsewhere. A further aspect of the spatio-temporal identity of phenomena concerns the temporal expression of the phenomena. From a position termed endurantist (Loux 1998) it can be argued that for a phenomenon to persist through time implies that the phenomenon must exist separately and distinctly in all the different temporal parts of its ‘life’. By contrast, the perdurantist position argues that the phenomenon is temporally (and spatially) extended in a physical sense (Heller 1990), which is close to the argument presented in this book. The perdurantist position is arguably a more powerful one since it allows for the gradual or abrupt change any of the attributes of the phenomenon through time. By contrast the endurantist account needs to show a relationship between the various attributes of the temporally distinct worlds. The vision of spatio-temporally constituted and contingent phenomena identity is compatible with four dimensionally extended phenomena, but often it does not match our psychological or linguistic notions of space and time. Brown (1996) captures the sense of this problem: ‘The world is full of entities and processes we cannot sense but that we can still study…[which]…are often more important for understanding nature than items we can detect with our unaided senses’ (p17). Such a disjunction is problematic but offers opportunities: the kind of phenomena we conceptualise at lower dimensions may well not include all the causally important elements of an explanation as they are dimensionally underdetermined. As such we may be restricting ourselves conceptually by the limited nature of our contemporary psychological/linguistic apparatus for spatially and temporally extended geo-phenomena. The set of identified and identifiable phenomena available to conceptualise should be both multidimensional and as rich as possible. Then it is possible to engage the cycle of reflexivity between conceptualisations of geo-phenomena and the new generation of multidimensional geo-representations. Spatial and temporal structures It is argued in this book that the ‘timeless space’ concepts used in mapping, geography and earth science have been a limiting factor in conceptualisation and, therefore, in representation and modelling. The implication is that richer spatial and temporal structures are needed as Brunsden and Thornes (1977) argued. Focussing on the enrichment of geo-representations to meet these needs is a major research objective of

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contemporary geographical information science. The necessity for new approaches has been recognised by Sui (1998) who called for a rethinking of the conceptual foundations of GIS, given its limited representational foundations. A number of possible approaches to spatial and temporal structuring can be suggested: each brings with it a set of associated theoretical commitments. Three main distinctions mark out the possible approaches. Firstly, the connections between space and time (hybrid or integrated), secondly, how space and time are discretised (continuous or discrete), and, thirdly, the nature of the models of space and time (absolute or relative) that are employed. Looking at the combinations of these approaches helps mark out the opportunities for the enrichment of geo-representations. Space and time connection—hybrid Many authors in geographic information science argue that spatio-temporal structures must be hybrid, that is, capable of treating space and time differently. For example, Peuquet (1994) stated that ‘homogenous four-dimensional representation is not sufficient for use in GIS because time and space exhibit important differences’ (p446). This view led Peuquet (1994) to propose the TRIAD conceptual model in which phenomena are referenced by spatial, temporal and attribute metrics and ordered by timeslice, event or object identities. Peuquet argued that measurement of spatial, temporal and attribute metrics for a phenomenon allows the formation of a ‘world history model’, which can be converted into a process model by explanation of regularities. This approach can only be applied to geographic entities with a discrete spatial and temporal identity. An earlier and qualitatively different hybrid approach was offered by Getis and Boots (1978) who characterised spatial processes in terms of birth/death (time), and diffusion/agglomeration (space). When the two spectra are plotted at right angles, they yield four sets of combinations (figure 4.2) for individuals:

Figure 4.2 Spatial processes

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• births>deaths; diffusion>agglomeration=the ‘contagion’ effect • births>deaths; agglomeration>diffusion=the ‘group development’ effect • deaths>births; diffusion>agglomeration=the ‘waste and disperse’ effect • deaths>births; agglomeration>diffusion=the ‘diminishing focus’ effect. This approach is most applicable to discrete individual-based models whose aggregate behaviour has a spatio-temporal expression. Space and time connection—integrated Spatio-temporal structures can also be constructed that integrate space and time (Raper and Livingstone 1995) in perdurantist fashion. One possible integrated approach would be the use of a Minkowski space-time manifold that is fully four-dimensional in nature. In this case, both space and time could be measured in commensurate units such as lightseconds although such standardisation is not a precondition for integration. Kelmelis (1998) shows how an event has causal influence through a spatio-temporal ‘extent’ whose size depends on its propagation through space and time. In the mesoscopic geographic world such causal propagation can regionalise space and time but there are complex forms of attenuation and amplification. Sound propagation provides many examples: wind can carry or inhibit sound and surfaces can reflect or amplify it (Shiffer 1995). System science can also provide a framework for the integration of space and time through its origins in thermodynamics (Von Bertalanffy 1950). Systems can be defined as sets of relationships between entities abstracted from the world (Thorn 1988). In a geographic context, these relationships are constituted by the spatio-temporal interaction of the processes that then change the state of the entities (Chorley and Kennedy 1971). Discretisation—continuous Space and time can be treated as physically continuous as they lack any intrinsic metrics (Grünbaum 1963). This continuity can be expressed in the algebraic symbology of a mathematical function. Behaviour in the spatio-temporal continuum can be represented through the use of functions in dynamic wave and flow models (Martinez and Harbaugh 1993). In such models space and time are fully integrated in sets of continuous differential equations, however, they must be approximated numerically (made discrete) to obtain predictions of conditions obtaining at any space-time point (Dalrymple and Ebersole 1979). Thill and Wheeler (1995) show how the logistic equation produces different forms of behaviour depending on whether it is implemented using continuous differential or discrete difference equations. This implies that the choice of discretisation may have consequences for the dynamics observed as continuous versions of the logistic equations never produce chaotic behaviour (Baker and Gollub 1990). Discretisation—discrete Physically continuous space and time can be discretised in a variety of ways that have been extensively documented in geographic information science (Herring 1991,

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Goodchild 1992a, Raper and Maguire 1992, Langran 1992, Worboys 1995, Molenaar 1998). Discretisation of space and time is focussed on the selections of metrics, geometries and orderings. Metrics of space and time have evolved from the practices of surveyors and astronomers respectively. The pre-eminent spatial unit is the metre, which was originally a 1/10,000,000th subdivision of the northern quadrant of the Paris meridian. Likewise, the pre-eminent temporal unit is the second, which is derived from a subdivision of a customary clock time originating with the ancient Babylonians. Geometries for the discretisation of space and time are derived from algebraic topology, which concerns the manipulation of geometric configurations of various types (Alexandroff 1932). Geometric configurations (see below) can be embedded in a space of dimension up to three or in a space-time of dimension four. Orderings of space and time are generally based on qualitative topological distinctions (see chapter two) originating with the work of Allen (1984). Cohn et al. (1998) showed how relations between spatiotemporally extended regions could be described topologically and hence ordered. Model—absolute In the ‘absolute’ model, entities are made within a universal reference frame of space and time and are identified by spatial and temporal boundaries marked by physical discontinuities in space and events in time (see chapter 3). This implies that representation of entities in space and time should proceed by identifying the spatial configurations corresponding to events. However, representation of absolute space and time must handle a spatial configuration for every event affecting any entity. Langran (1992) reviewed the spatial database designs that have been proposed as solutions to this problem. Model—relative In the relative space model, time is made of entities with a spatial and temporal extent. This implies that representation should proceed by identifying individuals by the role they play in the world and the relations they enter into. Multidimensional representation can be achieved by using methodologies to identify constitutive processes that produce individuals with distinctive attributes. However, representation of relative space and time requires a prior ontology and sophisticated methods of construction for individuals. Thorn (1975, 1983) suggested that the singularities associated with catastrophe theory could provide such an ontology and he argued specifically that a relative space-time could be built from these ontological foundations. He also notes that such a formulation requires that existence is determined by essence (‘the set of all the qualities of being’ Thorn 1983, p 91). This is the opposite of the absolute view that essence is determined by existence, which is ultimately provided by the space-time field. Combinations of space-time structures The three pairs of space-time structures can be combined to identify eight qualitative combinations of space-time properties and the associated geo-representations, which have

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been implemented for each type (see table 4.1). These space-time structure types are representational options for the geographic information scientist: commercial GIS have only generally implemented type 2. • Type 0: Integrated discrete absolute approach—corresponds to a four-dimensional GIS, which was suggested by Hazelton, Leahy and Williamson (1990) and implemented experimentally by Pigot and Hazelton (1992). • Type 1: Integrated discrete relative approach—suggested by Raper and Livingstone (1995) in their OOgeomorph design of a four-dimensional database of discrete points which could be conjecturally assembled into four-dimensional relational entities. • Type 2: Hybrid discrete absolute approach—typical of the design used by current GIS with temporal extensions, for example, the ESTDM model by Peuquet and Duan (1994). • Type 3: Hybrid discrete relative approach—corresponds to spatio-temporal autocorrelation between points in space and time (Griffith 1981). • Type 4: Integrated continuous absolute approach—the domain of field equations in physics. • Type 5: Integrated continuous relative approach—corresponds to a model of deterministic chaos with attractors in space-time (Orford and Carter 1995). • Type 6: Hybrid continuous absolute approach—equivalent to a four-dimensional process model implemented using differential equations (Ebersole andDalrymple 1979). • Type 7: Hybrid continuous relative approach—corresponds to the Catastrophe Theory of Thorn (1975) which can capture discontinuous change (e.g. jumps at cusps) through the operation of continuous change in variables controlling a system.

Table 4.1 Space-time structures supporting geo-representations

Space-time structure type Properties

Geo-representations

Type 0

Integrated discrete absolute

4D GIS

Type 1

Integrated discrete relative

e.g. OOgeomorph

Type 2

Hybrid discrete absolute

e.g ESTDM

Type 3

Hybrid discrete relative

Spatio-temporal autocorrelation

Type 4

Integrated continuous absolute Field equations of physics

Type 5

Integrated continuous relative

Chaos

Type 6

Hybrid continuous absolute

4D process model

Type 7

Hybrid continuous relative

Catastrophe theory

Several of these space-time structure types offer the possibility of richer georepresentations than those currently in use in GIS. Importantly, several of these space-

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time structure types offer a wider range of possible ways for space-time to constitute entities than the simple ‘timeless’ boundary-drawing approach. Models of time Theories of time offer a variety of ways of conceptualising events and change (Le Poidevin 1998). However, models of time are required to implement temporal conceptualisations. Frank (1998) argues that models of time can be classified by a consideration of types of temporal representation primitives (points or intervals), the distinction between linear and cyclic times, the contrast between ordinal and continuous times, and the viewpoint employed. Using Frank’s lattice-type classification of time models the primary distinctions are between: • ordinal time (time made of points marking events) and continuous time (time is dense); • linear time and cyclic time; • sequential ordered time and branching time; • valid time and transaction time. These distinctions allow the scope of a temporal model to be expressed. Most GIS can store ordinal, linear, sequential order and valid time concepts in object attributes, which defines the scope of the temporal model. As a consequence, GIS are unable to store or manipulate more sophisticated concepts such as continuous, cyclic, branching and transactional time, with knock-on consequences for representation. However, the physical sciences concerned with mesoscopic space and time have also developed models of time. Models of time have also been developed in geographical approaches to system science (Thorn 1988). System science introduced equilibrium models of time in which the output of a system could oscillate around an equilibrium value. Chorley and Kennedy (1971) identified various types of equilibrium found in systems including the metastable equilibrium (stability disturbed and re-established when the system crosses a threshold) and dynamic equilibrium (stable progression in line with a trend). The regulating mechanism for equilibrium maintenance is system feedback: positive feedback is the amplification of an input, negative feedback is the dampening of an input. Currently, GIS cannot represent equilibrium models of time and therefore they cannot be used to identify spatio-temporal phenomena associated with equilibrium and feedback behaviour, such as threshold conditions. In geomorphology, models of time have focussed on the temporal dependence or independence of processes describing a system such as a drainage basin at different time and space scales. In a classic paper Schumm and Lichty (1965) argued that the processes contributing to causal explanations of a geomorphic system such as a drainage basin were a function of the time (and space) scales of enquiry. For example, at short timescales (say days) Schumm and Lichty argued that geology, climate, relief, drainage network and hillslope morphology are independent variables, and only water/sediment discharge is a dependent variable in the explanation of landform morphology. Thus, Schumm and Lichty argued that the assessment of physical change is (time)frame-dependent in open physical systems, as a cascade of causal forces operates in a complex space-time fabric. However, Lane and Richards (1997) pointed out that the Schumm and Lichty analysis

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is focussed on immanent ahistorical processes (using the terminology of Simpson 1963) and does not take account of the contingent configurational circumstances. The ‘memory’ of a geomorphic form (such as the landform shape inherited from the last storm event) can be seen to condition process outcomes, which may then generate system feedback. In geomorphology this implies that immanent processes acting in space-time and the historically-contingent disposition of matter and energy are engaged in constant mutual feedback. This is the way that four-dimensionally extended phenomena are constructed through the operation of spatio-temporally constituted and contingent processes. Massey (1999) argued that this realisation should commit us to the treatment of time as historical rather than immanent and noted that the convergence of these viewpoints could bring together social studies of agency and physical studies of process. Raper and Livingstone (2000) supported this view and discussed the implications for representation. Wolman and Miller (1960) noted an empirical relationship between the magnitude of geomorphological events and their frequency of occurrence: high magnitude events occur infrequently and vice versa. This realisation has led to the search for the ‘return periods’ for events with a given magnitude, for example, the magnitude of the ‘50-year storm’. The return period can also be seen as an immanent conception if the causal elements underlying the geomorphological system are treated as ‘stationary’ through time. Orford and Carter (1995) analysed the records of storminess in tide gauge records in Atlantic Canada and found that there were 6 and 22 year forcing factors in the processes affecting landforms in the time series. This work can be interpreted as showing the need for the ‘historical’ approach to return period analysis. It also reveals another sense in which four dimensionally extended phenomena can be identified through the operation of spatiotemporally constituted and contingent processes. Scale and space Concepts of scale also play an important role in the process of spatial and temporal reasoning. In chapter two scale was characterised as a framing control that selects and makes salient entities and relationships at a level of information content that the perceiver can cognitively manipulate. It is clear that if both space and time are jointly constitutive of ontological schemes then scale is an important control over salience and, therefore, the identity of geo-phenomena and their inter-relationships. To phenomenologists this view is consistent with idealist arguments that entities are constructed and not discovered. However, it can be argued from a realist perspective that scale-dependency is an aspect of the world and that there really are structures in space-time corresponding to particular frames of reference. Thus, without an understanding of scale and its ontological role, realism will be an inadequate basis for spatial and temporal reasoning. Several approaches to the understanding of spatio-temporal scales have been developed in geomorphology. By adopting a systems approach, de Boer (1992) argued that scale could be identified with hierarchical levels of organisation in the physical system. A given level or ‘holon‘ in a hierarchy (Allen and Starr 1982) exchanges matter, energy and information with other levels, both above and below. The identity of a holon is determined by the entities with which it interacts: it is made up of entities with slower behaviour and smaller size, and it forms part of the environment for faster, larger entities.

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In this framework scale is defined by the identity and associations of the holon. Finding the context for a holon in geomorphology corresponds to discovering space-time structures with an appropriate functional identity. Church (1996) saw scale as a resolution at which information transfer, in the form of matter and energy movements, could be detected within the landscape. He argued that information transfer is constitutive of scale through its role in defining observables of behaviour and form (using the terminology of Casti 1989). Thus, every scale of consideration involves averaging and ‘censoring’ of entities and processes at larger and smaller scales in order to identify patches in space and persistence in time at the scale of consideration. This procedure produces functional geo-phenomena. Church (1996) suggests that different forms of explanation are available depending on the scale used: small spatial and short time scales are stochastic, mesoscopic scales are deterministic and chaotic, and large scales are contingent. That explanation at the largest spatial and longest temporal scales is contingent, is a function of the limited analogy that the present affords (Frodeman 1995). Scale is also coupled to explanation through the limits to the spatial dependency of processes. Phillips (1988) argued that the scale of spatial variability of a process can be studied by the use of geostatistics to discover the structure of spatial autocorrelation. Spatio-temporal process dependency is equivalent to ‘areal’ memory for a physical system; Trudgill (1976) termed geomorphic systems with short memory over large areas to be ‘labile’ and long memory over small areas to be ‘sluggish’. The spatio-temporal dependence of process may also lead to allometry, i.e. the tendency of landform types to change their shapes with size, through limits to process operation (Church and Mark 1980). Evans and McClean (1995) argued that allometry demonstrates that the land surface is not unifractal but multifractal, thereby showing the limits to self-similarity in the mesoscopic world. Evans (1998) argued that at least nine variables were necessary to characterise terrain, and that multifractal models of terrain need to be linked to fractal slopes and drainage networks.

THEORY AND PRACTICE OF GEO-REPRESENTATION The reflexivity between conceptualisations of phenomena and the new generation of multidimensional geo-representations is the key to the process of spatio-temporal reasoning in multidimensional geographic information science. The previous section has shown how space-time structures are constitutive of geo-phenomena identity. In this section the theoretical and practical preparations for the use of geometric tools that can be used for the representation of geo-phenomena states and processes are discussed. There are two methodological approaches to multidimensional geo-representation in three- and four-dimensions (Raper 1999). Firstly, the representation of forms, structures and properties of entities as three-dimensional states; this can be termed spatial data modelling. Secondly, the representation of processes as fluxes; this can be termed process modelling. Both approaches to geo-representation have had different histories, and hitherto they have mostly been developed by different research communities. However, with the proliferation of new computational tools, both kinds of geo-representation are

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now becoming more widely used both to implement spatio-temporal reasoning and to explore the identity of geo-phenomena in a wide range of disciplines. The following sections focus on the link between conceptualisation and geo-representation through spatial and spatio-temporal data modelling. Geo-representation of forms, structures and properties The representation of the forms, structures and properties of entities has mostly been the concern of geography and the geosciences. In its two-dimensional form georepresentation of forms, structures and properties has been used for mapping while in its three-dimensional form it has been used for the reconstruction of atmospheric, solid earth or oceanic domains. The representational tools used in such geo-representation for the most part have been drawn from database design and from geometry (Molenaar 1998). The rules and syntax of the design procedure for the construction of static georepresentations are often referred to as ‘data modelling’ although this term is understood differently in different disciplines (Raper and Maguire 1992). In database design, the data model is understood to be a mapping of a conceptual model about crisp ‘real world’ entities, relationships and processes onto a logical model of computable objects, associations and transformations (Tsichritzis and Lochovsky 1982). The ‘computable objects’ in this definition are usually understood to refer to elementary computer data types such as integers, real numbers, Boolean values, dates and monetary units. Frank (1992) extended the scope of this definition by defining a data model as ‘a set of objects with the appropriate operations and integrity rules defined formally’ (p410). Herring (1991) noted that no single approach to data modelling equivalent to that used in database design is available in geographic information science due to the diversity of the required modelling domains. Spatial data models must represent the spatial extension, structural character and qualitative spatial variation of entities, which forces spatial data modelling to use hybrid representational approaches employing geometry and databases. By definition, spatial data modelling must project the state of dynamic entities onto a static two-dimensional plane. Spatial data modelling must also provide approaches to the representation of the fuzzy as well as the crisp entity (Burrough 1996). Spatial data modelling has, therefore, developed methodologies that are coupled to conceptualisation and that use a variety of methods of spatial discretisation. Hitherto, the conceptualisation carried out by most geographical information scientists has been founded on an endurantist ontology and the discretisation has been based on a positivist epistemology employing a conjectural boundary drawing approach. This book argues the case for conceptualisation based on a spatio-temporally constituted perdurantist ontology and discretisation based on a neo-positivist epistemology. Entity identification involves ‘emergence’ from the spatio-temporal fabric. The ‘traditional’ conceptualisation has been based on reductionism about entities on a ‘timeless’ spatial plane. The alternative formulation suggested here recognises the inherence of spatio-temporal extension in entity identity. Spatial data modelling has been coupled to error modelling as a means of assessing the validity of the representational data and the operations carried out on them. Hence,

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Heuvelink (1998) defines error as ‘the difference between reality and our representation of reality’ (p9) to give a measure of the extent to which the geo-representation is out of step with the conceptualisation of the world in use. This is an absolute measure but one clouded by metaphysical and epistemological issues. By contrast accuracy can be defined as the ‘closeness of results, computations or estimates to true values…or values accepted to be true’ (Unwin 1995, p550). This definition permits the accuracy of a georepresentation to be de-coupled from the world entirely, allowing accuracy to be a property of the axiomatic system from which the geo-representation is drawn. This manoeuvre could lead geographic information science into ungrounded and internally justified statements when used uncritically. There is a choice in the use of systems for geo-representation between the kind with a fixed representational approach, requiring the user to adapt to the system, and the kind of system flexible enough to adapt (to some extent) to the user’s conceptualisation. This dichotomy has, ironically, marked out a distinction between systems imposing representation that are simple conceptually onto users, and systems allowing the incorporation of rich concepts that are complex to design and use! Two-dimensional data modelling The conceptualisation phase of spatial data modelling currently involves the identification of two-dimensional spatial expressions capable of geo-representation. The most common source and methodology is conventional cartography (see chapter 2) which employs a number of standard conventions to project from the world to a twodimensional map. This book has outlined a number of richer methodologies available for the constitution of geographical identity from social and environmental geo-phenomena. In particular, it is clear that there are space-time structures unused by GIS with the scope to reveal significant two-dimensional configurations or interactions as well as the scaledriven ‘framing’ of functional geo-phenomena. The challenge is now to develop these methodologies and to make them available in, or in association with, geo-representational tools. The representational phase of two-dimensional spatial data modelling is concerned with the range of geometric structures available to represent discretised configurations. Commercial GIS have each introduced a large number of ad hoc geometric formalisms and terminologies with which to construct geo-phenomena. Herring (1991) argued that these methodologies could all be made commensurable by the use of a universal template employing topological concepts. Topology can be defined as the study of those geometric properties that remain invariant under topological transformations such as a stretching or folding. Such properties, for example, connectivity, adjacency and containment can be termed topological properties. Distance, area and directional bearings are not topological properties as they are changed by any topological transformation. ‘Pointset’ topology based upon set theory is the study of topological properties. In pointset topology a theoretical ‘neighbourhood’ is conceptualised with an arbitrary shape or dimension that is made of an infinite number of points. If the points on the boundary are included in the neighbourhood it can be modelled as a closed set and termed the ‘closure’. If the points on the boundary are not included and the neighbourhood is only

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made up of its ‘interior’ then it can be modelled as an open set (figure 4.3). A counterpart to these concepts in the world of experience might be a garden (interior), its wall (boundary) and the legal property (closure) if the property included both the garden and the wall. Pointset neighbourhoods can be embedded in any dimension, although only a two-dimensional embedding is considered here. In a two-dimensional embedding such pointset neighbourhoods are the infinite set of points from which one-and twodimensional geometric forms can be instantiated. Pointset neighbourhoods can be transformed while retaining their topological properties if they are ‘connected’. Connected neighbourhoods have an unbroken path from any point to any other point within the neighbourhood. A connected neighbourhood with no holes is ‘simply connected’. Theoretical geometric objects can be made from pointset neighbourhoods. There are two main approaches according to Herring (1991): feature-based approaches in which the geometric primitives are entities, and positionbased approaches in which the primitives (usually squares in a grid) are locations for which attributes are available.

Figure 4.3 Definitions of topological terms

Worboys (1995) has suggested that in feature-based approaches all theoretical objects can be divided into either points and ‘extents’ (see figure 4.4). The ‘extents’ can be further subdivided into one-dimensional extents (boundaries with no interior) and twodimensional extents (the full closure of the object). Note that if the ‘boundary’ of a onedimensional neighbourhood is non-self crossing it can be termed ‘simple’. The names of these precisely defined topological forms have been made generic to avoid confusion with the wide range of terminologies used in commercial GIS. Such generic terms are of considerable use when designing data transfer standards for the exchange of data between different GIS. Algebraic topology is the study of how such theoretical topological objects can be

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assembled into complex objects using discrete geometric primitives (Alexandroff 1932, Massey 1967). The simplest approach to algebraic topology is to use ‘simplices’ as primitives, i.e. point (zero simplex), straight line segment (one simplex) and triangle (two simplex) forms. More sophisticated ‘cellular’ approaches of the kind used in many GIS allow multiple segment lines and closed two extents (‘cells’) formed from multiple segment lines. These approaches to algebraic topology require that the pointset neighbourhood be regularised so that ‘cells’ are forced to be closed, connected and nonoverlapping to avoid any ambiguity. In many GIS this step, known as ‘planar enforcement’, forces representational compromises since many geo-phenomena cannot be closed naturally (for example, a bay). Graph theory covers the manipulation of sets of nodes (junction points) and edges (lines) which may form objects or trees and which may be directed or undirected. There is no notion of interior in a graph, which is only concerned with connectivity.

Figure 4.4 Geometric objects in pointset topology (after Worboys 1995)

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Three-dimensional data modelling The conceptualisation phase of spatial data modelling in three-dimensions is quite different to that used in two-dimensional cases as there is no equivalent to conventional cartography as a source of information. This means that three-dimensional conceptualisation has to proceed from first principles in each case (Raper 1989b). Consequently different conceptualisation methodologies have developed in each application area and these are often incommensurable. Three-dimensional spatial data modelling is often also defined by professional codes of practice or standard workflows, especially in the hydrocarbon and mining industries. Three-dimensional spatial data modelling involves consideration of structure as well as configurational form and the spatial variation of qualitative properties. In fact, threedimensional conceptualisation can be driven by a variety of different imperatives, which differ depending on the domain of interest in the earth, ocean or atmosphere. Structure can be drawn from a geological ontology of strata and faulting in the earth (Houlding 1994), from a meteorological ontology of air masses, streams and weather fronts, or from an oceanographic ontology of tides, currents and basins (Li 1999). Three-dimensional spatial data models such as the model of Minneapolis on the cover of this book have also been made for urban environments. Three-dimensional models are, by definition, static and have to be made for a given time point or interval. This constraint is minimal for earth science and maximal for meteorology, given their respective typical rates of change. Turner (1989) identified the chief problems for three-dimensional spatial data modelling in the geosciences as: complexity of variation, fuzziness of geo-phenomena, poor sampling, uncertain information, and a lack of access to the domain of interest. The available information was divided by Kelk (1992) into samples of geo-phenomena (descriptions, test values, remote sensing) and indications about their character (heuristics from the geosciences). Kelk pointed out that consequently three-dimensional spatial data modelling is highly knowledge-driven. Frodeman (1995) argued that the process of piecing together a holistic picture from this kind of information requires the use of ‘narrative logic’ using global knowledge of sequence and succession to understand the local context. Achieving crisp definition in three-dimensional geoscientific ontologies involves conjecturing configurations with available samples or characterising spatial variation. In the former case, this means building on the dimensionality of sample points, lines or volumes collected by various devices or remote sensing methods to create georepresentations. In the latter case, it involves exploring the patterns of autocorrelation in the sampled variables using geostatistics (Houlding 1994). By plotting the difference in value between all possible spatially separated sample pairs against the distance they are apart, it is possible to characterise spatial variation using Kriging techniques. The average difference in value of all the sample pairs falling within given distance ranges can be plotted on a semivariogram to show how sample value varies with distance and direction. This information can be used to characterise a field model of spatial variation. The representational phase of three-dimensional spatial data modelling involves choosing geometric primitives that can mimic the discretised forms, structures and

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properties of entities. Three-dimensional solid modelling implies a geo-representation that encloses space or uses overfolded surfaces requiring three independent axes of description. This definition excludes non-overfolding surfaces since they can be treated as two-dimensional maps where the z value for each x, y location is treated as an attribute. Algebraic topology can be extended from two-to three dimensions to create three-dimensional simplex tetrahedron forms or cellular forms (Lattuada and Raper 1995). Such geometric forms can be embedded in a three-dimensional Cartesian frame. Similarly, a physical field can be discretised in three dimensions and represented using tesselations of regular solids such as cubes known as voxels. In three dimensions, since the process of conceptualisation is closely coupled to discretisation and representation, the commercial and research implementations of threedimensional GIS often proscribe both aspects of the spatial data modelling. The procedures employed by each system are described below in the section on threedimensional geo-representation: only the most generic aspects of geo-representation are discussed here. The first step in the geo-representation process is to obtain samples of the phenomena in the study domain in the form of property data for x, y, z locations at a time t which meet a specified set of criteria. Each of these data records x, y, z, t, property 1, property 2...property n can be called a tuple. The collection of these tuples of data is a sampling exercise. These tuples provide the starting point for solid geometric modelling techniques. Typical means of obtaining such samples are seismic profiling, aerial remote sensing, weather balloons, probes, systematic survey and borehole drilling. However, there are several drawbacks associated with point sampling of geo-phenomena using vertical sampling lines through a domain. Firstly, it can be very difficult to distinguish between the multiple occurrence of a similar feature down a line and the repeated occurrence of a single object through folding, re-entry or faulting. Secondly, the continuity between any two occurrences of any geo-phenomena taken from two neighbouring point samples cannot be assumed to be simple or predictable. The ‘device’ and ‘phenomenon’ exploration approaches are two alternatives for the gathering of tuples of data to describe geo-phenomena. In the case of the device exploration approach, the measurement technology defines the geometric arrangement of the observed tuples, and there is no search for an a priori geo-phenomenon (Houlding 1994). Thus, boreholes impose a linear structure on the measurements, characterising the sequence of points down the hole, and a photogrammetric survey of a terrain or section can generate a grid of measurements over the earth’s surface. However, a survey of the dispersal of tracer pebbles over a river bar will be contrained by hydraulic processes and recovery factors, and will generate a spatially non-regular set of observed tuples. In this approach the tuples recorded may only have the means of collection or selection in common. In the case of phenomenon exploration approaches, the search for an a priori geo-phenomenon will define the geometric arrangement of the observed tuples. The located tuples identified by the combination of ‘suggestive’ variables can form a spatial cluster with an arbitrary three-dimensional configuration. If geo-phenomena can be identified by a single key parameter and are known to exist in a discrete form from other knowledge of the domain (e.g. mine access, destructive examination) then the geo-phenomenon can be termed ‘sampling-limited’ (Raper 1989b).

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An example would be a perched aquifer, a salt dome or a fault-limited block. By contrast if the geo-phenomenon is transient or continuous (e.g. a temperature field), or exists only as a spatially clustered set of observed tuples defined by a group of ‘suggestive’ parameters, then the geo-phenomenon can be described as ‘definition-limited’. An example of a definition-limited phenomenon would be a pollutant plume in the ocean defined by a threshold, or a sedimentary facies defined by limiting percentages of sand and clay (Orlic 1997). Hence, the ‘data model’ for a geo-phenomenon believed to exist in the earth, atmosphere or ocean may be defined by form, property and structural parameters in a specific combination. The three-dimensional spatial identity of the geo-phenomenon is then established by searching the population of selected characteristics for the boundaries of the defining conditions and recording the x, y, z coordinates. This means that by altering the contents of the data model, and iterating the search process, a new set of x, y, z coordinates defining the object can be created (Raper 1989b). The overall architecture of a domain can often be defined in different ways, depending on the contents of the data model for each element of the sequence defined. It is clear therefore, that establishing the spatial identity of definition limited geo-phenomena in the subsurface is highly sensitive to the contents of the data model. A key point is that the errors or bias inherent in the data model can be as great, if not greater than those introduced in the sampling of the parameters defining the geo-phenomena or in the process of its visualisation. Geo-representation of processes Representing processes has been the concern of a wide range of disciplines including physics, engineering, geosciences, geography, psychology, economics and planning. In these disciplines, geo-representation of process has generally been carried out either to predict (Haines-Young and Petch 1986), or to improve understanding of processes making up geo-phenomena (Richards et al. 1998). As in the representation of forms, structures and properties of entities, the geo-representation of processes in models depends critically on the discretisation of space and time. Models of processes making up geo-phenomena have been developed both for two dimensions of space plus one of time (2D+T), and for three dimensions of space plus one of time (3D+T). In these endurantist approaches, the time dimension tends not to be integrated with the spatial dimensions in the geo-representation of processes. In this section, it is argued that much current work is epistemologically dependent on endurantist forms of space and time discretisation. This has implications for the scope of process modelling and the scope of the spatio-temporal identity that can be constituted in such representations. The representation of processes in a dynamic computational environment necessitates spatio-temporal data modelling. As processes are fluxes of individuals (sensu lato) or the dynamic behaviour of geo-phenomena, spatio-temporal data modelling involves reasoning about identity and/or discretisation in both space and time. Methodologies for spatio-temporal data modelling are largely application-specific (Kemp 1993) and data driven (Smith et al. 1995) at present, meaning that the representation of processes often drives conceptualisation, rather than vice versa. Given the arguments above for the constitutive nature of space- time structures and the importance of knowledge for spatial

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data modelling, it is argued here that it is conceptualisation that should really drive the geo-representation of process. This approach involves selecting the representation that is appropriate to the conceptualisation during spatio-temporal data modelling, or extending existing modelling approaches (Raper et al. 1999). This is operationally challenging but it is argued here that such an approach is perhaps the only way to break new ground in the multidimensional modelling of processes. Approaches to process modelling A wide range of models has been produced to represent processes making up geophenomena. These models have been classified on their characteristics by a number of authors. Kemp (1993) reviews mathematical modelling applied to environmental domains and shows that implemented models can be distinguished using a dichotomous classification developed by Jorgensen (1990). According to Kemp mathematical models can be distinguished by their: • time-related behaviour (e.g. dependency of model variables on time and temporal parameterisation); • space-related behaviour (e.g. dependency of model variables on space and spatial parameterisation); • type of data, parameters and expressions (e.g. whether deterministic or probabilistic in nature); • model structure (e.g. holistic or reductionistic nature); and • mathematics. In a conceptually similar scheme, Burrough (1995) divided models into the following types: rule-based (based on logic), empirical (based on regression), physical (deterministic) and physical (stochastic). Burrough characterised each of these models in terms of their: • time/space discretisation (finite difference grids or finite element meshes); • mathematics (linear or feedback terms raised to powers); • formulation (global or local rules for behaviour); and • spatial variation (distributed or lumped parameterisation). Watney, Rankey and Harbaugh (1999) classified models from a geological perspective by purpose: models as learning tools; models as status calculations focussing on a specific question; or, models as simulations which are usable to address a wide variety of questions. From a geological perspective they divide models into the ‘inverse’ type (focussed on the reconstruction of past processes from extant geo-phenomena) and the ‘forward’ type (focussed on prediction of processes and the potential emergent geophenomena). Watney, Rankey and Harbaugh (1999) also classify models by their dimensionality (2D+T or 3D+T), since models with only two spatial dimensions do not allow the representation ‘out of plane’ (three-dimensional) physical processes. They look forward and characterise the future work needed on process models as relating to: • Input (lags, boundary conditions, scaling inputs, 3D+T datasets, non-linear conditions);

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• Model engines (scale-dependent algorithms, 3D nature of spatial processes, mixed stochastic/deterministic operation); and • Output (goodness of fit criteria, integration of inverse outputs into forward models, measures of uncertainty in output). Process models can also be classified by the way they implement theories of modelling. Ziegler (1976) defined modelling as an application of the theory of computation, which is grounded in general systems theory. Ziegler’s formalisation of modelling involves the definition of a ‘base model’ as an analogue for a ‘real system’ by the observation of inputs and outputs using the conditions specified by an experimental frame. Computed solutions are usually based on what Ziegler calls a ‘lumped model’, i.e. a simplification of the ‘base model’. By contrast Casti (1989) defined a model as ‘an encapsulation of some slice of the real world within the confines of the relationships constituting a formal mathematical system’ (p1), thereby acknowledging the dichotomy of concepts and mathematical symbols. Casti bases his modelling ontology on the concept of an ‘observable’, which is ‘a rule [for] associating a real number with each abstract state’ (p5). Since there are an infinity of ‘real’ states, the modeller must conceptualise and measure a meaningful subset of abstract states that can be represented by observables. By assembling a set of mathematical equations of state expressing the dependency relationships among observables, a modeller can implement a computable model. Finally, models can also be classified by their epistemological role. Haines-Young and Petch (1986) argued that models should be seen as part of a critical rationalist methodology, where models are ‘devices used to make predictions’ (p145). The model predictions can then be used to suggest possible falsifications for the theory, although the question of what constitutes a valid falsification has proved problematic for critical rationalism. By contrast, Richards et al. (1998) argue that models should be focussed on the improvement of understanding through a realist methodology. This can be achieved by the use of simulation modelling to assess system behaviour and to carry out sensitivity analyses. In a realist methodology, simulation modelling of causal processes implicitly lacks closure since the spatio-temporal setting is subject to uncertainty in boundary conditions and scale considerations. Thus, model results are only meaningful if contextualised in terms of contingent spatio-temporal configurations applying to the simulation model. For the most part the models that have been ordered and classified by the authors in this section have been based on an endurantist and critical rationalist epistemology. While they have brought new insights into processes making up geo-phenomena, they often lack true multidimensional scope. Spatio-temporal data modelling The aim of spatio-temporal data modelling is to represent functional and spatiotemporally extended entities whose behaviour can be modelled. The most common organising principle for this activity is the discretisation of space and time from the continuum of the conceptualised world. Kemp (1997) addressed the problem of dealing with continuity in modelling by reviewing the geometric solutions to the discretisation of

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space and time. She argued that there is a fundamental dichotomy between a ‘field view’ (geo-phenomena are continuous but can be discretised on a grid) and an ‘object’ view (geo-phenomena are discrete and can be discretised by mapping boundaries/structures). Couclelis (1992b) suggested that this dichotomy was analogous to the ancient Greek debate between the atomist and plenum ontologies of space (see chapter 2). Kemp (1997) argued in favour of the field view for the discretisation of a continuous space and time. She argued that fields can either be represented using finite difference numerical solutions solved for regular grids, or using finite element analytical solutions where the homogenous applicability of terms in the ruling equations allows the identification of elements delineated spatially. However, the finite element approach arguably belongs in the ‘object’ view. Note also that Kemp’s approach is definitively endurantist in nature as it accepts that it is necessary to discretise space and time separately. Since the field approach elaborated by Kemp (1993, 1997) is the dominant approach to spatio-temporal data modelling, then this has defined the typical scope for modelling the processes making up geo-phenomena (Goodchild et al. 1996, NCGIA 1996). In this approach, GIS have been seen as systems for sourcing the inputs to the lumped model (Ziegler 1976) or the observables (Casti 1989). This has led to debates about whether GIS and environmental models should be coupled (Nyerges 1992) or represented in a unified modelling language with spatio-temporal concepts (Smiths et al. 1995). However, these approaches to spatio-temporal data modelling leave much of the richness of spatio-temporal behaviour unrepresented. Certain concepts like multiple resolution processes, spatio-temporal latency, positive and negative feedback and chaotic behaviour are rarely accomodated by spatio-temporal data models developed by geographic information scientists. Tzetlaff and Harbaugh (1989) and Günther (1998) also drew attention to the difference between the Eulerian multiple grid-based models of many endurantist process models and the Lagrangian vector-based models for the movements of individuals. Cellular automata approaches to modelling have allowed the representation of more sophisticated inter-relationships between the cells in a field (Zijlstra 1999). However, these models have still involved sequential operation rather than the parallel processing seen in intelligent spatial agent models (Rodrigues 1999). Finally, spatio-temporal data modelling can be implemented in a 2D+T or 3D+T framework. The 2D+T framework aims to project from four dimensions to three without significant information loss. The 3D+T framework involves decisions about the constitution of spatio-temporal identity.

TWO-DIMENSIONAL GEO-REPRESENTATION Data models of conceptualised geo-phenomena as described above are represented in computational form using geometric tools. Two-dimensional computational tools are briefly described here since they provide foundations for three-and four-dimensional methods; comprehensive treatments can be found in Van Oosterom (1993), Worboys (1995) and Molenaar (1998). Theoretical topological objects defined in algebraic

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topology need to be realised in the world of human experience to be used in a GIS. By embedding objects from discrete ‘cellular’ algebraic topology in a two-dimensional plane with a fixed metric, geometric representations can be made using Euclidean geometry. Euclidean geometry defines points by the angle and distance they are from an origin (the straight line from the origin to the point is known as the ‘vector’). One and two extents can then be created from sets of point ‘vectors’. It is possible to carry out operations on the geometric objects using trigonometric procedures e.g. the angles of arbitrary shaped triangles can be calculated using the cosine rule and distances could be calculated by creating rightangled triangles and using Pythagoras’ theorem. Euclidean geometry can be embedded in a two-dimensional Cartesian frame and objects can be expressed in coordinate form in the feature-based approach. This has subsequently facilitated the implementation of coordinated Euclidean geometry in finite precision computers. In coordinate form a point can be represented as an x,y coordinate pair, a one extent by a straight line between such points (multiple line segment lines can be termed polylines) and a polygon by a polyline closed on itself (figure 4.4). The Cartesian coordinate framework is usually a ‘projection’ of the earth from three dimensions to two. The creation and management of topological relationships for georepresentation using the feature-based approach relies on the use of planar enforcement routines to ensure that all polygons are closed, connected and non-overlapping.

Figure 4.5 Coordinatised Euclidean geometry

In the alternative position-based approach, the formation of theoretical objects from

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pointset neighbourhoods begins by discretising locations with attributes from the underlying physical ‘field’. A physical field is a measurable quantity that can be defined anywhere at an infinite number of points. As in the case of algebraic topology (implementable using coordinated Euclidean geometry), the spatial variation of the field can be discretised using geometric tesselations (‘sets of connected discrete twodimensional units’). Whilst regular tesselations can be formed from triangles, hexagons and squares, only squares arranged in a grid are commonly used. A grid of squares (‘cells’ or ‘pixels’ [PICTure ELementS]) are easy to handle in computers as memory arrays are logically similar to the physical imaging technology of faxes, scanners, satellite sensors, cameras, videos and visual display units (figure 4.6). Such imaging systems capture/display the reflectance of a real world ‘scene’ for each pixel in the ‘raster’ within its range of sensitivity in the visible/non-visible part of the electromagnetic spectrum. The ‘scene’ can vary from the flat surface of a map to the surface of the earth viewed orthogonally or obliquely from an aerial or terrestrial platform which itself may be static or moving. Imaging devices capture ‘raster’ imagery in the optical band (e.g. map colours or reflected visible light from the earth) or in a combination of infra-red, optical and ultraviolet bands (earth surface spectral response), which can be recombined to form a composite image. The field approach is also suitable for storing sample values in nominal, ordinal, interval or ratio form obtained on a regular grid (Chrisman 1996). The most common form of data derived from sampling is terrain elevation (ratio data). However, any sample value can be assigned to a cell, for example, residential population counts (ratio data), risk factors (ordinal data) or origins/destinations of journeys (nominal). A key characteristic of raster data is the spatial relationship of each pixel to the geophenomena, as, by definition, the stored value in the raster must apply homogenously within the pixel. When the systems capture continuously varying geo-phenomena by taking all the values obtained by the sensor within the area of the pixel they must then apply ‘pixel averaging’ to get a mean value (e.g. satellite imaging and map scanning). By contrast, single measurements/samples at a point can be ‘assigned’ to the whole area of a pixel although in reality there may be (unsampled) internal variation within it (e.g. digital elevation models and risk factors). In both cases, the boundaries of the pixel will become sharp discontinuities (if the values stored in each pixel are different), even if in reality the variation is smooth and continuous. When the systems capture discretely varying data each pixel must be assigned a value corresponding to the spatially dominant observation within the pixel. Some GIS offer the possibility to store point measurements as regular grids of points called ‘lattices’ where the point values are not assigned to pixels by default but remain stored as points. This data structure offers the flexibility of dual display as either a surface with linear interpolation between the grid of points or as a ‘point assigned’ raster. The size of the pixel on the ground or the frequency of sampling of points defines the resolution of the data set in relation to the observed geo-phenomena. Such pixel resolutions may be pre-fixed as in the case of some earth observing imaging systems and some fixed resolution sampling. Frequently, however, pixel resolution can be arbitrary. In some cases the underlying field being discretised in a raster can be non-isotropic, i.e.

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there is a directional bias in the values. This is the case in travel time isochrones for calculating areas at equal travel time from some point. An early convention developed in spatial data modelling was that entities must be described separately in terms of their non-spatial and spatial attributes. This convention originated in the software architectures of the early GIS, where a geometry engine was integrated with an alphanumeric relational database management system (Shekhar et al. 1999). In later research ‘extended relational’ (Güting and Schneider 1993) and ‘objectoriented’ approaches (Egenhofer and Frank 1992) have been used in GIS so that spatial data models can now be constructed in most GIS without separating the geometry and the attributes. At their simplest geo-phenomena can be represented using two dimensions with one or more attributes, as in most current GIS (Burrough and McDonnell 1998). Such GIS are normally based on an x, y coordinate system projected from the earth with no third z coordinate. There are clear compromises in the use of such two-dimensional representations to represent geo-phenomena (Raper and Kelk 1991). Firstly, the surface elevation z coordinate must either be ignored or treated as a single valued attribute of x, y, which then restricts the representation to an infinitely thin surface which cannot overfold without giving multiple values of z. Secondly, temporal change must be ignored or treated as a series of two-dimensional ‘snapshots’ maps. While these compromises can be accommodated in GIS that are used for facility management or geodemographics, they usually cannot be tolerated for environmental and geoscientific applications.

Figure 4.6 Geo-representation using rasters

Single-valued surfaces can be mapped using GIS by storing the surface elevation as an attribute of x, y using either raster, vector or functional approaches. Raster approaches

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use digital elevation modelling (DEM) techniques (Hutchinson and Gallant 1999). Vector approaches involve either the storage of isolines that join points of equal attribute value or the use of triangulated irregular networks (TINs) to structure points (Weibel and Heller 1991). Interpolation may be necessary if the data source does not provide points prestructured in the form of a DEM or a TIN (Petrie 1989). Surfaces constructed with intrinsic linear constraints are needed for surfaces that are cut by faults, as in geological applications (Rüber 1989). The earth’s surface can also be classified and regionalised into slope elements by geomorphologically classified terrain shape (Dikau 1992, Wood 1996). If the peaks, pits and passes making up a terrain are identified from an interpolated surface model, then these surface-specific features can be connected to form a terrain network topology (Wood 1998). Functional approaches involve the use of continuous bivariate parametric equations for x, y and z coordinates to represent smooth and non-overfolding surfaces. The parametric equations used are usually based on bicubic polynomials for surfaces (Mortenson 1997). Hermite methods produce single patch surface solutions fitting approximately to a target set of points. B-spline methods produce multiple patch piecewise solutions that fit large point sets exactly. Auerbach and Schaeben (1992) used a triangulation as a source of the knots used to create and control quadratic B-splines to exactly represent a geological surface known from irregularly distributed data points. Single-valued surfaces can be mapped in two dimensions or visualised in three dimensions. Three-dimensional visualisations of single-valued surfaces use depth cueing to show the z attribute variation using perspective views and so they have become known as ‘two and a half dimensional’ (or 2.5D) models (McCullagh 1998). However, this kind of visualisation cannot cater for any situation where the phenomenon under investigation encloses space, e.g. in the atmosphere, solid earth or ocean, as is common in environmental applications. Approaches to this problem using two-dimensional representations typically involve the use of ‘stacked’ surfaces in an attempt to handle the occurrence of multiple z values (Siehl et al. 1992). This is usually not a very satisfactory solution since the solid geo-phenomena to be represented are often highly irregular with many occurrences of multiple z values and may even have internal holes. Accordingly, various new forms of three-dimensional geo-representation have been developed to represent this kind of phenomenon.

THREE-DIMENSIONAL GEO-REPRESENTATION Three-dimensional data models require geo-representations capable of capturing the form, structure and properties of the original geo-phenomena (Raper 1989a). In many cases, such geo-representations capture states of a dynamic system, which can be seen as a projection of the geo-phenomena onto three-dimensions. A wide range of computational geometric forms has been developed from algebraic topological forms to provide such tools, which are reviewed below. The issues discussed in this section are: generic solid geometric modelling techniques, the data structures developed for georepresentations, the design of associated databases and the functionality of the developed systems. This review aims to illustrate the scope and limitations of the three-dimensional

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geo-representations available to implement the spatial data modelling of states already discussed. Solid geometric modelling Three-dimensional geo-representation is a branch of solid geometric modelling. In solid geometric modelling all points have x, y and z coordinate values making it possible to model the distribution of form, structure and properties in three dimensions. Research in geographic information science and the geosciences has concentrated on the extension of generic techniques of solid geometric modelling (Mäntylä 1988). This research has been driven by the special challenges of three-dimensional geo-representation, i.e. large data volumes, complex data configurations, uncertain data, the need for interpretive control of the models, attribute linkage and the need for multiple resolution solutions (Houlding 1994). Requicha and Völcker (1983) and Requicha and Rossignac (1992) surveyed generic solid modelling techniques and divided them into three: constructive; boundary; and decomposition approaches. These approaches are explored in turn below and examined for their suitability for use in geo-representation.

Figure 4.7 Parametric solids

‘Constructive’ methods of solid geometric modelling are based on simple ‘primitive’ solids represented using continuous trivariate parametric equations for x, y and z coordinates using Hermite or B-spline methods. Primitive parametric solids (such as a cuboid) are bounded by six patches, which are two-dimensional functional representations (figure 4.7). The three-dimensional morphology of B-spline parametric

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models is controlled by weighting points (poles) and the piecewise solutions are joined by knot vectors at irregular (‘non-uniform’) intervals. B-spline methods use rational functional forms capable of the integrated representation of free form three-dimensional morphology as well as primitive parametric solids. These forms are known as nonuniform rational B-splines (NURBS). Primitive solids can be ‘instanced’ by applying transformation operations to scale their dimensions differentially, by applying constraints to their parameterisation, or they can be created by sweeping a curve or a surface through three-dimensional space. These parametric solids are usually topologically single-celled although multiple-celled solids with holes can be parameterised using ‘group technology’. Within the solid, for any point x, y, z, the ‘isoparametric’ surface is one for which one of the three parametric variables is constant (Mortenson 1997). Primitive ‘instances’ can be combined to make arbitrary shapes using ‘constructive solid geometry’ (CSG) methods, which are based on a series of union, intersection and difference Boolean operations on the original geometric object. Solid geometric models made with CSG methods can be represented as binary trees where the terminating roots are solid geometric models and the non-terminating roots are Boolean operations (Mäntylä 1988). Although CSG methods are fast to compute and always produce valid models, they cannot represent some of the complex morphologies found among geo-phenomena due to the inherent limitations of the underlying parametric approach. ‘Boundary’ approaches to solid geometric modelling are based on the decomposition of the phenomenon to be modelled into faces (two-dimensional planar facets or surfaces), meeting at edges (one-dimensional lines or curves), which join vertices (zerodimensional points) (figure 4.8). Unique faces can be identified by orienting their edges counterclockwise around the face with respect to the facet or surface normal. To be wellformed, ‘boundary representations’ (B-reps) must be closed, orientable, non-self intersecting, bounded and connected topologically. This requires a construction process capable of generating valid B-reps. Applying the constraint that the faces are planar and bounded by vertices joined by straight edges means that the B-rep will be a polyhedron. This is akin to the assumptions of two-dimensional vector geometry in GIS. Simple polyhedra obey Euler’s formula relating the vertices (V), edges (E) and faces (F):

(4.1) The Euler formula can be used to test the validity of the simple polyhedra including the regular polyhedra—the cube, tetrahedron, octagon, dodecahedron and icosahedron (figure 3.1). However, it requires modification for non-simple polyhedra with holes where the faces are topological discs and the edges are arcs. B-rep data structures are usually based on a hierarchical graph listing the vertices, edges and faces and their interrelationships (Boissonnat 1984). If there are internal holes several graphs have to be created and each is contained within a shell such that each shell is made up of closed and connected sets of faces. One of the most widely used approaches to B-rep construction is the three-dimensional triangulated irregular network method where the data points become the vertices of tetrahedra, which fill the convex hull (Fang and Piegl 1995).

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Boundary approaches are suitable for geo-representation since they are conservative, efficient and they adapt to variable data density. However, the models require validation since the data structure does not contain implicit checks as in CSG. The decomposition approach to solid geometric modelling involves breaking down the modelled object into either horizontal slices, prismatic columns, volume primitives such as alpha shapes (Edelsbrunner and Mucke 1994) or regular cubic cells such as voxels (Requicha and Rossignac 1992). Approaches based on voxels are known as spatial occupancy enumeration (SOE) methods as the model consists of attribute records for all the voxels making up a universe. SOE methods have huge data demands: even a 100 by 100 by 100 cubic universe has 1 million voxels. Three methods have been proposed to minimise this overhead: firstly, the reduction of the model to the voxels touching the boundary of the modelled object (3DDT approach); secondly, the indexing and compression of the voxels (octree approach); thirdly, run-length encoding of the voxels. The three-dimensional discrete topology (3DDT) approach was proposed by Kaufman, Cohen and Yagel (1993) as a way to ‘voxelise’ representations. 3DDT algorithms generate a ‘covering’ set of voxels from a parametric or B-rep source through intersection, and then reduce the number of voxels needed to a minimal set. Minimality is defined as a function of voxel adjacency: there are 6 neighbours to a voxel where only a face is shared, 18 neighbours where faces and edges are shared and 26 neighbours where faces, edges and vertices are shared. Hence, 3DDT voxel models can be classified as 6-, 18-or 26- ‘separating’ if they have 3D voxel configurations that satisfy adjacency conditions at one of these three ‘N’ levels of separation. Voxels intersected by the modelled object can be eliminated until a predetermined level of ‘N-separation’ is reached when an ‘N-minimal’ set of voxels is produced. Models made up of such ‘Nminimal’ sets of voxels can be manipulated and visualised effectively due to their relatively low voxel counts. The octree is the three-dimensional equivalent of the quadtree that recursively divides a universe into eight (Samet 1992) (figure 4.9). At each stage the algorithm tests whether any of the eight subdivisions is empty (i.e. outside the object) or full (i.e. inside the object) (Meagher 1982). If they are not either empty or full, i.e. the edge of the object passes through them, then the process of subdivision continues to a predetermined level of resolution. When encoded and compressed by octree methods the model is made up of voxels of different sizes and each voxel is internally homogenous. If the voxel dimensions of the universe are set before octree encloding and the number of voxels along the edges of the universe cannot be divided by eight then extra empty voxels are added as necessary. The subdivision can be recorded using a linear octree encoding where only the leaves of the tree that are part of the modelled object are stored as octal numbers, which allows efficient storage and querying (Gargantini 1982). Carlbom, Chakravarty and Vanderschel (1985) and Carlbom (1987) proposed a modified version of the octree called the polytree that identifies the geometric content of each voxel, i.e. whether full or empty, and whether a vertex, edge or surface cell modelled object. This hybrid voxel/B-rep scheme has the advantage of being a solid geometric representation amenable to rapid Boolean operations for three-dimensional spatial operations, whilst also identifying the geometric content of an individual voxel. Ayala et al. (1985), and Brunet and Navazo (1989) proposed the similar extended octree

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where leaves contained pointers to a unique set of planar half spaces. An attempt to develop a three-dimensional run-length encoding of a voxel universe was made by Bright and Lafflin (1986) but this approach offers less efficient spatial access to the voxels than an octree or polytree. Tamminen and Samet (1984) presented an algorithm for converting from a B-rep to an octree encoded voxel model using a ‘connected components’ labelling approach. Xiao et al (2000) discuss a vectorised octree implementation.

Figure 4.8 A classification of 3D data structures

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Three-dimensional data structures for geo-representation Researchers in GISc and the geosciences have extended and applied the methods of solid geometric modelling for the purposes of three-dimensional geo-representation. The choice of a data structure should be part of a holistic process of conceptualisation, data capture, sampling and data structuring which is recursively updated depending on the aims of the geo-representation (Raper 1989b). Jones (1989) surveyed the threedimensional data structures available for geo-representation at an early stage of their development and assessed their potential for geological applications. Fried and Leonard (1990), and Jones and Leonard (1990) reviewed three-dimensional modelling in the petroleum exploration industry, while Pflug and Bitzer (1990) and Pflug and Harbaugh (1991) collected together work by geoscientists on geo-representation in geological reconstruction and simulation.

Figure 4.9 Octree encoding (from Lattuada 1998)

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Turner (1992) presented an overview of the representational problems for a wide range of geo-phenomena, evaluated the data structures developed in CAD and image processing and gave examples of new geo-representation approaches. Vinken (1992) surveyed a wide range of approaches to the digitisation of the geological mapping process, including several early approaches to geo-representation. Moulding (1994) focussed on the process of geological characterisation and the role of geo-representation in these procedures. Ozmutlu (1997) collected together work on geological characterisation, georepresentation, simulation and the creation of virtual environments for geosciences. Schmidt and Götze (1998) summarised the requirements of geophysics for threedimensional solid modelling. In this section data structures specifically developed for geo-representation will be (re)surveyed (cf. Raper and Kelk 1991) to evaluate the performance of the implemented systems in parametric, B-rep, voxel and hybrid categories. Parametric approaches Much of the work on constructive parametric approaches to geo-representation has focussed on the use of NURBS since their piecewise nature allows the construction of surfaces with multiple values of the z coordinate (Tipper 1977). Kelk and Challen (1992) used the Intergraph Engineering Modelling System (EMS) to fit NURBS-based parametric surfaces to construction lines drawn in three dimensions in order to represent geological surfaces. Fisher and Wales (1992) used the same package to model oil reservoir morphology by joining the top and bottom surfaces to create quasi-solid geometric models. While transformations and analyses using NURBS are rapid and efficient, as a representation it enforces a continuity of curvature between modelled data points. This is an acceptable assumption for many, but not all, applications of georepresentation, as Mallet (1992) has noted. By contrast, Saksa (1995) developed the Rock-CAD system based on the Medusa 3D GIS, which uses quadratic polynomial parametric methods to define the facets of polyhedra constrained by the data points. These polyhedra can be combined using Boolean operations to form complex models. Flick (1996) developed a three-dimensional urban modelling system by integrating the ACIS parametric volume models with the Open GL visualisation environment and converting the parametric surfaces to polygonal facets. Kriegl and Seidl (1998) developed a method to search databases of surfaces and solids in point form by comparing parametric approximations of surfaces and ellipsoids to the point set records in the database. B-rep approaches By contrast, B-reps have been widely used and further developed for geo-representation. In algebraic topology a B-rep can be constructed from arbitrary geometry, i.e. any zero-, one-, two- or three-dimensional geometric component that is embedded in a threedimensional space (Burns 1988). Pigot (1992) outlined the theoretical background to three-dimensional geo-representation using cell complexes showing how geometric realisations are dependent for their validity and indexing on topological definitions of

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orientability, connectivity and identification. Pigot (1992) shows how the use of specific topological definitions will constrain the assumptions that need to be made about threedimensional geometric relationships when designing solid geometric data structures for geo-representation. Although cell complexes are more general and more flexible, they are also more difficult to create and maintain when developing data structures. Hence, most data structures for geo-representation based on B-reps have employed the simpler topological concept of the simplex rather than the cell. A 0-simplex is equivalent to a point, 1-simplex to a line segment, 2-simplex to a triangle and 3-simplex to a tetrahedron volume (Carlson and Frank 1987) (figure 4.10). From these primitives many higher order geometric constructs such as grids (constructed from equilateral triangle pairs) and polyhedra can be formed.

Figure 4.10 Zero-, one-, two- and three-dimensional simplices

A number of researchers have developed systems to implement three-dimensional data structures based on B-reps. Houlding and Stoakes (1990) and Houlding (1992, 1994) outlined a method of three-dimensional modelling using ‘volumetric components’ that has been used in the 3D GIS ‘Lynx’. Prismatic volumetric components are created by using the edges of a geometric object outlined on two-dimensional vertical cross sections. The outlined shape on each cross section is projected onto a central ‘mid plane’ where the (inevitably) different shapes are reconciled using a best-fit approach. The result is a polyhedron bounded by the cross sections, which can then be joined with other polyhedra. Lynx allows the creation of a voxel model from the three-dimensional components identified which is oriented at any angle appropriate to the structure of the geometric object (Orlic and Rösingh 1995). Ganter (1989) outlined a prototype system for triangulating serial cross sections across caves. Sides (1992) developed a Geological Discontinuity Modelling System (GDMS) for mining applications that allowed the creation of intersecting multi-valued triangulated surfaces with fault and fault-set handling. Kraak and Verbree (1992) show how terrain models can be ‘tetrahedronised’ from a base triangulation. Pilouk (1996) developed a tetrahedral network (TEN) data structure based on simplices that was implemented in the Integrated Simplicial Network Application Package (ISNAP). At the data structure level the mesh is the most generic form of geometric construct, as meshes can be subdivided into structured (finite difference grids) and unstructured (finite element triangulation) forms. Lattuada (1998) argues that the easy computational access

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to structured finite difference grid meshes is outweighed by the flexibility and expressiveness that can be achieved using unstructured finite element meshes. However, data structures for three-dimensional unstructured meshes based on simplices require the elimination of ambiguities and the storage of explicit topological information. Gable, Trease and Cherry (1996) described the ‘Geomesh’ modelling system that imports valid and connected three-dimensional parametric models, triangulations or grids and creates an unstructured tetrahedral mesh from it. Geomesh contains a variety of mesh editing, checking and refinement tools to pre-process three-dimensional data before its use in finite element modelling. Building on work by Tsai and Vonderohe (1991) on the triangulation of an Euclidean space to n dimensions, Lattuada (1998) used the Bowyer-Watson triangulation algorithm to create an unambiguous three-dimensional unstructured mesh based on tetrahedra. Lattuada prevents three-dimensional point degeneracies by including points in a tetrahedron that actually lie on the boundary of the circumsphere, or by shifting the point location very slightly to force the point into the mesh. These heuristics force the creation of valid three-dimensional tetrahedra (unlike the two-dimensional case where no unique set exists), although subdivision of the original tetrahedra may be desirable to remove any very long, thin forms (figure 4.11). Lattuada allows the addition of constraints to the tetrahedralisation and indexes the tetrahedra using an octree-like N-tree that is capable of dynamic update. Lattuada and Raper (1995) show how this approach can be used to model coastal landforms from borehole data while Lattuada and Raper (1998) focussed on the problems of salt dome modelling with seismic data.

Figure 4.11 Three-dimensional tetahedronisations are not unique (from Lattuada 1998)

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Mallet (1992) outlines an alternative form of three-dimensional geo-representation using B-reps as employed by the ‘GOCAD’ system. Starting from one or more surfaces in TIN form, GOCAD adds additional points to those in the original dataset in such a way as to minimise local roughness using the Discrete Surface Interpolation (DSI) algorithm. The triangulated surface created by DSI can then be densified, if necessary, to allow the path of a fault to be entered into the data structure. The surface can also be modified by manipulating the free nodes interactively or by the use of defined vectorial constraints. The volumes between the surfaces can be filled with tetrahedra by GOCAD to create a true solid geometric model (Mallet 1999). Conreaux, Lévy and Mallet (1998) show that topologically degenerate configurations can be handled computationally, without resorting to heuristics, by using the n-dimensional combinatorial maps of Lienhardt (1994) to decompose cells provably correctly. When three-dimensional B-rep solid models are constructed from simplices or polyhedra they must be indexed for effective use. Early work on three-dimensional data structures for geo-representation was based on the concepts used in two-dimensional vector GIS. Fritsch (1990) developed a hybrid 2.5D/3D data structure in which ‘terrain’ (x,y) and ‘situation’ (z) were indexed separately and then integrated. Molenaar (1990) developed a three-dimensional solid object-oriented data structure based on four classes of element, viz. point, line, surface and body, which are instantiated respectively by node, arc, edge and face geometry. Molenaar (1990) identified twelve conventions through which the integrity of geometry in a database could be guaranteed by eliminating degenerate configurations. These included the constraints that the geometric elements be topologically simple (non-intersecting with no islands), that they be planar and that the bodies created be disjoint. Pilouk (1996) extended the Molenaar (1990) model to include multi-theme solid models using ‘sub-bodies’. Trott and Greasley (1999) described a three-dimensional data structure for the Vector Product Format (VPF) which is fully integrated with topological vector GIS data structures. The ‘Arcview 3D Analyst’ GIS module supports three-dimensional geometric objects in a GIS database alongside singlevalued grids and TINs. Recent work (post 1995) on three-dimensional data structures for geo-representation has employed object-oriented concepts from virtual reality environments such as ‘World Toolkit/WorldUp’ from Sense 8. In these systems, and in the generic virtual reality modelling language (VRML) derived from the Open Inventor format from Silicon Graphics, data structures are based upon the scene graph (see chapter 5). The scene graph approach used in VRML has become a standard way to create a three-dimensional solid model using either B-rep or voxel geometry (Raper, McCarthy and Williams 1998). The surfaces and solids of a VRML model can be draped with appropriate imagery to create a highly realistic representation (Flick and Coors 1998). Three-dimensional models based on the scene graph include urban GIS (Köninger and Bartel 1998) and environmental planning (Verbree et al. 1999). Gong, Lin and Lin (2000) developed a system called Cave3D in which cave solid models were constructed from TINs of surface, ceiling and interior objects and then integrated in a VRML model. However, the creation of a virtual geo-representation made up of surfaces or solids draped with map data or imagery in VRML format requires a particularly large number of shaded triangular facets to represent them. Level of detail (LOD) algorithms have been

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developed so that only those objects near to the user’s current viewing position are displayed using enough triangular facets to give a high resolution effect (Muxaxo, Neves and Camara 1999). It is also possible to reduce the number of triangles used to form the surface or solid models by using filtering techniques. These techniques reduce the number of triangles making up the surface or solid by amalgamating them when the angles subtended vertically between adjacent triangles are small. The large data volumes in surface and solid models can also be handled more effectively by using multiresolution storage schemes. De Floriani (1989) described the Delauney Pyramid approach in which the elements of the TIN of each different resolution were stored hierarchically without duplication. Ware and Jones (1997) developed a multi-resolution data structure for models of intersecting surfaces in which the elements of the TIN representing each resolution were stored in relational tables and indexed using a quadtree. Voxel approaches Some of the earliest approaches to geo-representation were based on voxel representations. These early systems stored the voxels as three-dimensional layer-and row-ordered rasters, with each voxel and associated attribute values, stored explicitly. These models were primarily built for hydrocarbon exploration and reservoir management, for example by Shell (the MONARCH system, Bryant, Paarkedam and Davies 1991) and by Exxon (the GEOSET system, Jones 1988). Voxel models are useful in this application domain as three-dimensional data is collected in both seismic reflection time and borehole depth formats. These datasets are easy to reconcile in voxel format by resampling, especially where seismic reflectors require three-dimensional migration to remove reflections drawn from outside the nominal x, z plane of the seismic cross section (Brown 1991). However, despite the advances in computing power allowing the manipulation of higher numbers of voxels, it has proved necessary to employ octree encoding methods to compress and index voxels for the best performance in large models. Kavouras (1987, 1992) developed an octree encoding system for georepresentation called ‘Daedalus’, which constructed solid models from B-reps sources. Daedalus was implemented within the CARIS GIS, which acted as a source of surface and solid data and as a storage location for linear octree codes. Bak and Mill (1989) and Bak (1991) developed a Geoscientific Resource Management System (GRMS) which converted B-reps into using octree-encoded voxels. The GRMS was used in the reconstruction of mine infrastructure and ore bodies with seven level octrees. The GRMS offered three-dimensional querying capabilities by search window, by object surface intersection and by connectivity, all of which demonstrated much higher performance than comparable B-rep models. In most cases octree encoded voxel models have only represented the solid geometry of a single geo-phenomenon. Prissang et al. (1996) developed the linear octree based ‘Property Management System’ (PMS) to encode and index voxel models that were produced by converting B-rep component models from the Lynx system into a raster form (Bak 1991). However, PMS creates a geometry octree for the geometry of the threedimensional domain and further attribute octrees for each of the geometric objects with distinct attributes. Each of these octrees can be compared by traversing the tree through

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the same path in order to perform attribute queries on the geometry octree. The primary disadvantage of voxel modelling is the fixed cuboid shape of the voxels. The ‘Stratamodel’ system aims to model geological structures and their internal variation with voxels whose x, y shape remains grid-shaped but whose z thickness can be varied. The Stratamodel ‘geocellular’ approach builds models by creating geological units from top and bottom surfaces and then warping, truncating and cutting them to mimic the shape of the investigated geo-phenomenon while retaining the grid framework. The finished geocellular model is made up of multiple geological units fused together into a single voxel framework such that each grid cell on the model surface is the top of a column of variable thickness voxels. The Intergraph ‘Voxel Analyst’ can form models using hexahedral voxels. Hybrid approaches Some approaches to geo-representation employ hybrid generation techniques involving the conversion of one data structure to another. This approach can make it easier to produce a validated three-dimensional model. Two approaches are discussed, one that converts from a B-rep to a voxel reprepresentation (Lynx) and the other that converts from a grid to a B-rep (Earthvision). Houlding (1994) shows how the B-rep components created by the Lynx system can be converted to a voxel-based representation by intersection with a three-dimensional grid. Each voxel produced by the intersection is normally assigned the attribute of the geometric object at the voxel centre. If the voxel produced is heterogeneous in composition Lynx can produce a volume-weighted average. Where the aim is to produce a set of voxels with estimated values for a continuously varying geo-phenomenon, a three-dimensional interpolator can be used. The simplest approach to the estimation of voxel values is the use of a spherical search volume, with a linear distance weighting of the qualifying sample values. Houlding (1994) shows how a three-dimensional point kriging approach can be used by scaling the search volume to the range of the x, y and z semivariograms. Three-dimensional volume kriging takes account of the volume of the voxel where the voxels are variably sized or scaled, allowing the calculation of the average voxel value. Smith and Paradis (1989) outlined a minimun tension approach to creating georepresentations from points with numerical attributes that are scattered in threedimensional space. Earthvision begins by calculating values for a coarse three dimensional grid of voxels and then fits multivalued bicubic spline surfaces to the grid for user-specified attribute values of the attributes. The system then proceeds iteratively, comparing the values of the three-dimensional grid with scattered data values so that new surfaces can be computed with progressively lower differences between the grid values and the closest scattered data values. This ‘minimum tension with scattered data feedback’ approach outputs a three-dimensional grid and a set of parametric surfaces each corresponding to a particular attribute level. The resultant attribute ‘isosurfaces’ are converted to B-reps for display and clipped by structural constraints such as faults where necessary. Eddy and Looney (1993) evaluated the results of Earthvision interpolation procedures against input parameters such as voxel size and the variation in shape of the

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search zone used in the three-dimensional interpolation showing significant variations in output. Databases for geo-representations Despite the wide range of geo-representations developed, few database designs have been produced for three-dimensional solid modelling. There are two main reasons for this: many geo-representations are only made to reconstruct the three-dimensional form of a sampling-limited geo-phenomena, and, the challenges of developing integrated threedimensional data structures for geometric and non-geometric data are considerable. Yet, such database designs are important to the further development of geo-representations. A database approach to representation brings all the advantages of security and integrity of data as well as support for the management of model versions, multiresolution representation and query-based model decomposition. Approaches to database design for three-dimensional geo-representation are constrained by the semantics of the available data models for databases, i.e. relational or object-oriented. Meier (1986) first outlined the potential of relational databases for the storage of three-dimensional models in parametric and B-rep forms. Meier noted that although relational databases can store geometric data in normalised tables using geometric identifiers as keys to relations, a greater expressiveness can be obtained by adding ‘part-of and ‘is-a’ relationships to the relational model. Such relationships require spatial extensions to Structured Query Language (SQL) permitting the storage of nonatomic, non alphanumeric geometric data types and their retrieval through ‘part-of’ and ‘is-a’ associations (Bundock and Raper 1992). However, such extensions to the relational model are known to reduce the performance of querying operations as they cannot be optimised (Egenhofer 1992). By contrast, object-oriented techniques allow the database designer to define data types and associated operators together, making for great expressiveness but often introducing complex design and querying. These considerations mark out three design options for the databasing of threedimensional geo-representations: • Store geometric and non-geometric information in standard relational tables using relational joins and SQL queries to compose solid models; • Store geometric information in extended relational tables using spatial data types and non-geometric information in standard relational tables, and use extended SQL to compose solid models; • Store geometric and non-geometric information in an object-oriented database and use their associated operators to compose solid objects and to define interaction rules. While most of the database approaches have employed B-rep geo-representations, Kavouras (1987) showed how the Daedalus voxel model could be linked to associated attribute tables through a voxel indexing scheme. The first of these three approaches was implemented by Molenaar (1990) as part of a formal data structure for three-dimensional geo-representation. Rikkers, Molenaar and Stuiver (1994) show how node, arc, edge and face geometry and associated topological relationships can be stored in tables so that point, line, surface and body objects can be

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instantiated topologically. By using standard SQL queries, solids can be composed and topological queries can be answered. This approach is an implementation for threedimensions of the geo-relational model that is common in two-dimensions. Note that this approach requires the acceptance of planar enforcement as an organising principle, i.e. all surfaces and bodies are closed, connected and non-overlapping. Pilouk (1996) extended this approach in the Simplicial Network Integrated Database (SNIDB) where zero-, one-, two- and three-dimensional simplices were stored in relational tables. The second, extended-relational approach was implemented by Waterfeld and Schek (1992) for the DASDBS Geokernal. The Geokernal data model stored three-dimensional B-rep geometric elements as abstract data types in relational tables and supported the creation of complex solid models by composition. The Geokernal also implemented a cell index to the items of B-rep geometry in the database so that the geometric data could be clustered spatially on disk for query optimisation. The third object-oriented approach to three-dimensional geo-representation was implemented by Breunig, Bode and Cremers (1994) who developed the Object Management System (OMS). OMS consisted of an Object Manager and Type Manager to store and manage zero-, one-, two- and three-dimensional simplices as object types. To optimise geometric operations, OMS formed two- and three-dimensional complex objects (called as e3- and e2-complexes) from aggregations of simplices, whose coordinates were encapsulated with their bounding box. This design was elaborated with the development of ‘Geostore’ (Balovnev, Breunig and Cremers 1997) within the object-oriented DBMS Objectstore. Geostore was developed in order to reconstruct the evolution of large geological structures from cross sections with interpreted strata and fault surfaces (Alms et al. 1998). Since this problem involves four-dimensional reconstruction, Geostore allowed the user to browse the model by logical structure or through a three-dimensional viewer. Balovnev, Breunig and Cremers (1997) generalised the object-oriented architecture of Geostore by developing a class library for three- and four-dimensional solid modelling called ‘GeoToolKit’. The GeoToolKit class library supports simplices, complexes (curves, surfaces, solids), compound objects, and analytical objects (line, plane) and allows the user to specify their own types. These objects make up a ‘space’ which is indexed using an R-tree (for geometric data only) or LSD tree (for both geometric and attribute data). In GeoToolKit objects can change their representation without changing their object identifier, making it possible to support multiple representations. The indexes provide a multidimensional key into the data, facilitating the exploration of spatiotemporal behaviour. Köninger and Bartel (1998) used the object-oriented database Postgres95 to store the Open Inventor classes representing the three-dimensional urban form. The database is indexed using an R-tree and the geometry is organised into three ‘level of detail’ nodes. Balovnev et al. (1998) developed a CORBA-based data and systems integration environment for the GOCAD and IGMAS modelling systems. Three-dimensional spatial query and analysis As the three-dimensional modelling workflow extends beyond capture and visualisation

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into structured storage, so the scope for spatial query and analysis has increased. This is so since data structures can make some operations trivial (Raper 1989b). Ideally the conceptualisation of the geo-phenomenon should drive the choice of geo-representation in order to achieve the objectives of the exercise. Achieving this kind of closure between conceptualisation and representation should become more common as users become liberated from the constraints of data formats through standardisation efforts such as Open GIS. Selecting a representation based on the performance of spatial query and analysis presupposes some knowledge of typical outcomes. Raper (1990) proposed a nonmaximal generic set of spatial query and analysis functions for three-dimensional modelling for which typical outcomes could be predicted. The six categories of functions in Raper (1990) included visualisation manipulation, transformation, selection (by intersection), inter-relationship characterisation, geometric characterisation, and modelling functions. Their notional performance when structured using voxel and B-rep representations is set out in table 4.2 and is illustrated in figure 4.12.

Table 4.2 Generic spatial query and analysis functions in three-dimensional modelling and their effectiveness under different data structures

SPATIAL FUNCTION

VOXEL

B-REP

Translate

fast

fast

Rotate

fast

fast

Scale

slow

fast

fast

fast

slow

fast

AND

fast

slow

OR

fast

slow

XOR

fast

slow

NOT

fast

slow

Metric

fast

fast

Topological

fast

slow

Volume

fast

slow

Surface area

fast

fast

Visualisation

Reflect Transformation Shear Selection

Inter-relationships

Characterisation

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159 fast

slow

slow

fast

fast

slow

Modelling Build

Some of these query and analysis functions have proved difficult to implement in any of the available data structures. One challenging task has been the development of threedimensional topological inter-relationships such as shortest path analysis. Kirkby, Pollitt and Eklund (1996) implemented a modified version of the Dijkstra (1959) shortest path algorithm in the ‘Vulcan’ 3D GIS, in which the gradient over a 2.5D surface was added into the computation. Scott (1994) implemented a shortest path algorithm for an unindexed three-dimensional voxel space using a cumulative distance cost approach. This approach produces a set of voxels that each contain an attribute with the cost of travelling to that voxel from a specified start point, if there is a uniform friction of movement throughout the representation. The three-dimensional pushbroom shortest-path algorithm moves through the ‘cost volume’ along the steepest cost slope from target to origin using a 3 by 3 by 3 search kernal. Kim, Lee and Lee (1998) implemented three-dimensional buffering and line of sight (or ‘lantern’) algorithms for solid geo-representations in VRML form. Three-dimensional buffering was carried out using a spherical extrusion function to surround the target object. The ‘lantern’ operation involves intersecting all geometric objects falling inside a cone with a specified azimuth, opening angle and length. The use of three-dimensional query and analysis functions creates a new feedback loop in the modelling workflow as the results of the queries/analyses may optionally be stored as new geometric objects within the database. This possibility raises the question of how appropriate metadata on the original and derived geometries should be stored. Livingstone and Raper (1999), and Duane, Livingstone and Kidd (2000) propose the use of the Hierarchical Data Format (HDF) as a means to store self-describing georepresentational datasets.

MULTIDIMENSIONAL GEO-REPRESENTATION Most of the geo-phenomena we seek to represent have spatio-temporal identities, and as such they demand multidimensional geo-representations capable of expressing behaviour through time. Since spatio-temporal identity involves temporal extension, appropriate multidimensional geo-representations require both spatial and temporal referencing. Multidimensional geo-representations with temporal referencing can be divided into the ‘spatio-temporal’ (two dimensions of space plus one of time) and the ‘four dimensional’ (three dimensions of space plus one of time). Spatio-temporal georepresentations can express temporal behaviour when projected from four dimensions to two spatial plus one temporal. A number of temporal GIS designs have been proposed and implemented, and are reviewed below. Four-dimensional geo-representations can

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express the full multidimensional character of the world: a few four-dimensional GIS and process modelling systems have been designed and implemented and are discussed below and in chapter 10. Some of these four-dimensional systems are capable of the implementation of the process modelling already discussed. The geo-representations available to implement multidimensional conceptualisations are discussed below. This section will review the foundations of spatio-temporal knowledge representation, the approaches to temporal GIS, object-oriented spatiotemporal GIS, the applications of time geography, the development of four dimensional GIS and multidimensional geo-representation. With the exception of temporal GIS, the relative lack of development in this field offers new scope for research into multidimensional geographical information science.

Figure 4.12 A taxonomy of three-dimensional spatial functions

SPATIO-TEMPORAL KNOWLEDGE REPRESENTATION A wide range of spatial knowledge representations based on two-dimensional ontologies have been developed from cognitive analyses and from a priori schemes (see chapter 2). However, these two-dimensional ontologies explicitly excluded time, seeing it as conceptually distinct from space and unnecessary in spatial knowledge representations. Langran (1988, 1992) was among the first to explore spatio-temporal knowledge representation, defining the concept of ‘dimensional dominance’ to describe how spatiotemporal information is usually dominated in display and query terms by either the space or time dimension. This situation is a function of the fact that uses of spatio-temporal

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information tend towards interest in space as an ordering (maps) or time as an ordering (case histories) rather than both. However, spatio-temporal knowledge representations need to express a unified spatial and temporal approach. There have been far fewer attempts to define spatio-temporal knowledge representations, as there are correspondingly fewer spatio-temporal ontologies available. Possible spatio-temporal ontologies divide into those based on absolute time and space and those based on relative time and space (Wachowicz 1999). Ontologies are defined by the spatial and temporal boundaries of events in the absolute approaches, and by the relationships between the geo-phenomena in the relative ones. These alternatives mark out different approaches to the definition of identity, and, therefore, different approaches to change. Peuquet (1994) proposed the TRIAD scheme where all geo-phenomena are defined by attribute, spatial and temporal references (‘what, where, when’) to form a ‘world history model’. This is an absolute time and space view that is equivalent to the ontological argument of attribute ‘bundles’. By contrast, Roshannejad and Kainz (1995) argued that while all multidimensional geo-phenomena need to be referenced by what, where, when information, object identity must be independent of referencing. This is a relative time and space view that is equivalent to the ontological argument of ‘essences’. In a formal approach to spatio-temporal knowledge representation, Claramunt and Thériault (1996) presented a typology of spatio-temporal processes from an absolute time and space perspective, based on the TRIAD scheme of Peuquet (1994). Claramunt and Thériault argue that there are three main types of spatio-temporal processes: the evolution of a single entity such as changes, transformations and movements; the functional relationships among multiple entities such as replacement and diffusion; and, the evolution of spatial structures involving several entities. On the basis of this typology they introduce an Event Pattern Language (EPL) which can describe the spatio-temporal evolution of a set of objects in terms of processes and operators. Although this is a useful and expressive formalism it cannot handle non-discrete geo-phenomena or gradual object identity change. The semantics of Claramunt and Thériault have recently been extended by Shu, Chen and Gold (2000). Hornsby and Egenhofer (2000) presented a formal scheme for spatio-temporal knowledge representation, based on possible changes to geo-phenomena, modelled as discrete objects at a high level of abstraction. In the Hornsby and Egenhofer (2000) Change Description Language (CDL), objects can be in the following states: existing; not existing with no history of a previous existence; or, not existing but with a history of previous existence. Changes from one state to another are defined as ‘transitions’, which in total allows nine combinations: continue existence without history; create; recall; destroy; continue existence; eliminate; forget; reincarnate; and continue non-existence with history. This scheme is an axiomatic system for the exploration of change semantics that produces a classification of the changes to an object identity defined in this way. The constitutive nature of ‘transitions’ (object inter-relationships) in the scheme implies that this approach is a relative time and space view. An alternative conceptualisation of change might be based on a psychological concept of ‘difference’ that is independent of referencing and representation. The set of all possible forms of change defined as difference, with the human construction placed on these scenarios is:

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• Same place, same geo-phenomena, different time (progression of geo-phenomena) • Different place, same geo-phenomena, different time (geo-phenomena that have moved) • Same place, different geo-phenomena, different time (monitoring place) • Different place, different geo-phenomena, different time (elsewhere) • Same place, same geo-phenomena, same time (real time feedback) • Different place, same geo-phenomena, same time (contemporaneous monitoring). This schema classifies difference, and, by implication the scope of multidimensional identity. Temporal GIS Temporal GIS are systems for representing the temporal behaviour of geo-phenomena when they have been projected from four dimensions to two spatial plus one temporal. Early approaches were based on the extension of commercial two-dimensional GIS to handle time with the attributes, which Langran (1992) classified into three types: sequent ‘snapshots’; ‘base state with amendments’; and, ‘space-time composites’. These designs mirrored the early approaches to developing temporal relational databases to handle change in the stored entities (Snodgrass 1992). Here, ‘snapshots’ are equivalent to the addition of new tables to the database; ‘base state with amendments’ is equivalent to the addition of tuples to a table; and ‘space-time composites’ are the equivalent of adding new items to an attribute. Snodgrass (1995) developed a temporal version of SQL TSQL2 to support temporal queries in relational databases, but this has not been widely adopted pending progress on the ISO standard SQL/MM. In both GIS and relational database, Langran (1992) showed that the creation of temporal ‘versions’ at relation, record or attribute level leads to unacceptable extra data volume and violations of integrity in the tables. Violating integrity rules, for example, by adding extra items to an attribute, meant that the standard query tools would not give valid results, requiring further potentially non-standard extensions to the system. Several alternative theoretical schemes for spatio-temporal data storage and access using GIS were evaluated by Langran (1992). These ranged from the insertion of objects into a versioned grid index (which expanded the number of objects unacceptably) to approaches using versioned map partitions based on R-tree indexing (which reduced the efficiency of searches due to the overlapping partitions). Xu, Han and Lu (1990) showed how to extend the R-tree to handle changing spatio-temporal data by adding nodes to the tree as change occurs to the spatial objects. Abraham and Roddick (1999) have surveyed and synthesised work in this area. Subsequent innovations in temporal GIS involved further extensions to geo-relational GIS designs. Raafat, Yang and Gauthier (1994) proposed a system in which temporal behaviour leading to changes is stored by the addition of tuples in the database. However, unlike the earlier users of this technique they propose a two-tier system in which only a master relation has the ‘essential property’ attribute conferring identity on an entity, while ‘slave’ relations contain all other data. This allows the temporal change to be stored as additional tuples at the level of entity identity, without expansion in all other tables— except where new geometric data is required to create the new spatial configuration. Although data volumes do increase, the system supports temporal queries on vector

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geometric entities using standard SQL and no extensions to the relational model are needed. Peuquet and Duan (1995) proposed an event-based approach to temporal change in raster geometric maps called the Event-based Spatio-Temporal Data Model (ESDTM). In ESDTM temporal behaviour is stored by recording changes to an initial raster map in an event list in the form of a sets of changed raster grid cells. In a more sophisticated design, Peuquet and Qian (1996) used the TRIAD scheme to define the TEMPEST temporal GIS in which all changes to the stored spatial entities are referenced to a set of unequal ordered temporal intervals. To capture the semantics of the change TEMPEST stored change to the extent and type of objects in a feature view, the times and locations that had changed in a time view, and the changes at-a-location in a location view. Mennis, Peuquet and Qian (2000) have developed the Pyramid scheme to add the semantics of object identity to TRIAD. These GIS-based or GIS-like approaches to storing temporal behaviour are really only suitable for a coarse temporal granularity of change which takes place in discrete ways, for example, changes in ownership or dimensions of an urban land parcel. In environmental applications highly dynamic phenomena change at a fine temporal resolution (minutes to weeks) in a continuous way, for example, in the seasonal migration patterns of animals or the hourly change of the tides in the coastal zone. Morris, Hill and Moore (1999) outline the Water Information System database design of the Spatio-Time Environmental Mapper (STEM), which uses a relational database to store what, where, when information in an optimised record-versioned data model. Recently, Yuan (1999) has argued that what temporal GIS have lacked is a means to handle spatio-temporal identity through semantic links between spatial and temporal information. She presents a three-domain model in which snapshot, space-time composite and spatio-temporal object approaches are fused by linking the storage of data in the semantic, temporal and spatial domains. The three-domain model allows efficient entitybased and location-based queries by storing the semantic associations and temporal transitions in a ‘space graph’ that indexes all the stored discrete spatio-temporal entities. In effect, the georelational implementation Yuan presents is a normalisation of the snapshot, space-time composite and spatio-temporal object models. Object-oriented spatio-temporal GIS In a search for more flexible and expressive forms of geo-representation to handle temporal change, a number of authors have developed object-oriented spatio-temporal GIS. The key design issue in object-oriented approaches to handling spatio-temporal behaviour is how to structure the object classes and attributes to handle temporal change, when projected from four dimensions to two spatial plus one temporal. This in turn depends on the temporal and spatial ontologies that are to be used, and in the case of time, whether the time used will be world time (valid time), database time (transaction time) or both together (Worboys 1998b). In the ‘absolute space and time’ approach objects are made within a space and time referencing system, and are bounded by events (ontologically, an ‘endurantist’ approach). ‘Events’ are defined as ‘instants in time’ when objects were extended in the third

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dimension in proportion to their temporal duration to create spatio-temporal (ST-) objects with individual identities. ST-objects can be decomposed into right prisms bounded by spatial boundaries and temporal events, called ST-atoms, each with its own identity. Worboys (1992) suggested ST-atoms could be implemented using zero-, one- and twodimensional simplices. Spatio-temporal queries could be evaluated by exploring the space-time intersections of ST-atoms. Yeh and de Cambray (1996) proposed a similar approach to spatio-temporal representation called the Behavioural Time Sequence (BTS) in which a three-dimensional B-rep scheme is used to represent temporal change of two-dimensional vector geometric objects. The BTS system can handle the gradual and discrete evolution of objects through time, as the change is defined using behavioural functions. Wachowicz and Healey (1994) suggested a design in which ‘events affecting objects’ created ‘versioned objects’ such that new and temporally different versions of an object would exist on either side of an event. This approach to spatio-temporal representation was implemented in the SpatioTemporal Data Model (STDM) approach of Wachowicz (1999), developed for the mapping of public boundaries. Ultimately spatio-temporal identity is a function of the boundary/event bounding. In the ‘relative space and time’ approach time is a property of the objects. Space-time is made of objects with a spatial and temporal extent, and where there are no spatiotemporal objects there is no space or time (ontologically, a ‘perdurantist’ approach). In most ‘relative space and time’ systems using object-oriented techniques, the objects are time stamped to create temporal versions of the original object. Kemp and Kowalczyk (1994) used the ‘Zenith’ object management system to develop a spatio-temporal data store capable of storing ‘has_version’ relationships for geometric objects. Events, therefore, do not force any change in the identity of the object or instance. Kemp and Kowalczyk point out that it is possible to divide attributes between levels in the object class hierarchy such that the time invariant attributes are stored at a higher level than the time variant attributes. The key question of implementation concerns the appropriate identity criterion to use, since all the attributes of an object may eventually change. Ramachandran, McLeod and Dowers (1994) proposed a design called TCObject in which objects with geometric and non-geometric attributes are given past, present and future states: the temporal reference is established using dates of birth and death for the object. In a similar approach, Hamre (1994) proposes a design based upon OMT (Rumbaugh et al. 1991) where a ‘four-dimensional dataset’ object is composed of a spatio-temporal component (including a ‘time of creation’ temporal reference) and a nonspatiotemporal component. Voigtmann, Becker and Hinrichs (1996) develop a timestamped attribute approach by extending their Object-Oriented Geodata Model (OOGDM) to form the T/OOGDM that can be queried using the T/OOGQL query language. El-Geresy and Jones (2000) have presented a typology of spatio-temporal representational architectures and the queries they can each support. They distinguish three state-oriented spatio-temporal models: the ‘where’ view of changes at a location (e.g. the Langran 1992 raster change model), the ‘what’ view of changes to objects (e.g. Raafat, Yang and Gauthier 1994), and the ‘snapshot’ view of change (e.g. Peuquet and Qian 1996). They recognise three change-oriented spatio-temporal models: the ‘when’

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view of temporal relations between events (e.g. Peuquet and Duan 1995), the integrated event view of changes in location, object and sequence, and the ‘space composite’ view in which relations between successive states are recorded in a single geometric layer. ElGeresy and Jones (2000) argue that these event and change models are limited by their descriptive capacities: new advanced models of change are now focussing on process (the ‘how’ view) and causality (the ‘why’ view). Chen and Molenaar (1998) have developed a model of spatio-temporal change motivated by coastal geomorphological applications, which is focussed on process. In their ‘star’ model they link views of attributes, location, sequence, object and process in a single integrated approach to representing change. The processes that they define viz. shift, appear, disappear, split, merge, expand and shrink can be compared to those put forward by Claramunt and Theriault (1996) and Hornsby and Egenhofer (2000), although they are less formally based. Allen, Edwards and Bédard (1995) presented a model of change driven by causal relations among objects, based on the Bunge (1966) model of causality. In the Allen, Edwards and Bédard model, causal chains originate with intentional or non-intentional agents, which precipitate a cascade of events that change the state of objects. This model facilitates the tracing of causes and effects in time and space, at least insofar as the causal chain is well founded. Research on spatio-temporal geo-representation is now focussed on the modelling of change rather than events. Hence, Tryfona and Jensen (1999) present a Spatio-Temporal Entity-Relationship (STER) model based on an ontology of entities in motion (e.g. a car) and discrete change in entities (e.g. land parcels). The STER model adds spatial, temporal and spatio-temporal modelling constructs to the Entity-relationship model of Chen (1976). Renolen (2000) reviews the alternative conceptual modelling frameworks for spatio-temporal information system design. These include the structural perspective of entity-relationship modelling, the functional perspective of data flow diagrams, the behavioural perspective of statecharts, rule-based approaches, object-oriented designs, action-workflow diagrams and agent models. Erwig et al. (1999) introduce ‘moving data types’ into a spatio-temporal database design using a many sorted algebra approach. Time geography Another context within which spatio-temporal geo-representation has been developed is ‘time geography’, which is the study of the spatio-temporal behaviour of individuals. The origins of time geography can be traced to Hägerstrand’s (1968) work on migration, but it was codified and developed by Pred (1977). Parkes and Thrift (1980) set time geography in the context of social studies of place and time. Time geography is concerned with the space-time paths marked out by individuals, and the problem of how such paths both create and constrain the fabric of human interactions. In this formulation, ‘place’ can be seen as a pause in movement, while the superset of all paths form ‘movement geographies’ such as a commuting pattern for a city. As such, this is a relative space and time view, since the patterns created form spatio-temporal identities (Wachowicz 1999). Adams (1995) used time geography concepts to explore the ‘ability of a person/group to overcome the friction of distance through transportation or communication’ (p267). Adams described individuals as simultaneously points at a location, which are grounded

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in space-time, and as ‘dendritic extensions’ engaging in social and natural phenomena at various distances, which are ungrounded [spatially] as they can take place at any distance. Kwan (2000) has noted significant gender differences in space-time constraints on personal time geographies.

Figure 4.13 Space-time prism

In order to realise time geographic concepts several distinctive spatio-temporal georepresentations have been.created. In a study of urban accessibility, Lenntorp (1976) calculated the area that was reachable by a traveller from a given location, within a specified time. The zone of accessibility can be represented as cone in a threedimensional space in which the z axis is time. The apex of the cone is at the current location and the slope of the sides is set by the attainable velocity. If the journey has to end up back at the same place by a certain time, then two identical cones of accessibility fit together to form a space-time ‘prism’ (Figure 4.13). Miller (1991) implemented the space-time prism concept in Arc/Info GIS as potential path areas (PPAs) by identifying which links in a road network were ‘reachable’ in the time interval available. Forer (1998) reviews time geographic concepts and applications and argues that it is

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time to re-evaluate the possibilities of this form of representation. He argues that the greatest potential lies in the implementation of space-time prisms in raster representations (Angel and Hyman 1976), rather than in vector representations as used by Jânelle (1968) and Miller (1991). Forer (1998) proposes a novel voxel-based spatio-temporal georepresentation called a ‘taxel’ referenced by two dimensions of space and one of time. Using the taxel representation Forer defined four kinds of spatio-temporal volumes: space-time prisms, space-time paths (lifelines), and both static and mobile facilities. Spatio-temporal queries can be implemented as masks excluding taxels that are either not reachable or denied access. The intersection of a space-time prism with the available facilities defines spatio-temporal opportunities. Forer suggested the use of octree encoding to compress the vast amounts of data that would be required to implement realistic spatio-temporal volumes. He calculated that the city of Christchurch, New Zealand (300,000 people and 180km2) would require 1100 million taxels to represent at 10 metre and 5 minute resolution. Four-dimensional GIS While spatio-temporal geo-representations can handle two dimensions of space and one of time, four-dimensional GIS are designed for three dimensions of space and one of time. A small number of fully four-dimensional systems have been designed to represent the forms, structures and properties of geo-phenomena and dynamic physical processes. Pigot and Hazelton (1992) showed that four-dimensional geo-representations for nonbranching time could be based on topological cellular complexes if snapshots of discrete configurations (for example in B-rep form) were available. Since algebraic topological theory can be extended to k-dimensions (Massey 1967), connected, homogenous and bounded k-manifolds can be defined with a k-cell geometric identity, when k=4. Pigot and Hazelton (1992) show that four-dimensional operations are equivalent to assembling and disassembling the k-cell complexes corresponding to the time between the snapshot representations. Hazelton, Leahy and Williamson (1990) developed a database design for a four-dimensional GIS based on simplices aggregated into temporally extended polytopes. Other approaches to four-dimensional representation have focussed on the indexing of hypercubes where data is referenced to three dimensions of space and one of time. Mason, O’Conaill and Bell (1994) developed a four-dimensional bintree to index a temporally extended three-dimensional ocean temperature grid. The bintree consisted of two 32 bit words, one for the four-dimensional location and one for the attribute field and object membership in terms of volume boundaries. The storage was not efficient compared to the raw data storage, however, the geo-representation offered rapid querying, interpolation and generalisation tools. A method based on Riemannian Helical Hyperspatial indexing called the HHCode was described by Varma (1999). The HHCode is a transformation of the geometric into the topological and can be used to break down an n-dimensional space into storage buckets of user-defined size with very high levels of compression. Since the HHCode implicitly stores the neighbourhood of the bucket and since it can be dynamically resized, it is a flexible representational tool and an efficiently queried index. The HHCode can be used

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to index temporally extended three-dimensional volumes that Varma terms ‘toxels’, which can then be ‘fused’ in an operation conceptually similar to a two-dimensional overlay. Raper and Livingstone (1995a) presented an object-oriented four-dimensional georepresentation called OOgeomorph, which assigned four-dimensional referencing to every attribute of every ‘observable’ stored. The set of ‘observable’ attributes is then assembled into a ‘phenomenon’ class based on application needs. This design makes it likely that the attributes of the ‘phenomenon’ class stored will be spatially and temporally heterogeneous, ranging from highly observation-dependent forms (‘over this space at this time’ attributes) to infinite steady forms (‘always, everywhere’ attributes). The approach forces the user to create phenomena with a functional identity as the phenomena will have multiple spatio-temporal identities needing rationalisation, i.e. an ontology is generated from phenomena rather than imposed onto it through a space and time framework. Since data storage is atomic at the scale of ‘observable’ data points, data storage is highly compressible and accessible through four-dimensional range queries (see chapter 10). Four-dimensional geo-representation can also be achieved by interpolation (Zhang and Hunter 2000). Hence, Mitasova et al. (1996) use a minimum tension approach to interpolate hypersurfaces of time series environmental data in the GRASS GIS environment. Shibasaki and Huang (1996) generate a set of voxels representing a spatiotemporal domain by optimising likelihood using a genetic algorithm to search the solution space. Miller (1997) developed a four-dimensional kriging approach (Deutsch and Journel 1992) based on a spatio-temporal semivariogram to estimate variable values at unknown spatio-temporal locations. Multidimensional process modelling While four-dimensional GIS aim to represent the forms, structures and properties of geophenomena, dynamic multidimensional process modelling aims to develop functional models of behaviour for systems with a spatio-temporal expression. Despite the fact that such processes surround us in society and the environment there are few multidimensional geo-representations of this kind. Watney, Rankey and Harbaugh (1999) note that this shortfall derives both from computational limitations and from the lack of knowledge of the dynamic systems concerned. A small number of multidimensional process models have been developed for geomorphological and geological environments. Tzetlaff and Harbaugh (1989) pioneered the SEDimentary SIMulation model (‘SEDSIM’) to represent the processes of erosion and deposition by numerically approximating the differential equations that model flow. They implemented a hybrid ‘marker in cell’ approach to unify the Lagrangian fluid element flow representation with the grid-based Eulerian representation within a 3D+T implementation. Martinez and Harbaugh (1993) extended SEDSIM with the WAVE model to represent incident waves, wave breaking, surf zone radiation stress, longshore currents, wave-current interaction and nearshore sediment transport over threedimensional deformable sea bed surfaces. Since computation limitations do not allow the modelling of realistic populations of fluid elements and sedimentary particles, SEDSIM

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calculates representative behaviour and scales the changes to user-defined intervals and spaces. Raper et al. (1999) modified SEDSIM/WAVE to grow coastal spit landforms through time given incident waves, an estuarine setting and a sediment supply. This study showed that a physically-based multidimensional process model could generate dynamic threedimensional forms that resemble those empirically observed (see chapter 10). Tuttle and Wendebourg (1999) also used SEDSIM to simulate a glacier ice-marginal deltaic environment in order to explore the spatio-temporal distribution of sedimentation and its likely influence on the hydraulic conductivity of the resultant deposits. Both these models used a procedure referred to as inverse modelling by Cowell, Roy and Jones (1991), who argued that the only way to develop an understanding of such environments is to ‘reverse engineer’ the processes responsible for the generation of forms by trial and error. The results of such modelling can then inform the ontologies and the behaviour of subsequent modelling efforts. In a distinctive approach, Penn and Harbaugh (1999) developed the ‘DYNASED’ model to explore the interdependencies among the coupled variables of land elevation, sea level and sediment transfer rate that DYNASED uses to model continental shelf deposition. Since DYNASED employs the logistic equation in its state equations, the results ranged from the cyclic through quasi-cyclic to chaotic depending upon input. Penn and Harbaugh point out that coupling is a fundamental feature of multidimensional processes and models, yet little is known about its sensitivity.

THE POTENTIAL FOR MULTIDIMENSIONAL GEOREPRESENTATION This chapter has explored three-and four-dimensional conceptual modelling and georepresentation in depth in order to evaluate their potential to realise the opportunities of multidimensional geographic information science. The evidence suggests that when conceptual modelling is coupled with geo-representation in a multidimensional framework, then powerful new insights can be obtained and fed back into concepts. The benefits of such a view are manifesting themselves in many different fields ranging from hydrocarbon exploration to urban planning and from water management to the mapping of time geographies. Insisting that multidimensional geo-representation always moves from concepts to tools and never the other way around means that the concepts of identity, change and spatio-temporality have become more important. Before the design of the current generation of multidimensional tools, representation was frequently driven by implementation, which often led to the destruction of spatio-temporal identity as it was divided up into the formats the system supported. With the emergence of systems that deal with change by updating identity in a four-dimensional framework, we see new possibilities for realist representations in explanation. While this chapter dealt with the representations that can be built from geometric foundations, the next chapter explores the potential of spatial multimedia and virtual reality systems to represent in a more direct fashion. Rather than representing through

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geometry, chapter 5 examines the direct spatio-temporal exploration of spatial multimedia and virtual reality geo-representations.

CHAPTER 5 Multidimensional geo-representations for exploration INTRODUCTION While three- and four-dimensional GIS have been developed to represent multidimensional geo-phenomena using geometry, the development of spatial multimedia and virtual reality systems has opened up new possibilities for multidimensional representation of a more direct nature (Câmara and Raper 1999). Spatial multimedia and virtual reality systems use dynamic imagery, sound, perspective viewing and real time feedback from the geo-representation to recreate multidimensional geo-phenomena. These spatial multimedia and virtual reality systems give much more responsibility to the ‘reader’ of their representations than to their ‘writer’ (unlike GIS), since the imagery, configurations and feedback invite exploration and interpretation. Gilbert (1995) argued that this kind of system is a more postmodern mode of expression, and goes further towards the phenomenological account of representation than a GIS approach. This approach marks out a distinction between the conjectural reconstruction purpose that characterises three-and four-dimensional GIS, and the insight/exploration purpose that characterises spatial multimedia and virtual reality systems. This chapter focusses firstly on multimedia and virtual reality architectures through which spatio-temporal behaviour can be represented and examined. Then, the management, retrieval and analysis of multimedia and virtual geo-representations are reviewed from the perspective of the new GIS applications supporting these concepts. Finally, the multidimensional exploration of these resources is discussed through applications of multimedia and virtual reality systems.

SPATIAL MULTIMEDIA AND VIRTUAL REALITY ARCHITECTURES Definitions ‘Spatial’ multimedia and virtual reality are distinguished from the generic technologies by their focus on the capture of geo-phenomena and the georeferencing of the data storage. Câmara and Raper (1999) feature urban planning, tourism, transportation engineering, coastal zone mapping, environmental monitoring and GIS education among the applications of spatial multimedia and virtual reality discussed. The georepresentations employed by these applications are dominated by the use of video, but dynamic imagery, sound and virtual worlds are also used.

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The generic technologies of multimedia and virtual reality have been defined in a variety of different ways. Multimedia has been defined by Laurini and Thompson (1992) as ‘a variety of analogue and digital forms of data that come together via common channels of communication’, thereby emphasising the information integration aspects. By contrast Steinmetz, Rückert and Recke (1990) argued that multimedia systems deal primarily with ‘processing, storage, presentation, communication, creation and manipulation of independent information from multiple time-dependent and timeindependent media’, thereby emphasising its time-based nature. In the context of GIS applications, Raper (1997) defined spatial multimedia as ‘the use of hypertext systems to create webs of multimedia resources organised by theme or location’, thereby emphasising the information structuring offered by hypertext. However, the term ‘multimedia GIS’ has often been used in the GIS literature in a much wider sense than this. Bill, Dransch and Voigt (1999), extending Raper (1997), identify three uses: ‘GIS in multimedia’, where spatial functionality is incorporated into multimedia applications; ‘multimedia in GIS’ where multimedia data types are incorporated into GIS software; and, ‘web pages with spatial multimedia or virtual reality content’. Bringing these definitions together, when multimedia resources are structured and geo-referenced they can be referred to as multimedia geo-representations. Virtual reality has also been defined in a variety of ways. Kalawsky (1993) suggested that the science of virtual reality encompasses the ‘creation, storage, manipulation of models and images of virtual objects’ (p9). Carr and England (1995) contrast definitions based on the experience of virtuality with definitions based on the nature of computergenerated environments. In the former case of virtuality, Ellis (1995) defined a ‘virtualisation’ as ‘the process by which a viewer interprets patterned sensory impressions to represent objects in an environment other than that from which the impressions physically originate’ (p15). Ellis argued that there are three levels of ‘virtualisation’: a virtual space in which layouts and pictorial cues are perceived; a virtual image where objects are perceived in depth; and, a virtual environment where a field of view is perceived through motion parallax. In the latter of Carr and England’s (1995) definitions relating to computer-generated environments, virtual reality systems can be said to create an environment in which the user can experience simulated visual, auditory and force sensations. Virtual reality systems can be further sub-divided into two sub-groups: firstly, ‘immersive’ virtual reality which uses a helmet-mounted video/audio system to give the user the experience of interactive immersion within the virtual environment; and, secondly, desktop or ‘through the window’ virtual reality, which displays the virtual environment on a traditional two-dimensional monitor screen. Virtual reality systems can be said to create the experience of a virtual environment for the user both in the sense of virtuality and of computer simulation. Virtual environments are made up of content (actors and objects), geometry (metrics and topology) and topology (a set of interaction rules) (Ellis 1995). Jacobson (1991) was one of the first to see that geographic virtual environments would have considerable representational power. Raper, McCarthy and Williams (1998) defined geographic virtual environments as ‘multidimensional representations of geo-phenomena in natural and built environments permitting the realistic monitoring, analysis and evaluation of the component

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phenomena’ (p1). Examples of the data types that can be used to create geographic virtual environments include satellite imagery and aerial photography, surface modelling, three-dimensional modelling, real-time positioning and dynamic process modelling. When four-dimensional virtual environments with interaction and feedback properties are georeferenced they can be referred to as ‘virtual geo-representations’. In summary, multimedia and virtual reality technologies have the power to create rich new forms of multidimensional geo-representation. The key challenges have been to give multimedia and virtual environments geographic qualities and to show that the use of such representations has had ontological significance and epistemological validity. Multimedia data types as geo-representations Multimedia systems have considerable scope for geo-representation in the form of video and sound resources. Video is a system for the recording, storage and playback of television pictures, although the term has become synonymous with the imagery itself (Trundle 1994). It is a cognitively rich representation that can encode and store dynamic visual imagery that has sufficient quality to be comparable to that experienced by a user directly through their own vision. The near universal familiarity of television pictures has led to the widespread comprehension of video imagery. Laurillard (1997) has argued that the widespread comprehension of multimedia can be used as a powerful means to present formal models in a familiar form. This comprehension is also important because it can be argued that video filters the world rather than (re)constructs it, as many forms of georepresentation do using geometry. Note that video imagery is ultimately a limited facsimile of visual imagery as it has a finite frame rate and it extends into the infra-red band of the electromagnetic spectrum. In a general sense all video is representational since its captures imagery of the world. However, video imagery is also specifically geo-representational in certain respects: firstly, through the location of the camera when recording; secondly, through camera field of view movement, i.e. whether panning, tracking or zooming; and thirdly, by vantage point context (figure 5.1). Geo-representation can also be achieved through time lapse analysis of video imagery in order to map nearshore wave breaking behaviour (Lippmann and Holman 1989). Video imagery can also be photogrammetrically processed to recover elevation information if ground control with world coordinates is visible in the imagery, as Eleveldt, Blok and Bakx (2000) have shown for a coastal environment. Video is also implicitly temporal by virtue of the regular sequential sampling offered by video imagery. A video image sample can be played back at any desired speed enabling the ‘slow motion replay’ or speeding up of specific sequences, creating a distinction between ‘world time’ and ‘playback time’. However, the temporal structure of the world is not fully incorporated into such a video sequence. Firstly, the frame per second rate of video sampling implies limits to the temporal representation by limiting the shortest event that can be captured. Secondly, a fixed frame rate provides the same granularity of sampling for all circumstances, thereby restricting the ability of video to capture accelerations and decelerations (Foote and Horn 1999). Hopgood (1993) argued that the twin ‘world’ and ‘playback’ time models required for video meant that only

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relative time referencing could structure the temporal relationships in the imagery. This is because the world time in the video imagery and the playback time of the recorder cannot be related to each other or to a universal absolute timeline in any simple fashion. In video presentations perhaps time is best represented by imagery sequences with appropriate orderings in world time and in playback time.

Figure 5.1 Georeferencing video imagery

Since video is a spatio-temporal projection of the world in imagery, it can be considered capable of fully multidimensional geo-representation. It can be used for mapping from moving platforms (Livingstone, Raper and McCarthy 1999), for target positioning (McCarthy 1999), for the measurement of geo-phenomena such as air pollution (Ferreira 1999), and as a process monitoring system (Holland and Holman 1997). Video imaging has also become a recognised and valuable new technique of remote sensing in the 1990s (Mausel et al. 1992, King 1995). Analogue video imagery is recorded by the camera as brightness/colour levels, line by line at 30 or 25 frames per second, and is then modulated onto a waveform to be transmitted to a remote receiver or recorded on to tape. Digital video imagery is recorded by the camera as brightness/colour levels, pixel by pixel at 30 or 25 frames per second, and is stored in memory to be compressed in ‘key frame plus changes’ format. Georeferenced videography can be defined as the linkage of positional information such as Global Positioning System (GPS) coordinates to individual video frames (Cooper, McCarthy and Raper 1995). The GPS positional information can be stored with a frame once per second either using the audio track (Paragee 1997) or by using the inter-frame Vertical Line Interval (VLI) (Raper and McCarthy 1994a). Sound is also intrinsically representational as it is time-varying and spatially distributed. Sound can be recorded using georeferenced directional microphones and played back in such a way that the hearer can recover movement across the field of

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sound. Sound recordings in audio data form can convey changing volume levels at different locations through time. Shiffer (1995a) has demonstrated the sound of aircraft taking off as heard from different locations for a planning enquiry, while Cassettari and Parsons (1993) discussed the representation of sound in a GIS for airport noise monitoring. D’Souza (1994) studied road traffic noise in a neighbourhood in London noting that since noise levels varied from continuously high levels near major roads to only periodically high levels in residential areas, noise is very difficult to map in twodimensions. The transient nature of noise means that it must be sampled spatio-temporally before it can be represented. The very wide acoustic range of noise in the urban environment also means that it must also be measured in the logarithmic decibel scale. Sound is also reflected and blocked by obstacles, making sound propagation very complex. Taken together, these factors make sound representation complex. However, since sound can be described using a wide range of variables it is suitable for use as a symbolisation as well as a direct representation. Krygier (1994) showed how sound characteristics could be used as cartographic variables including: location, loudness, pitch, register, timbre, duration, rate of change, order and attack/decay. Fisher (1994) discussed the use of audio playback as a measure of reliability when browsing classified remotely sensed imagery. Compression of video and sound is of crucial importance to their effective storage and delivery. Compression techniques can be divided into lossless methods (the images compressed are recovered exactly) and lossy methods (the images compressed are recovered approximately). Lossless methods are appropriate for the compression of data which must be preserved exactly such as many geo-representations and can generally achieve an average of a 3:1 reduction in data volume. However, lossy techniques can be used to compress images-to-be-viewed/sounds-to-be-heard such as photographs or speech recordings since human perception of the high frequency variations in imagery/sound is poor. Most systems now use the Joint Photographic Experts Group (JPEG) standard for still image compression which in lossy mode can achieve an average 25:1 compression while retaining excellent reconstruction characteristics. Similarly, audio can be compressed at up to 10:1 ratio using the MPEG2 Layer 3 Audio (usually known as MP3). For video, a further data reduction can be obtained over and above that of individual image frames by using the Motion Picture Experts Group (MPEG) video standards. The MPEG standards designate some frames of the video as ‘reference frames’ and other frames are then encoded in terms of their differences from the nearest reference frames. The MPEG1 standard was limited to video captured at 288 by 352 pixels in 24 bit colour at 24/30 fps and is now largely superseded. MPEG2 is the new standard as it allows for full screen video playback on digital television and on computers. The commercial Quicktime and RealVideo systems have been designed for streaming video presentations over the Internet. While video imagery can be seen as a cognitively rich representation, many factors influence exactly what video imagery is recorded (Foster and Meech 1995). Access to the video technology and the skill to use it are primary constraints; secondary constraints include the place and time in which the ‘videographer’ is able to operate; finally, the ‘interest’ of those who capture video must be considered. Which events or dialogues were recorded, and which were left out? Despite these constraints video is now routinely

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captured for security surveillance, environmental monitoring, traffic monitoring and by individuals, and can now be considered to be a mass form of representation both at the level of capture and consumption. Virtual environments as geo-representations Virtual environments function directly as geo-representations through their reconstruction of environmental content, geometry and topology (Ellis 1995). Mesoscopic virtual environments that are larger than an individual room and smaller than the earth have been widely constructed for virtual exploration (Raper, McCarthy and Williams 1998), the visualisation of geo-phenomena (Neves et al. 1999) and for planning and urban management (Verbree et al. 1999). While virtual environments are much less cognitively rich than video and sound, they are qualitatively different from three- and fourdimensional modelling since there is interaction with, and feedback between, user and model. Batty et al. argue that it is this ‘connection’ between the user and the model that is the distinctive measure of the virtual environment. Dykes, Moore and Wood (1999) suggest that interaction with virtual environments can provide a ‘sense of place’ (or ‘spatiality’) through the ability of the user to situate themselves within the model. Bodum (1999) proposed a spectrum of abstraction from reality through enhanced reality, enhanced virtuality to full virtuality for interaction with virtual environments. Neves and Câmara (1999) survey the use of virtual environments with GIS. Virtual geo-representations reproduce the characteristics of geo-phenomena in the virtual environment, specifically the physics and dynamics used, the spatial and temporal referencing system, the geometric form, the view characteristics, the interaction rules and the scale dependency of the display. Although a number of virtual reality systems have been developed e.g. World Toolkit/WorldUp from Sense 8, most virtual georepresentations are now made using the Virtual Reality Modelling Language (VRML), which, in the form of VRML 1.0, was developed from the Silicon Graphics Open Inventor format. The design of the more sophisticated VRML 2.0 format led to the specification of VRML97 as an ISO standard language (ISO 14772) for describing threeand four-dimensional virtual environments (or ‘worlds’), which is now maintained by the Web 3D Consortium. The majority of virtual environments are now based on desktop virtual reality using VRML 97 files in browsers, which are accessed using a mouse and on-screen navigation tools. The experience of immersive virtual reality now extends beyond head-mounted displays to include virtual reality theatres and ‘caves’, where the virtual environment is projected onto the four walls, floor and ceiling of a room (Batty et al. 1998). Kraak, Smets, and Sidjanin (1999) outlined the design of an immersive virtual environment designed to allow the geographic exploration of the Delft Technical University campus. VRML 97 is based upon the ‘scene graph’ data structure, which is a hierarchical arrangement of ‘nodes’ representing geometric objects and their properties, sensors, behaviour and relationships. A VRML97 world file is displayed in a browser after it has been validated by a parser and the scene graph recovered. The scene graph is composed of a transformation hierarchy (containing nodes) and a route graph (connected to the sensors), which collectively represent the virtual environment. The transformation

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hierarchy represents objects in the virtual environment using a shape node, which includes primitive geometric objects (Box, Cone, Cylinder, Sphere), surface grids (ElevationGrid), B-reps (IndexedFaceSet), and other geometry (IndexedLineSet, PointSet, Extrusion). Shape nodes can have further sub-nodes that specify their geometric properties and their appearance (e.g. texture mapping), and they can be grouped by behaviour. Other nodes in the transformation hierarchy describe light sources, sensors, interpolators and time dependent nodes such as audio or video clips. The route graph describes how nodes receive events and how they act upon them. Each VRML97 world has a viewpoint from which the virtual environment is (initially) being viewed, and offers navigation ‘paradigms’ such as walking, flying and examining, by which the user moves through the model. The script node allows developers to add functionality using programming languages like Java or link other applications (Brutzman 1998). Physics and dynamics are properties of virtual geo-representations rather than part of a ‘given’ external framework. Hence, many virtual reality systems make gravitation and collision detection optional, and different settings can be assigned to the various objects within the scene graph. Spatial referencing systems are typically three-dimensional Cartesian coordinate systems with limited precision, which normally have their origins at the geometric centre of the world. This is the case in VRML97, which uses a ‘righthanded’ coordinate system in which the horizontal plane is defined by x and z axes, and where the y axis defines the vertical (figure 5.2). These conventions on origins and the directions of the axes are different to many two-and three-dimensional geo-representation systems, leading to specific data transfer difficulties between them (Williams 1999).

Figure 5.2 VRML coordinate space (after Williams 1999)

The limitations of fixed precision right handed world-centred coordinate systems in VRML97 has led to the development of new nodes for geographic data within the GeoVRML framework (Rhyne 1999). The GeoVRML version 1.0 Recommended Practice adds facilities to VRML97 to support non-Cartesian coordinate systems, origin

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shifts, geographic metadata, navigation and animation, without changing the underlying referencing of the standard. Coordinate system support for projected and geographic coordinates has been built on top of the Synthetic Environment Data Representation and Interchange Specification (SEDRIS) Geographic Reference Model (Rhyne 1999), and is accessed through a new geoCoordinate node. Origin shifts and axis rotations are accessed through the geoOrigin node. The GeoVRML version 1.0 Recommended Practice also provides facilities for georeferencing VRML97 worlds (geoLocation node), locating mouse clicks on a shape node (geoTouchSensor node), positioning a viewpoint in geographical space (geoViewpoint node) and animating objects in that space (geoPositionlnterpolator). In each case the GeoVRML approach transforms the standard VRML97 model using geographic functions. Time is represented in VRML97 by timestamping events using double-precision floating-point numbers counting seconds since 1st January 1970; time can be speeded up or slowed down if the application calls for it. Events are either generated by time sensors when activated by user interaction with a scene graph node (e.g. direct manipulation or proximity), or they are generated when continuous changes (e.g. movements) are temporally intersected by discrete events. This concept of time does not accommodate the need to replay user interactions with the world or to animate change in a time other than the system time (Lutterman and Grauer 1999). Accordingly, Lutterman and Grauer propose the addition of a history node to VRML97 that allows the grouping of nodes in a temporal scene graph by their time varying behaviour. Lutterman and Grauer used the Java interface to the script node to display time dependent geometries and textures read from a three-dimensional GIS of ground water levels. The geometric form of objects in a virtual geo-representation using VRML97 are usually based on ElevationGrid and IndexedFaceSet node types. These are equivalent to rasters and TINs in GIS respectively: the former render quickly as they are compact but are fixed resolution, while the latter offer more a data dependent and adaptable display (Brown 1999). Two-and three-dimensional GIS can be used to convert the syntax of georepresentations into that of VRML97 using import/export tools, although this can only generate shape nodes which do not have any associated behaviour (Raper and McCarthy 1994b). The GeoVRML version 1.0 Recommended Practice adds a geoElevationGrid node to VRML97 so that the elevation grids can be manipulated using projected and geographic coordinates. Virtual geo-representations also present specific challenges to the characterisation of viewing. Since virtual environments use planar coordinate systems, in theory any object can be seen at any distance, as long as there is enough light and no fog (in practice, a fixed minimum pixel resolution limits what is displayed). The same is not true of views in the world, as there are limits to visibility due to the curvature of the earth and atmospheric attentuation. Williams (1999) shows how some virtual reality systems can specify artificial horizons beyond which the model will not be rendered. These ‘yon clipping’ distances need to be viewing height-dependent, otherwise when the viewpoint is high above the ground then the artificial horizon may cut off a large part of the model which the user expects to see. Virtual environments have also been defined for spherical spaces where the virtual geo-representation is made from imagery that has been integrated seamlessly using a photo-stitching tool and accessed using ‘enhanced reality’

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systems such as Quicktime VR (Bodum 1999). Dykes (2000) shows how stitched imagery can be explored using the Panoramap application, which links the panoramic view to an associated map by displaying the angle and direction of the current view. Panoramap allows the rapid exploration of the virtual environment by allowing the user to ‘see what the view is like’ from points with panoramas. Interaction with virtual geo-representations requires new skills to use them effectively. Neves et al. (1997) argue that users of virtual geo-representations need to synthesise the direct manipulation skills used for the haptic space of sensorimotor experiences, and the camera manipulation skills needed for the pictorial space of visual experiences. The synthesis of haptic and pictorial spaces over time results in the creation of a new ‘transperceptuaP space that requires way finding skills to move through the sensed virtual environment, i.e. remembering how a given virtual location was reached. Neves et al. (1999) developed the immersive Virtual GIS Room with wall poster maps, a table on which selected maps become surface models, and pen manipulation tool in order to explore the use of these different spaces (see chapter 8). The use of photographic imagery by Dykes (2000) confers an important advantage in virtual environment navigation as the transperceptual space is based on cognitively richer representations. Note that different skills are required for desktop and immersive virtual reality experiences. In desktop virtual reality the user must adapt to being situated within the transperceptual space and must develop skills in the interface tools that control movement (Brown 1999). In immersive virtual reality systems the user must become used to the experience of head-mounted displays, and, typically, a slight latency of system response to head movements and gestures (Kraak, Smets and Sidjanin 1999). Multi-user virtual environments have also been developed for groupware and chat services, where individuals are represented as ‘avatars’ within spaces designated for specific purposes. Lin and Smith (1997) developed an architecture for collaborative virtual environments where distributed users could work together on three-dimensional models. The creation of virtual geo-representations made up of surface models draped with map data or remotely sensed imagery usually requires a particularly large number of shaded B-reps (usually simplices) to represent the virtual environment. This processing overhead is minimised by reducing the data volumes before import and by employing real-time generalisation algorithms during viewing. Reducing the size of the surface model involves the use of filtering techniques that cut the number of triangles making up the terrain by amalgamating them when the angles subtended vertically between adjacent triangles are small. This procedure is usually empirical and applied uniformly across the surface, although there would be benefits in developing density or elevation specific surface generalisation. Wright, Watson and Middleton (1997) discussed the use of preprocessing polygon decimation techniques to improve the speed of display of surface models. Virtual reality generalisation algorithms have been developed so that only those objects either near to the user’s current viewing position or orthogonal to their viewing direction are displayed with adequate enough triangles to give a high resolution view (Neves and Câmara 1999). Those triangles further away or viewed obliquely are displayed at a simplified level by real time generalisation or by recalling an appropriate set of nodes from a level of detail (LOD) quadtree data structure. Level of detail (LOD) nodes group

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together shape nodes so that progressively more detail can be displayed as the levels of the quadtree are traversed, i.e. when the user looks in a given direction or moves close to a given area. Muchaxo, Neves and Câmara (1999) describe a wavelet compressed quadtree LOD technique which is based on a terrain adaptive TIN. The GeoVRML version 1.0 Recommended Practice adds a geoLOD node to allow access to LOD indexes in projected or geographic coordinates. There are contrasting views on the value of virtual environments to understanding. Dykes (1999) characterised a virtual environment as a model understood by a geographic metaphor. Bishop (1994) raises the question of the appropriate level of (photo)realism in virtual geo-representation: highly abstract representation may be incomprehensible, while highly realistic representation may be dominated by aesthetic considerations as the expense of comprehension. Dykes, Moore and Fairbairn (1999) defined a representational spectrum from the (photo) realism of Imhof’ s terrain drawings to the abstraction of Chern off’s symbolic faces, and suggest that VRML offers new possibilities all along the spectrum. Boyd Davis and Athoussaki (1997) argue that the construction of virtual environments is a design process in which (photo) realism is neither achievable or desirable. They point out that ‘viewing’ is an active process in which the user is engaged through authorial devices such as those used in film or theatre to change focus or perspective (Laurel 1991). Foster and Meech (1995) explored the social dimensions of virtual reality through Baudrillard’s (1983) view of simulation in which reality can be reflected, perverted, denied or invented in an all-encompassing paradigm of representation. This is the view that virtual environments do not and cannot mimic the world: in this sense, at best, virtual environments are ‘consensual hallucination’ (Gibson 1986). Likewise, Pimentel and Teixeira (1993) divided approaches to virtual environments into those based on ‘here’ (the current reality), ‘there’ (a reflection) and ‘elsewhere’ (a simulacrum or invention). In these terms, virtual geo-representations are mostly simulacra (so far). Database storage of multimedia and virtual geo-representations Since multimedia and virtual geo-representations cannot be handled by standard relational database systems, they must be stored either in extended relational databases, object databases or in application-specific data stores (Nwosu, Thuraisingham and Berra 1997). While some database solutions have been defined for these geo-representations, many application-specific solutions have been developed. Subramanian (1998) has identified three main requirements for a multimedia database management system: storage and query of heterogeneous data types, the management of very large amounts of data and the presentation of a query result in an appropriate viewer. In contrast, virtual reality systems require support for the hierarchical data storage of the scene graph. For example, Köninger and Bartel (1998) used the database Postgre95 to store virtual georepresentation data. One of the most advanced virtual reality database systems is the object-oriented dVS operating system from Division, which is designed to distribute activities between different processors in a multiprocessor system. In dVS ‘actors’ are responsible for sensing the attitude of the user, the user’s position in the virtual environment, display and

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control of the virtual environment and other activities such as collision detection. The virtual environment is composed of ‘elements’ such as boundaries, constraints, visuals, audios and lights which are grouped together in hierarchies (e.g. a wall is a hierarchy made of a visual and boundary). The ‘actors’ communicate by placing instances of ‘elements’ in a shared data space (the VL database) monitored by all actors. Division’s dVISE virtual world simulation system runs on top of dVS. Given the need for heterogeneous data storage, multimedia database design is focussed on efficient organisation of this content and support for queries on it. Subramanian (1998) has suggested that designs can be based either on autonomous storage of each data type, uniform indexing of all data types on a semantic basis, or on hybrid schemes. The autonomous approach is efficient in storage terms but requires the computation of joins across data types during queries; object-oriented databases are the preferred method of implementation. The uniform approach requires the creation of metadata for each data type so that queries can be made efficiently on the metadata. The extended relational database is the preferred method of implementation. Many extended relational databases are now introducing support in tables for multimedia data types such as video and sound, in a move towards the implementation of the ‘universal server’ capable of managing all types of data. In these extended relational designs tables are able to support both alphanumeric and multimedia data types, although the latter are not used as a key. The querying of such hybrid tables involves the use of vendor-specific extensions to SQL, since SQL does not support non-alphanumeric data types in versions 1 and 2. This restriction in the data types supported, and, in consequence, the types of queries permitted, is being addressed by the release of SQL version 3 or ‘SQL/multimedia’. Object-oriented databases offer more flexible methods of integrated alphanumeric and multimedia data storage, since they permit the unified treatment of both kinds of data. This means, for example, that keys can be defined over heterogeneous sets of attributes made up of both alphanumeric and multimedia data. Hence a ‘multimedia object’ can be defined by its key, and the similarity between it and any other ‘multimedia object’ can be ascertained by comparing their keys. Grosky (1994) suggested that the similarity of content-based multimedia keys could be based on a ‘multidimensional distance function’ (p18) defined over the attributes. The result will not usually be an exact match but a fuzzy similarity measure. This procedure is limited to those attributes originally extracted from the multimedia data using content-based methods, which of course is specific to the system creator. Multimedia data contains information that can be recognised and extracted in different ways by different users. This means that users of multimedia databases can derive their own attributes in order to form new keys defining ‘multimedia objects’ of interest. Users can therefore interactively define multimedia objects of interest and then query the database for other objects that are ‘similar’, i.e. multidimensionally close in attribute space. Little et al. (1993) developed such an approach for a digital video system although the multimedia objects could not overlap along the movie timeline. These approaches could have a wide range of applications for multimedia geo-representations, such as the content-based extraction of dynamic process signatures like sea wave direction and speed (Raper and McCarthy 1994a) (see chapter 7).

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Multimedia development and standards Multimedia application development involves the synthesising of alphanumeric and multimedia data into a multimedia presentation. While multimedia data can be played back in its native form, storing it in a structure which is aggregated with other data allows it to be explored and queried using a multimedia authoring tool. Such tools can be classified by the informational structures and metaphors they use to give access to the multimedia resources. The simplest informational structures for multimedia are based on slide shows (such as Microsoft Powerpoint), scenario-building and evaluation based on user interaction (such as Authorware) or movie making (such as Director or Premiere), although the sophistication of some of the latter systems has been extended using scripting languages. More complex informational structures allow the linking of multimedia data types grouped into abstractions in semantic nets (Subramanian 1998). Researchers have created more complex applications offering richer forms of structuring and retrieval. Weiss, Duda and Gifford (1995) developed the ‘video algebra’ system using C++ in which video ‘expressions’ (which may overlap each other on a master timeline) are created from a video stream by a ‘creation’ operation and interactively assigned content-based attributes. Using a ‘composition’ operation, a hierarchically organised ‘presentation’ is created in which the ‘expressions’ are ordered temporally and by position on the display device. The web browser interface to the system invoked Tool Command Language (TCL) scripts to dynamically create Hypertext Markup Language (HTML) documents in response to user requests. Video algebra queries search the content-based attributes hierarchically for a match, which can then be played or displayed with reference to the master timeline. By contrast, Hirzalla, Falchuck and Karmouch (1995) developed an advanced temporal model for interactive multimedia, which can manage alternate timelines based on user choices. The actual timeline followed by the user is called a timepath and can be visualised as a path through a tree of possible timelines. This system aims to ensure that each possible timepath preserves the integrity of the basic multimedia elements in the system, i.e. not playing one piece of video before another piece that sets the first piece in context. With the proliferation of software tools in the multimedia field, the need has been recognised for data exchange standards capable of translating one proprietary system into another. There are several standards in development. HyTime is an international standard ISO 10744 (1997) for the representation of information structures for multimedia resources (Newcomb, Kipp and Newcomb 1991) through the specification of document type definitions, and is based upon Standardised Generalised Mark-up Language (SGML) (ISO 8879). The Multimedia and Hypermedia information encoding Experts Group (MHEG) is a standard (ISO 13522) for representing hypermedia in a system independent form (Meyer-Boudnik and Effelsberg 1995). It is optimised for run time use where applications are distributed across different physical devices or on networks. The PResentation Environment for Multimedia Objects (PREMO) is a standard (ISO 14478, 1998) which defines how different applications present and exchange multimedia data. It defines interfaces between applications so that different applications can each simultaneously input and output graphical data. Each of these standards has developed a different concept of space and time. The

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PREMO and MHEG standards support a single three-dimensional space plus onedimensional time to provide a comprehensive frame of reference for all events in a multimedia presentation. HyTime allows multiple space and time reference systems, for example, permitting both ‘video frame rate time’ (30 frames per second) and ‘user playback time’, the latter describing how the multimedia resources are actually played by a user who is responsible for pauses and fastforward events. The resolution of these debates and the concepts of space and time that are implemented have important implications for the spatio-temporal analysis of multimedia geo-representations, e.g. security camera records. Hypermedia development environments The hypertext or hypermedia model is a semantically rich method of structuring multimedia data (Nielsen 1995) which is suitable for structuring geo-representations. The origins of the ‘hypermedia’ concept go back 50 years to the mid 1940s when Bush put forward his ‘Memex’ idea—a kind of multidimensional diary with links between all ‘connected’ things (Bush 1945). This early suggestion remained an unimplemented idea until Nelson explored its implications in terms of the associative linking of facts and ideas in the 1960s and created some early prototypes (Nelson 1965). Early Hypermedia designs such as Nelson’s Xanadu envisaged text-based and single-media applications. The technology and theoretical structures required to fully implement these ideas were not developed until the 1980s when the ability to handle non-alphanumeric multimedia data and new high-level computer languages became available. Later systems such as Notecards (1985) and Guide (1986) added static graphics to the data types supported, while Hypercard (1987) supported a comprehensive range of multimedia data, and offered a scripting language called Hypertalk. These tools inspired the development of the World Wide Web in the mid 1990s when hyperlinked multimedia data in HyperText Mark-up Language (HTML) form became accessible through browsers (Berners-Lee et al. 1994). Browsers are now the definitive hypermedia applications. In the abstract, the hypermedia model can be described as a set of nodes connected together by links, where the nodes are abstractions consisting of multimedia information elements (McAleese 1989). According to Campbell and Goodman (1988) the architecture of a hypermedia system can be divided into three levels (from bottom to top), i.e. the multimedia database, hypertext abstract machine (HAM) and presentation levels. At the bottom is the database where all the raw multimedia data is stored, above which is the HAM that houses the logical model of the hypermedia system. The HAM also describes the possible link forms: explicit links which are anchored in screen buttons; implicit links that are made when the user makes a request; and, computed links which are determined on the basis of some context-specific heuristic. Links are not always bi-directional and can also take a one-to-many form, although this is not supported on the web. The superset of node information, content and links, as found in an HTML-formatted web page or a Hypercard stack, is often referred to as a hyperdocument. In the case of Hypercard the nodes are called cards, which can contain as many information elements such as text fields, graphics, video, sound and links as the developer wishes to place there. Deciding on the content and organisation of the nodes (and constituent information

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elements) is often a problem of knowledge elicitation and abstraction from the information available. Design decisions in this process involve the transformation of knowledge into the nodes—which itself requires a definition of their semantic proximity and distinctness. Note that this process is unconstrained by the need to define a complete set of attributes for any node, as there are no explicit integrity constraints as there are in relational databases. Since hypermedia models aim to provide maximum flexibility in the connectedness of knowledge, a key problem has been how to define an organisational framework without dictating a rigid user model. This has been achieved by treating the nodes in a hypermedia application as part of a semantic network (Jonassen 1989) where links are made based on knowledge of the information domain. Hence, the web structures information using low-level link constructs, leaving the user to impose their own high level structure through interaction patterns. Sutcliffe (1997) set out a scheme of taskrelated information analysis that preferred hypertext methods for information delivery when non-sequential pathways are needed. Above the HAM is the presentation level, which controls the appearance of the HAM to the user. Typically an organising metaphor such as a page or a gallery is employed to guide user interaction. The organising metaphor provides concepts such as a network or hierarchy to depict the arrangement of the nodes, e.g. as stops on a tour, or sections of a book. The greatest dangers in hypermedia design are avoiding the ‘lost in hyperspace’ problem and not overloading the user with too much information. The latter problem can be greatly reduced by customisation of the presentation level according to the user’s knowledge and employing all the modalities of perception in the metaphor including depth cueing and colour. Note that many of the most common of such metaphors are spatial, such as the tour and map metaphors, providing a variety of visualisations for the arrangement or content of the nodes. This is one particular characteristic which makes the hypermedia model an appropriate way to store and organise spatial data as these metaphors can also be used to structure the nodes (Raper 1991). The implementation of the hypermedia model has also become intrinsically linked to object-oriented programming (OOP). The concept of classes and sub-classes in OOP matches the hypermedia notion of nodes and information elements grouped according to a scheme of abstractions. In most hypermedia systems information elements and nodes, as well as links can be typed and named providing a basic form of organisation which application programs can exploit (see figure 5.3). OOP has made it possible to create robust hypermedia applications where arbitrary associative links can be established and complexly nested in any configuration. The hypermedia form of information structuring also infers new forms of access to multimedia data. McAleese (1989) identified a ‘navigation’ mode of use, where the user followed a pre-defined path through a hierarchy or network of nodes. Nielsen (1995) described some of the aids to navigation in hypermedia such as backtracking, history lists, bookmarks and overview diagrams (which can be generalised or nested if they become too large). The overview diagram often takes an explicitly spatial form such as a map (Raper 1991) or uses a spatial transformation. By contrast, McAleese (1989) distinguished a ‘browsing’ mode where the user accessed the nodes by associative links between abstractions based on knowledge of the information domain. In the browsing mode there need be no pre-existing links since the user can make them in real time.

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McAleese described distinct browsing, scanning, searching, exploring and wandering strategies, which he saw as different approaches to traversing the nodes. Blades (1994) analysed hypermedia navigation in terms of the wayfinding theories of Siegel and White (1975), suggesting that designers need to present information as landmarks which can be connected together to form routes. Passini (1999) argued that such routes are best thought of as decision plans, implying that sign posting is an essential design element.

Figure 5.3 Scheme of links between information elements and abstractions in a Hypertext application

These hypermedia approaches contrast with conventional database designs which require the use of querying facilities to extract a specific subset of information which can be displayed or input into an analysis procedure. In this sense the hypermedia model is particularly useful for heterogeneous collections of data where many abstractions have unique properties and cannot be typed or named in advance, or where arbitrary aggregations are meaningful. It is also possible to define abstractions with widely differing granularity, such that the user of the system appears to move between nodes at different levels of information aggregation, or between different ranks of any pre-existing hierarchy. Such moves between nodes may also reflect decision-making, permitting the recording of a decision history. While small scale hypermedia systems have been implemented widely, and the web has enabled global information access, many users would find it useful to be able to turn their whole computing environment of file handling, word processing, spreadsheets and programming into a hypermedia system in itself. This is the goal of open hypermedia systems (OHS). Engelbart (1990) classified OHS into those designed to intemperate within an individual’s workspace and those designed to allow interoperability within and between groups. Hall (1994) argued that explicit links have come to dominate the presentation level of hypermedia systems such as browsers on the web, making them rigid and unresponsive to user concepts. In such hypermedia systems, the links must also be stored with the node data making it difficult to update and change nodes without disturbing the links. Hall, Davis and Hutchings (1996) argue that the links should be

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dynamically created by the user or by a query operation that finds the most ‘similar’ match using information retrieval techniques employing relevance criteria. The ‘Microcosm’ database maintains a set of links associated with each node in an application that is ‘fully or partly aware’ of Microcosm and allows the user to edit the links and customise the interface. Open hypermedia systems like Microcosm have been proposed in order to reduce the dependence on package-specific file structures and to provide operating system level support for associative linking of multimedia resources. Hypermedia systems in the form of browsers reading web pages have now become the dominant information access mode for most computer users. There is now scope for microbrowsers on other information devices such as mobile phones and hand-held computers to extend hypermedia systems into new settings (Dobrowolski, Nicholas and Raper 2000). The arrival of such a widely used new information infrastructure demands new approaches to information systems and visual communication (Horn 1999), which Jacobson (1999) has called information design.

SPATIAL MULTIMEDIAAND VIRTUAL REALITY SYSTEMS The software architectures of multimedia and virtual reality systems have made it possible to develop multidimensional geo-representations with new expressive power. These geo-representations offer richer concepts than two-dimensional GIS as they extend the dimensionality, the data types, the analytical powers and the information management capabilities of existing systems. In addition to these architectural extensions, the new systems have developed new interfaces and new forms of interaction which engage the user, and allow a greater reflexiveness in the use of geo-representations. These new georepresentations are discussed under the headings multimedia/hypermedia GIS, web GIS, virtual reality GIS, real-time GIS and geolibraries. Multimedia/hypermedia GIS Attempts to design and develop multimedia/hypermedia GIS have focussed on the questions of how to combine the semantics of hypermedia with georeferencing and how to construct multimedia geo-representations (Buttenfield and Weber 1993, Cartwright, Peterson and Gartner 1999). An early multimedia/hypermedia GIS system was developed by Polyorides (1993) who developed the Great Cities of Europe using Toolbook extended with C++, georeferencing the multimedia data through the city maps. Shiffer developed the Collaborative Planning System (CPS) based on Supercard and Quicktime to evaluate planning scenarios for Washington, DC. The CPS allowed the user access to a wide range of multimedia data by selecting resources from a geo-referenced image map base. The geographic footprint and orientation of multimedia data such as simulations or videos were shown on the image map base to orient the user. More recently Chen, Wang and Zu (2000) developed a multimedia atlas for the Yuxi tourist information system in China. Raper and Livingstone (1995b) developed a multimedia/hypermedia system called Scolt Multimedia Project (SMP) (see chapter 6) to store and explore multimedia georepresentations using the object-oriented Hypercard hypermedia system. Using the

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terminology of the HAM and figure 5.3, SMP stored the georeferenced multimedia data as information elements and grouped them into hyperdocument node abstractions based on location. Certain links were generated by the system designer, some were ‘computed’ by searching and some were added by the user when they edited the hyperdocuments. The presentation layer employed a ‘time-space’ diagram (figure 6.1) to plot the period and the place that the hyperdocument related to. As SMP permitted the annotation of hyperdocuments through the addition of comments and vector geometry (figure 7.1), integrity was guaranteed by the encapsulation of methods and data with the information elements. Jones et al. (1996) developed the Semantic Hypermedia Architecture (SHA) to structure semantic, spatial and temporal relationships among stored knowledge in the form of multimedia data. The semantic relationships ‘is_a’, ‘has_a’, ‘part_of’ and ‘kind_of’ were used to define spatial and temporal relationships using containment/adjacency and interval concepts respectively. The multimedia data was linked to these structural relationships using the semantic relations. Spatial, temporal and spatio-temporal queries creating links were implemented through the concept of semantic closeness between multimedia data. Although this approach allows the construction of rich multimedia geo-representations organically, it does not necessarily ensure semantic consistency within the stored and computed knowledge. When a multimedia geo-representation uses a map as the primary index to the multimedia data, then the links and abstractions are explicitly geographic, and the application can be termed a hypermap (Raper 1991). A hypermap is usually presented as a visualisation of a metric or topologic space that is accessed by browsing. Laurini and Milleret-Raffort (1990) and Laurini and Thompson (1992) presented data structures for a hypermap containing points, lines and areas forming geographic features on a map, and proposed the use of R-trees to store their spatial inter-relationships. They suggested that spatial to non-spatial relationships might also be structured using R-trees, although this requires the transformation of the documents into rectangles in 2D coordinate space. Since the hypermap does not impose integrity constraints or planar enforcement of geometry in its design, there is a flexibility in the implementation that is attractive when the overall size of the multimedia database is not too great. Kraak and Van Driel classified hypermap functionality into access by spatial, temporal or thematic criteria using the TRIAD model of Peuquet (1994). Early work on bringing multimedia data types into GIS led to the development of a number of conceptual models based on GIS designs such as Wallin (1990) and Yeorgaroudakis (1991). Kemp (1995) evaluated the alternative implementations of this approach concluding that the geo-relational model falls short of aspirations, since the multimedia data and processing are not really integrated into the GIS. Instead, Kemp suggests that multimedia/hypermedia GIS should be implemented as applications using object-oriented languages constructed over object oriented database systems. Examples of this approach include Kemp and Oxborrow (1992), who developed a system to handle ambulance journey-related multimedia data in the object-oriented database Zenith. Groom and Kemp (1995) developed an endangered species database using the multimedia data type support of Postgres. Boursier, Kvedararauskas and Spyratos (1996) developed the Magic Tour system by linking a multimedia authoring system to databases

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and GIS through inter-application communication protocols. Hall, Davis and Hutchings (1996) linked the open hypermedia system Microcosm to the SPANSmap GIS (Simmons, Hall and Clark 1992) in order to link spatial and non-spatial data referring to a development site. Recently, Christel, Olligschlaeger and Huang (2000) have showed how geographic information can be extracted from videos of news bulletins containing maps. Web GIS Widespread access to the Internet, the ubiquity of browsers and the explosion of commodified geographic information has made it possible to develop new forms of multimedia geo-representations on the web. These include hypermaps, image browsers and cartographic visualisers. The simplest form of web GIS is a clickable raster hypermap with an associated ‘imagemap’ consisting of vector outlines identifying specific features. In this approach the vector data is restricted to unstructured polygons and the coordinates are local and not geographic. Kraak and Van Driel (1997) developed a prototype hypermap on the web called the Delft hypermap, which offered query capabilities, information filtering and allowed users to update the hypermap by adding features. Sarkola (1997) described how Finland’s base maps have been made available via hypermaps on the web. Fernandes et al. (1997) outlined the design of the Portugal Interactive project that offered web access to a national database of orthophotos in a service called GeoCid. Cartwright (1999) outlined the design of the GeoExploratorium, a web-based interface to multimedia georepresentations with multiple access modes. Huang and Lin (2000) describe the webbased 3D Visualisation and Analysis Server, which uses extensions of Arcview. Browser functionality can also be extended through the addition of ‘plug-in’ code to their component architecture. Plug-ins allow the browser to display and manipulate additional data types referenced by the HTML including multimedia, animation, VRML, raster and vector data. Plug-ins have allowed the inclusion of geo-representations on web pages to: play geo-referenced video (McCarthy 1999); animate mapping (Cartwright 1999); present high resolution aerial photography compressed using wavelets; and, display vector data in standard forms such as computer graphics metafile (CGM). Browsers can also be extended through the use of network-portable languages such as java. Java ‘applets’ are embedded in a web page and compiled locally on the users’ computer by a ‘virtual machine’ that cooperates with the operating system. As java is machine-independent, applets should run in the same way on all operating systems and in all browsers, although this rarely true in reality. Java applications can also operate in standalone mode. A wide range of java applets and applications have been developed for geo-representation, ranging from the digital terrain modelling application Landserf (Moore, Dykes and Wood 1999) to the cartographic visualisation applet Descartes (Andrienko and Andrienko 1999). Browser software using plug-ins or java can now be used as a platform for the delivery of geographic information and the software functionality necessary to explore it. Brinkhoff (2000) explores the server and client support required for efficient map serving on the web including multiple sorting and look-ahead fetching, while Wang and Jusoh (1999) discuss the data integration aspects. The next-generation markup language called

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Extensible Markup Language (XML) can be extended so that developers can add support for new data types such as those required to support both multimedia and virtual georepresentations. XML will also facilitate the adaptation of the web page content to the kind of device that is displaying the content. Support for geo-representations will also be found in the Scaleable Vector Graphics (SVG) format for web pages, and in the geoVRML extensions of VRML97 (Rhyne 1999). Virtual reality GIS Virtual reality GIS have been developed to allow the creation, manipulation and exploration of geo-referenced virtual environments. Fairbairn and Parsley (1997) described an early virtual geo-representation using VRML modelling of the University of Newcastle campus in north east England. Most of the virtual reality GIS have been developed for desktop platforms, although the Virtual GIS Room used immersive techniques (Neves et al. 1999), and the Internet GIS for London used a virtual reality theatre (Batty et al. 1998). Raper, McCarthy and Williams (1998) used the Sense 8 WorldUp platform to develop a four-dimensional virtual environment using geo-referenced terrain data and moving vehicles. The virtual geo-representation was created by the export of a TIN surface model from GIS and its conversion into an indexedFaceSet format terrain using geographic coordinates. The VRGIS system consists of a model window for interactive access to the virtual environment and a map window for the display of a moving map. The map window displays an arrow symbol to display the location and orientation of the user in the virtual environment. Vehicle models can be introduced into the virtual environment with geographic behaviour that defines their location and movement as plotted on the map. McCarthy (1999) showed how the VRGIS system could display in real time each triangular fece directly below an aircraft moving over the surface of the terrain in the virtual environment. Moore, Dykes and Wood (1999) outlined the architecture of the traVelleR and Urban modeller systems implemented as Java applets communicating with VRML97 models through the script node interface (Brutzman 1998). TraVelleR is designed to support the interactive exploration of a virtual geo-representation draped with imagery by providing an adjacent map interface with orientation and query tools. The traVelleR virtual environment is scriptable so that pre-defined tours around the virtual environment can be offered to users. Verbree et al. (1999) outlined the KARMA VI system that is implemented in Sense 8’s WorldToolKit and closely integrated with the Spatial Database Engine of the GIS Arc/Info. This architecture allows users of Karma VI to manipulate objects within the virtual environment and to commit the changes to the spatial database. Brown (1999) proposed the use of a virtual environment as an interface to geographic information. The Virtual Reality User Interface (VRUI) is presented on a web page with one frame containing a VRML97 model displayed with the CosmoPlayer plug-in and another frame describing the content of the model. A Java applet controls the imagery draped over the VRML model and allows the user to query the geo-representation. As the user moves around the VRML model the different types of geographic information available for each location are reported to the user.

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Some work has also been carried out on collaborative work within virtual environments. Batty et al. (1998) describe the use of the Alphaworld virtual world server for experiments in urban planning where ‘visiting’ avatars can give their opinions on the constructions they ‘see’ there. This methodology has been adapted for the purpose of collaborative planning in the Wired Whitehall project (Doyle, Dodge and Smith 1998). Gong and Lin (2000) discuss the different senses of space employed in a virtual world server including Internet, data, graphics, cognitive and social spaces and describe the VirtualPark prototype. Real-time GIS With the availability of real-time positioning systems and cost-effective mobile telecommunications, it has become possible to develop real-time GIS that monitor, transmit, record and analyse the movement of mobile agents such as vehicles, people or animals. Laurini (2000) presented a typology of ‘telegeomonitoring’ architectures, dividing them into centralised (mobile agents communicate through a single control centre), co-operative (mobile elements communicate with each other directly) and federated (mobile agents are communicating with multiple control centres) types. However, real-time GIS can also include location-based services, where a moving agent receives information depending on its location, and real-time ranging systems. Real-time GIS have been developed for transportation, monitoring, geographic messaging services, tourism, and ecological applications. In transportation many organisations need to monitor the position of their vehicles for scheduling or safety reasons. Each mobile agent transmits positioning information to appropriate control centre(s), where it is entered into a database of timestamped positions. The database can be summarised by static geometric primitives or cleared at specified intervals. Some applications can monitor the proximity of the mobile agents to specified locations or advise on alternative routes based on traffic reports (Laurini 2000). Real-time GIS have also been used in monitoring applications where positioning, video and ranging systems must all be integrated on a common timebase (Raper, McCarthy and Williams 1998, McCarthy 1999). Such integration requires the standardisation of event timing by calculating the intrinsic time delay (latency) between the world time of measurement and database time of storage. Once the latencies of the different sources are determined, the real-time data can be re-based on a common timeline. Figure 5.4 shows an error analysis of a real-time multimedia GIS from McCarthy (1999) in which latency errors are shown to overwhelm sensor and data processing errors. Real-time GIS are also being used for geographic messaging services (GMS), where information is sent to agents on the basis of their location. Imielinski and Navas (1999) outlined architectures for the implementation of GMS, including geographic routing where a message is forwarded to geographically appropriate wireless transmitter nodes, and mobile clients pick it up when they enter the service area of the node. In tourism applications, a number of real-time GIS have been developed to provide a location sensitive information service, where details of attractions are given to users as they approach, for example in the GUIDE project Jose and Davies 1999). The GUIDE project defined a hierarchy of locational ‘contexts’, each with a geographic footprint, such that

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location based servers provide information only to appropriate contexts. Mountain and Raper (2000) developed the Location Trends Extractor (LTE) for the user to automatically define their own dynamic ‘contexts’ such as daily envelopes, by data mining their spatio-temporal behaviour. Real-time GIS architectures have also been developed for ecological simulations. Westervelt and Hopkins (1999) outline a method of high level coupling between the GIS GRASS and a modelling system (IMPORT/DOME) that permits the simulation of agent movement over terrains and their consequent social behaviour. This individual-based modelling architecture allows the use of both static and dynamic terrains as a backdrop to the simulation of animal movement. Bian (2000) developed an object-oriented system for representing mobile objects in an aquatic environment. Rodrigues (1999) outlines the architecture of a real-time GIS for the simulation of vehicle decision-making and behaviour in car parks using an intelligent agent-based approach.

Figure 5.4 Latencies in a monitoring system

Geolibraries The commodification of geographic information envisaged by Openshaw and Goddard (1987) has now generated a massive global collection of data covering: • base mapping of topography; • imagery, photography, videography; • elevation and terrain data; • environmental information; • census, electoral and government information;

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• property and utility facilities. However, these collections of data are highly heterogeneous in organisational and storage terms, making it difficult for a potential user to access and integrate the data with which to create new geo-representations (Larsgaard 1998). Kacmar et al. (1994) outlined the design of a digital library architecture for spatial datasets. Goodchild (1998) has argued that these data collections should be structured for access in a distributed network of ‘geolibraries’. The key practical barrier to the creation of the geolibrary is a working definition of the fundamental unit of resource. Goodchild (1998) made a case for distinguishing georeferenced information (any phenomenon that can be located geographically), from geographic information (descriptions of geographic configurations). The former category is much easier to implement in a geolibrary as simple geometric data types can be used for georeferencing; this approach implies the extension of traditional library indexing models such as US MARC (z39.2). The latter category is more difficult to implement as it requires the storage of a wide range of geo-representations. Such geo-representations cannot be handled in library indexing models and require interoperable geographic data architectures. Library indexing models depend on metadata, i.e. data about data, which has not traditionally included much support for geographic referencing (Holmes 1990). The simplest approach to georeferencing has been the use of gazeteers or geographic thesauri, which link place names to geographic coordinates (Brandt, Hill and Goodchild 1999). Woodruff and Plaunt (1994) described a scheme for the automatic extraction of place names from text documents to allow their indexing by gazeteers. Storage of geometric data to describe geo-representations implies the extension of library indexing schemas, for example by storing bounding coordinates or representative geometric data for a geophenomenon. The US standard for information retrieval (z39.50) has been extended by the GEO profile to handle spatial and temporal referencing and queries on topological and metric criteria. Nebert (1998) discussed forms and hypermap approaches to defining a search and the results of the query as a download or metadata about the dataset. Dublin Core has also been considered as a standard metadata form. Duane, Livingstone and Kidd (2000) have shown how environmental modelling output can be described and queried by using the National Center for Supercomputing Applications Hierarchical Data Format (HDF). A wide range of geographic metadata libraries have been developed; Larson (1997) reviews and summarises a number of systems. Walker et al. (1992) described the Midlands Regional Research Laboratory spatial metadatabase and the free text methods of querying it using spatial and temporal constraints. The MEGRIN project is a consortium of European national mapping organisations who have worked together to create a catalogue of geographic data available on the web. The European Spatial Metadata Infrastructure (ESMI) project is developing a distributed spatial metadata catalogue. In the USA the Federal Geographic Data Committee (FDGC) have developed a Content Standard for Digital Geospatial Metadata (CSDGM) to provide the framework for information retrieval from the Federal Geospatial Data Clearinghouse. In Portugal, the National Centre for Geographic Information co-ordination agency (CNIG) has developed a metadata library called the National Geographic Information System (SNIG) that

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structures geographic metadata produced by government agencies. In the UK the National Geospatial Data Framework (NGDF) has developed a metadata query service (‘ask Giraffe’) capable of searching federated government geographic databases. Bishr and Radwan (2000) outline the software architecture options for the development of geospatial data infrastructures (GDI). Yuxia, Zhengyi and Jianbang (2000) discuss solutions to the problems of poor semantic interoperability in geographic metadata libraries using metadata mediation. By contrast to the creation of metadata libraries, the storage of the full range of georepresentations has implied the implementation of geolibraries in distributed databases on the digital library model (Bawden and Rowlands 1999). The first major attempt to establish a geolibrary was the ‘Alexandria Project’ which was established by a consortium of US libraries, research groups and industrial corporations (Smith and Frew 1995). Users of Alexandria could access, browse and retrieve specific items from the data collections of the library by means of web-based interfaces that integrated visually-based and text-based query languages. The Alexandria Project initially included access to maps, orthophotos, AVHRR, SPOT and LANDSAT images and geodemographic data for California. The Microsoft Terraserver project also showed how geo-representations (largely imagery) could be served through a hypermap interface. NASA has also developed the Data Information and Access Link (DIAL) server to support metadata searching of the heterogeneous spatial databases and downloading of spatial data through the Earth Observing System (EOS) Data Gateway (EDG). DIAL supports the HDF metadata format and interfaces to Open Database Connectivity (ODBC) and Java Database Connectivity (JDBC) compliant data sources, which support the EOS VO interoperability protocol for catalogues. Goodchild (1998) suggested that the geolibrary should consist of browser, basemap, gazeteer and collection components. While the collections in a digital library can be considered to consist of ‘information bearing objects’ (IBO), in a geolibrary the atomic information entities corresponding to geo-representations have been termed ‘geographic information bearing objects’ (GIBO) by Goodchild (1997). Raper (1999) argued that information ontologies defined by processes of recording, ordering, signification and control in society are emerging that will determine the precise semantics of the GIBO. Goodchild (2000) noted that geolibraries must also take account of the changes that take place in GIBOs as they pass through the collection, structuring, transformation and dissemination processes of the data lifecycle. Geographic metadata must reflect ‘truth in labelling’ so that metadata records function as a form of communication between the producer and the user about lineage and error. Such considerations will become more complex when geolibraries are seen not just as production environments but as sharing architectures such as the Hubserver developed by Dykes, Moore and Wood (1999). Larson (1997) outlined a proposal for the design of a geographic information retrieval architecture supporting point-in-polygon, region, distance/buffer zone, path and multimedia queries. Larson developed a geographic browser toolkit based on the Sequoia 2000 Tioga architecture for information browsing, supporting known item searching and probabilistic retrieval based on document contents.

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MULTIDIMENSIONAL EXPLORATION OF GEOREPRESENTATIONS Given the availability of multimedia and virtual geo-representations, architectures for their structuring and their integration with information infrastructures, many new systems for their multidimensional exploration have emerged over the last decade. These systems extend the nature of geo-representation and offer new scope for the exploration of spatial multimedia and virtual environments. A selection of applications allowing multidimensional exploration in hypermedia spatial databases and visualisation/animation is surveyed in the following sections. Hypermedia spatial databases When multimedia/hypermedia GIS are used as the front-end to a heterogeneous database of geo-representations, the combination can be termed a ‘hypermedia spatial database’. Before the arrival of multimedia data support in web pages (c.1996), the creation of such databases usually relied upon hypermedia authoring tools such as Hypercard/Supercard, Toolbook or Microcosm. Recent web-based hypermedia spatial databases have tended to use javascript embedded in HTML for development. Hypermedia spatial databases typically contain multimedia geo-representations that need to be accessed by geographic criteria. This requires the ‘typing’ and naming of geographic abstractions made from sets of information elements, which may be aggregated into collections of higher level abstractions in the sense of the HAM model (Campbell and Goodman 1988). An example of this approach would be a database of tourist information in which museums, historic buildings and parks (with their component information elements) are typed as ‘attractions’ and aggregated into tours (Buttenfield and Weber 1993). Such abstractions can be transitory, such as the one-off route of a special road race like a marathon. Using this approach hypermedia spatial databases have been created and explored for a variety of educational, planning, tourism, environmental and facilities management purposes. Perhaps the earliest hypermedia spatial database to be developed was the Domesday System based on BBC microcomputers and the analogue Phillips LaserVision discs (Rhind et al. 1988). The Domesday system was accessed by map gazeteers or tours and contained a huge number of multimedia geo-representations relating to population, employment and environment. Lewis and Rhind (1991) demonstrated how hypermedia interfaces could be constructed to provide new forms of access to the data on the Domesday LaserVision discs after the BBC microcomputer became obsolete. Multimedia encyclopedias such as Encarta from Microsoft and the New Grolier Multimedia Encyclopedia (NGME) have also incorporated multimedia geo-representations since the early 1990s. DiBiase (1999) showed how the multimedia geo-representations of the NGME were planned with respect to the required interactive exploration functions for the instructional objectives. Another educational application of the hypermedia spatial database is the digital atlas (Hocking and Keller 1992). Al-Faraj (1998) suggested that four generations of digital atlas could be identified. Firstly, there were systems replicating the static format of the

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paper analogue, such as the Electronic Atlas of Arkansas, released in 1986. Secondly, there were systems with interactive control over map display and gazetteer look up facilities. These included the electronic atlas of the North American French-speaking communities (Raveneau et al. 1991) and the National Atlas Information System of the Netherlands (Koop and Ormeling 1990), both developed using Hypercard. Thirdly, systems offering interactive cartography were developed, such as the cdv tool for census data access developed by Dykes (1996), and the system developed by Fonseca and Câmara (1997) to explore planning-related multimedia geo-representations. Fourthly, web based atlases delivered on the web to user’s specifications have been developed, such as the National Atlas of Switzerland (Spiess and Richard 1997) and the Descartes system (Andrienko and Andrienko 1999). Using this classification scheme exploration can be seen to have evolved from the simple following of authored hyperlinks to the interactive specification of the user’s own computed hyperlinks which generate customised geo-representations. Another common motivation for the development of a hypermedia spatial database has been the need to visualise the environment for planning purposes, as in the following cases. Camara et al. (1991) described Hypersnige, which was developed in Hypercard for the exploration of regional planning information by the Centro Nacional Informação Geografica (CNIG), Portugal. Parsons (1992) described the London Covent Garden explorer in Hypercard, which used an aerial photo hypermap index annotated with points of interest which are then illustrated by animation or video if activated. Ertl, Gleixner and Ranziger (1992) described the Move-X system, which was designed to merge video footage of vacant sites with architectural models and GIS data. Grüber and Wilmersdorf (1997) developed the three-dimensional CyberCity hypermedia spatial database of the built urban form in Vienna. Shiffer (1999) described a Level of Service Representation developed using multimedia geo-representations of traffic movements and volumes through intersections accessed through a web browser. One of the most ambitious hypermedia spatial databases was the ‘Great Cities of Europe’ (GCE) system developed as part of the European Union COMETT programme (Polyorides 1993). The GCE contained georeferenced planning information on a number of European cities organised by city, theme and image collection. The thematic information was accessed by a thesaurus while the city information was accessed from a map base. The GCE was based on the multimedia GIS architecture developed by the University of Patras and Exodus Multimedia, which uses Toolbook extended with C++ and integrated with the Windows multimedia extensions. It was delivered with data for 29 European cities on CD-ROM. These planning applications of hypermedia spatial databases have attempted to familiarise users with proposed developments through exploration of the geo-representations. However, typically the technical barriers to use have prevented their widespread use: Shiffer (1995a) found that a technically competent ‘facilitator’ was needed to ensure productive use in public enquiry situations. Tourism applications have also made wide use of hypermedia spatial databases. Mogorovitch et al. (1992) described an approach based on the integration of Arc/Info with videodisc images and video for tourist planning applications. The user could interactively access points of interest on the map and see images and video for that feature, search for all occurrences of a particular type of tourist sight, or they could plan

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tourist routes. Blat et al. (1995) described the creation of the PARCBIT CD-ROM, which contains a large quantity of tourism-related data for the island of Mallorca. The user is presented with various methods of structured browsing which tests conducted on users showed had considerable time advantages over traditional approaches. Al-Faraj (1998) developed a hypermedia spatial database for Kuwait using javascript to customise web pages, which had distinct use modes of use for students, citizens, business users and tourists. Hypermedia spatial databases have also been used in facility management applications. Green and Kemp (1993) described the development of a pipeline management system developed in Toolbook on the PC which integrated a map base showing the pipeline at various different scales with detailed photographs (aerial and terrestrial) of the pipeline route. State (1993) developed a railway track information system based on video footage of the line and trackside equipment. By integrating inertial navigation systems with the video footage the distances were exported to Arc/Info and stored with details of the trackside equipment. Craglia (1994) summarises work by Aurigi to develop a hypermedia spatial database for the public transport system of Florence, which is implemented by integration between Hypercard and the GIS MapGrafix. Giertsen, Sandvik and Torkildsen (1997) developed an oil pipeline database linked to terrain data for Western Norway. Given the wide variety of multimedia geo-representations created for environmental management, many applications of hypermedia spatial databases have been developed for multidimensional exploration. Fonseca et al. (1995) and Fonseca and Câmara (1997) developed a system in Supercard which integrated a hypermap with a hypermedia spatial database for environmental impact assessment at the former Expo’ 98 construction site in Lisbon. The user could browse and overlay images, maps and video of the site and morph one site design into another to visualise the differences between alternatives. Raper and Livingstone (1995b) described the design and implementation of a spatial data explorer called SMPviewer which allows the user to extract interpretations of images and maps digitised on a hypermap using the mouse. Simmons, Hall and Clark (1992), Simmons (1993) described a hypermedia spatial database developed using Microcosm linked to the SPANSmap GIS for an environmental management system. Romão et al. (1999) presented the CoastMAP application for visualising coastal change using a hypermap linked to other databases, which is overlaid with symbols representing change. The CoastMAP interface allowed movement along the coast through a seamless aerial photography mosaic at one of several levels of image resolution, while additional contextual information was displayed alongside the imagery. Visualisation, data mining and animation of geo-representations The traditional way to visualise representations of the world over geographic spaces is the map. Cartographic processes have been developed over centuries to conceptualise, select, classify and symbolise geo-phenomena on the map (Robinson et al. 1995). However, the new opportunities offered by computer visualisation and geographical information systems have led to profound changes in cartography. Fisher, Dykes and Wood (1993) suggested that there have been three main consequences of these

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technologically driven changes: firstly, the availability of new visual variables, secondly, new computational possibilities for representation and transformation, and thirdly, increased levels of interaction between the user and the map. The implications of these changes have been far-reaching as the map production of traditional cartography has been transformed by the pattern exploration of geographical visualisation (GVIS). Thus, Harley (1989, 1990) deconstructed the map by asking who made maps and why, a point taken up by Dorling and Fairbairn (1997). DiBiase (1990) reconceptualised mapping as part of the scientific process, distinguishing between the visual thinking of the private realm and the visual communication of the public realm. MacEachren (1995) argued that GVIS should be concerned with techniques to allow gestalt understanding of multidimensional patterns in real time. These techniques included recognition and noticing in maps and relationship identification in dynamic models. However, Kraak (1995) pointed out that while the new technologies of presentation have undoubtedly assisted visualisation, there have been few developments which codify the exploration and analysis of new multimedia data types in the context of the theories of semiology and the ‘grammar’ of cartography. Work on the multidimensional exploration of geo-representations has focussed on developing Exploratory (spatial) Data Analysis (ESDA) ools (Hearnshaw and Unwin 1994, McEachren and Taylor 1994). Such tools enable users to focus on re-basing the information by time, scale or unit of reporting and to attempt exploratory analysis of the relationship between spatially and temporally distributed variables. Exploratory (spatial) Data Analysis has been realised for spatial data through systems such as REGARD (Haslett, Willis and Unwin 1990) and Exploremap (Egbert and Slocum 1992). Unwin (1996) identified the problems of exploring spatio-temporal data series such as the large number of cases and variables, the difficulty of identifying time lags in associations and the complexity of flows in complex systems. Pictorial simulation models for spatial datasets such as those defined by Câmara et al. (1991) over a simple raster offer powerful alternative tools for spatial analysis using multimedia primitives. Gluck (2000) used sonification methods to facilitate ESDA based on augmented seriation. Multidimensional exploration of geo-representations has recently been reconceptualised in terms of data mining and knowledge discovery in databases (KDD). Such approaches call for the selection of appropriate datasets from a data warehouse, their data mining for knowledge discovery and the analysis of the extracted patterns. Spatio-temporal data mining involves the development of multidimensional knowledge discovery strategies for characterisation, classification, association and clustering operations. Han, Koperski and Stefanovic (1997) described the Geominer system, which uses KDD techniques to query patterns in a multidimensional data cube, although Lee and Kemp (2000) warn that such on-line analytical processing (OLAP) must take account of the modifiable areal unit problem. Andrienko, Jankowski and Andrienko (2000) developed a spatial data mining tool using a Classification Tree algorithm for the Descartes dynamic mapping system and integrated it into the Kepler data mining architecture. Gaheganetal. (2000) developed the Java-based GeoVISTA studio as a visual approach to abduction, by producing hypotheses that generate classifications). MacEachren et al. (1999) attempted to bridge the cognitive approach of GVIS with the analytical approach of KDD by facilitating the application of GVIS ‘interaction

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forms’ (e.g. colourmap manipulation) with KDD representations (scatterplots, threedimensional views and parallel plots). These techniques can be seen as part of a wider set of information searching models (Wilson 1999), in which the user’s cognitive space plays an important part (Ingwersen 1996). In developing an automated query processing system for tropic cyclone monitoring, Yuan (1998) showed that all these operations are critically dependent on the form and richness of spatio-temporal representation employed. Gahegan (1999) argued that further GVIS progress requires faster rendering, understanding the visual stimuli behind operations like ‘noticing’, reducing the complexity in the assignment of data attributes to visual properties, and improving the effectiveness of virtual environments as exploratory settings. The exploration of multidimensional representations can also be carried out using dynamic map displays, especially those organised by time (Dorling 1992). Shepherd (1995) classified the sources of time variation in visualisations by the temporal nature of data input, the dynamism of symbology, the change of observer viewpoint, the behaviour of visual elements and simulation characteristics. Shepherd argues that the extension of the graphical sign system of Bertin (1983) involves the use of four-dimensional displays incorporating visibility variations, locational change of symbols, and the growth and decay of displays. Giertsen, Sandvik and Torkildsen (1997) proposed an open architecture for dynamic visualisation based on Open Inventor and produced animation sequences by generating dynamic scene components viewed by (moving) virtual cameras. A wide range of different approaches to dynamic visualisation have been employed. Openshaw, Waugh and Cross (1994) suggested that animation of a temporal map series could be used to speed up time or to re-order the data within specified time periods for applications ranging from cancer cluster analysis to crime incidence. Weber and Buttenfield (1993) described a cartographic animation of average temperatures for the USA over the last 100 years that could be run in either direction in time. Schwarz von Raumer and Kickner (1994) show how Toolbook and Arc/Info can be linked together to show visualisation of pollution levels in real time. The Centennia interactive historical atlas of European history from Clock Software presents spatial animations of changing political boundaries allowing movement forward and backwards through time and generalisation of the hierarchical level of the political units shown. Koussoulakou (1994) presented an animation of air pollution change in which arrows representing wind magnitude and direction changed dynamically through time. Jomier, Peerbocus and Huntzinger, (2000) offer a classification of the ways to visualise spatio-temporal change.

CONCLUSIONS This chapter has classified the representational nature of the new multimedia and virtual geo-representations and examined how they can be explored. Ontologically, these georepresentations are richer than three-and four-dimensional geometry as they share the conceptualisation process between developer and user through interaction. Virtuality engages users in exploration and allows them to define their own geo-phenomena in

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multidimensional spaces. Hypermedia structuring then allows the association of geophenomena into semantic networks using both exploration and design approaches without the constraints of formal data modelling. Such applications may imply a greater focus on information representation techniques in future (Raskin 1999). However, epistemologically these new geo-representations pose further questions. MacEachren (1995) argues that ‘GVIS represents a substantial change in emphasis from maps as a presentation tool to maps as part of a thinking-knowledge construction process’ (p460). Implemented in this sense GVIS is a highly effective source of hypotheses generation about specific relationships. However, as Petch (1994) noted, such hypotheses are heavily context dependent, and the patterns noted may be partial or local. If, as many social theorists believe, there are no regularities of behaviour to be found in the world, then perhaps context-dependent outcomes are useful ends in themselves if they are documented and published.

Part II INTRODUCTION

Figure II.1 Location of Scolt Head Island and other sites in part II

In part I of this book a methodological platform has been built for the geographical information scientist. The central argument was that there is a coherent and valid rationale to the use of spatial and temporal representation, despite the various critiques. The representational apparatus of geographical information science was outlined and it

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was shown how recent theoretical and technological advances have made it possible to improve the richness and extend the modality of this apparatus. In this section these arguments are illustrated and exemplified. In the following chapters short case studies are presented to show how the new forms of spatial representation outlined in part I can be used. For practical and theoretical reasons these case studies all use the same location, that of Scolt Head Island on the North Norfolk coast of eastern England. The practical reason is that 10 years of research into coastal geomorphology, coastal sedimentology, coastal simulation modelling, airborne remote sensing and environmental management during the 1990s has led to the accumulation of a huge and diverse archive of georeferenced data for this location. The theoretical reason is that coastal environments present profound challenges to the ‘standard model’ of twodimensional spatial representation as they lack a comprehensive ‘built structure’ to provide identity criteria, they are chaotic and highly dynamic, and they pose complex interdisciplinary management problems. The use of a common location for all the case studies also permits the creation of a kind of representational scrapbook in which a wide range of views of the environment and society of the area can be placed. Such a wide range of views also offers its own argument for representation, as the very diversity on show demonstrates the scope of current methodologies. The potential use of these representations offers further evidence of the role that multidimensional representation can now play when they include: public enquiries, environmental impact assessments, field trip planning, nature conservation education, coastal engineering decision support and tourist management. Hopefully, in a small way this section of the book can also help write a turn-of-the-Millennium geography of a part of England’s rural coastline, highlighting some the issues that face geographers, biologists, engineers and residents of this area. The geography of the North Norfolk Coast Scolt Head is a barrier island consisting of a line of sand dunes backed by salt marshes which forms part of the low-lying N.Norfolk coast (figure II.1). It experiences a westerly longshore drift of sediment into a spit (sandy bar) at the western end reflecting the tidal circulation and the dominant north east wave energy in this area of the southern North Sea. Research into the origin and development of this coast in general and the island in particular has been continuous since the beginning of the century—a monograph by Steers (1960) gives a comprehensive introduction. The model of evolution for Scolt Head developed by Allison (1985) suggests that the island developed from a beach ridge during the Holocene marine transgression, and that since its inception has extended 7km to the west as a result of longshore drift. This development has taken place as a repeated cycle of extension, stabilisation and incorporation of recurved spits at the westerly end of the island. There are now 20–30 recurved spits of this kind extending southwards from the main ridge (figure II.2). Each of these spits encloses a salt marsh of westerly decreasing elevation, reflecting the progressively more recent initiation of marsh mud deposition when protected from wave attack by the spit. The initiation and development of these spit bars is, therefore, a crucial determinant of the development of the salt marshes which in turn provide coastal protection and calmer waters to residents and water users.

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The dynamic form of these spits reflects a balance between wave and tide energy in the short term and relative sea level change in the medium and long term. Since the tidal channels at either end of the island are barriers to longshore sediment movement the spits act as reservoirs for coastal sediments. Hence, spits and bars marginal to tidal channels may be both sensitive indicators of aggregate coastal change and reservoirs of sediment whose budgets may be of considerable importance to the management of the adjacent coastline on an annual and decadal scale.

Figure II.2 Map of Scolt Head Island in 1990, showing gravel spits in black, sandy dunes in stipple and marshes in white within the outline

A coastline such as this one poses many management issues for fanners, engineers and conservationists. If relative sea level rise continues then the question of how the coast will respond is of considerable importance, especially since some of the coast to the west of the island has been stabilised by engineers and some marshes south of the island has been reclaimed by land owners. So although the ‘natural’ response will be for washover and dune migration inland during storm surges in some places on the coast away from Scolt Head this process is being resisted. The aim of the research being carried out at Scolt Head is to provide the holistic understanding of the natural processes that will allow good management decisions to be taken. Potential visitors should note that Scolt Head is an isolated National Nature Reserve separated from the mainland by dangerous tidal channels. Local advice from English Nature wardens or the harbourmaster should be sought before attempting a visit.

CHAPTER 6 Hypermedia geo-representations for coastal management CONTEXT Coastal environments are amongst the most dynamic in geomorphology and the most troublesome for coastal managers (Carter 1988). This is because their landform and process regimes are characterised by rapid change over the short term (days and weeks), making them difficult to predict and manage over the medium term (periods of months and years). This dynamic behaviour is determined by the inherent variability of the forces driving coastal processes, meaning that the whole shape of the coastline can be rapidly changed, especially under storm conditions. This is especially true on low depositional coasts and in estuaries that are characterised by beach barriers, dunes and salt marshes, as in both cases the unconsolidated sand and gravel that makes them up is particularly mobile. Around the low depositional coasts of the southern North Sea in eastern England and the north-west of the Netherlands, large tidal ranges and frequent storms mean coastlines exhibit complex spatial and temporal behaviour. In addition, world-wide sealevel rise and the various forms of human intervention such as sea wall construction, land reclamation, and dredging each pose complex environmental problems in themselves. The dynamic nature of the coastal processes and landforms is paralleled by the diverse interests of the agencies and stakeholders who make the coast a social, political and economic battleground. Even a stable coast sees a conflict between economy, conservation and leisure interests over access to the shoreline, use of the sea’s resources, protection from flooding, and preservation of biodiversity and amenity. A changing coastline sees stakeholders and agencies of local and central government battle over the impacts of change on existing interests or potential new ones. With the acceleration of change driven by sea level rise has come the realisation that ad hoc decisions by individual agencies are not effective and a holistic approach is needed. Accordingly, using regular monitoring data, scientific studies, and evidence from interested parties, Shoreline Management Plans have been drawn up by the UK government to provide a framework for coastal management and planning (Cooper et al. 2000). Information and education must be at the heart of coastal planning as the dynamic nature of the coast means that a coastal engineering solution designed for the short-term can fail quickly if it is not designed well. The information needed to address holistic coastal management objectives such as whether to allow the coast to retreat takes a variety of forms, ranging from documents and tabular data to profiles, maps, imagery, surfaces and models (Raper et al. 2000). Storage of this heterogeneous collection of geo-representations poses challenges for most data models and database structures available and so data types are typically stored

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separately and brought together for individual studies. This set of geo-representations can be complex to understand and voluminous in nature, yet their holistic understanding is essential to policy, decision-making and learning. One approach to this problem is to use the hypermedia model to structure the data holdings and to provide an access model (see chapter 5). This chapter discusses some experiments in coastal data management using a hypermedia approach.

EXPERIMENTS IN HYPERMEDIA GEO-REPRESENTATION Hypermedia geo-representation offers new ways to access data, the means to annotate datasets, multimedia data storage and multidimensional exploration of datasets. These experiments have all been built using the North Norfolk coast datasets described at the beginning of Part II. Scolt Multimedia Project The Scolt Multimedia Project (SMP) aimed to provide a storage architecture and exploration metaphor for multidimensional geo-representations (Raper and Livingstone 1995b). The SMP took the form of a very large hyperdocument covering the socioeconomic and environmental evolution of the nature reserve. Implemented as a Hypercard stack, the hyperdocument consisted of heterogeneous nodes with socioeconomic and environmental resource data with spatial and temporal referencing. The system was capable of storing a wide range of data including statistical data, text, graphics, terrestrial photography, video, maps, air photos and other imagery. Primary access to the nodes was by selecting a resource type in an appropriate cell in a time-space diagram (a ‘zone’), that acted as an exploration metaphor. Figure 6.1 shows the interface and some specimen resources. This diagram defined a matrix of time/space zones that were chosen to reflect a progressive sequence of four time periods. These were: today, the turn of the century—100 years ago, the last millennium—1000 years ago and the end of the Ice Age—10,000 years ago); and, three different spatial scales defining different extents of the North Norfolk coast. Selection of the resource type for a time-space zone took the user to an index node where a comprehensive listing of qualifying resources was found for that timespace/resource combination. This index was implemented as a hypermap showing the appropriate outline map for the zone. Footprints, denoting available information, were located on this map according to their position and covering the area over which they actually extend. The footprint also acted as a hyperlink to the lowest level ‘basic’ nodes in the hierarchy and their resources. At this level the user could also create and position their own footprints on the time-space zonal hypermap and link them to any other resource to which they could navigate in the SMP. These connections formed a web of links corresponding to an ‘annotation structure’ which a user can re-access each time they use the system by navigation (McAleese 1989). Given the lack of entity integrity in a hyperdocument, nodes could be placed in one or more time-space zones as required, making for multiple links between basic nodes and zones.

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Clicking on a node footprint on a particular time-space zone hypermap linked to the basic nodes. If the basic node contained a map, image or orthophoto then the georepresentation was also treated as a hypermap. In the SMP hypermap geo-representations were opened through a separate module called the SMPviewer which provided some GIS functionality. Unlike the time-space zone hypermap in the SMP database, which is designed only to facilitate access to information, the hypermaps accessed by the SMPviewer are designed to support a full range of spatial functions including annotation, measurement, analysis and output.

Figure 6.1 The time-space diagram in the SMP

When accessing a geo-representation stored on a basic node in the SMP using the SMPviewer, the control and tool palettes are opened (figure 6.2) and any spatio-temporal metadata on the resource is read. These palettes permit the annotation, extraction and output of any user-defined features in vector form. This is achieved by on screen digitising using the mouse. The geometry defined is stored as a hypertext object with spatial and temporal attributes, rather than in a database table. Such user-created georepresentations were referred to as hypergeometry objects and were stored in the industry-standard Arc/Info ‘ungenerate’ data format. An experimental java application called GIS-scape was developed to provide SMPviewer functions on a generic software platform (Raper and Livingstone 1996). While this implementation was application-driven and based on a ‘closed’ hypermedia platform (Hypercard), the implementation is capable of wider application. The SMP offered overlapping and flexible access methods based on time-space metaphors, browsing and searches, it allowed users to save their paths through the semantic net of

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hyperlinks, and it offered users the chance to extract their own interpretations from the information resources. Six years after SMP was developed it is now possible to envisage a web-based interface linked to a (meta)database using a web portal servlet architecture to deliver the basic nodes to a client, and a java-based version of SMPviewer such as GIS-scape.

Figure 6.2 The use of the SMPviewer for the extraction of geographic information from imagery

The SMP design offers coastal management a way to index the vast amount of monitoring information in such a way that data from similar time-space scales can be readily browsed and annotated. Hypermedia interfaces are also easier to use than conventional applications making the SMP design suitable as a foundation for a public access information application. Multidimensional organisation of coastal georepresentations would promote a more historically aware view of the process of coastal planning and highlight the long-term cycles in coastal processes. Annotation of historical maps and images could also allow the local community to contribute its knowledge to the collection of geo-representations that will be considered during policy-making. Hypermedia functions in GIS Desktop GIS now support limited forms of hypermedia functionality, such as the hyperlinking of vector geometry to external and multimedia data types. This allows the implementation of a hypermap model in GIS, although it is not usually possible to

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semantically structure the external and multimedia data. The hypermap model is a suitable basis for coastal data management where the data types are highly heterogeneous but can be indexed spatially within a coastal corridor. Romão et al. (1999) developed CoastMap using this approach. In effect the GIS is used as a geolibrary index to the available geo-representations and georeferenced information. Multimedia geo-representations such as photographic images and videos can be linked to geometric data stored in a GIS using pointers containing the path to the storage location. Selecting a piece of hyperlinked geometry causes the geo-representation to be displayed using operating system specific applications. Plate 6.1 shows a 1:50,000 scale Ordnance Survey topographic map of the North Norfolk coast around Brancaster in Arcview GIS. The points plotted on the map represent the location of the photographic images: one was taken at the western end of Scolt Head Island, while the other shows the village hall. Other desktop GIS such as GeoMedia and Maplnfo have similar capabilities. GIS can also link to external database tables containing geometry. Plate 6.2 shows an SQL connect operation using ODBC in Arcview GIS, which links to a table in a Microsoft Access database containing geometric and attribute data for coastal landforms. The data in the Access database can be plotted on an outline map in Arcview GIS with a predetermined symbology, so that coastal management priorities can be visualised alongside process classifications. In the application shown in plate 6.2, a coastal metadatabase has been constructed in Microsoft Access, in which coastal spit and ness landform locations are linked to their source, dataset type and classification. By using Arcview GIS as a front end to this data, connections between features and a wide range of documents and images can be managed and queried. By using map views of different scales both overview and site-specific coastal management data can be accessed and hyperlinked. Web GIS architectures are also now emerging as potential hypermedia interfaces to geo-representations such as coastal management data. By using a plug-in GIS such as MapGuide, or a downloadable java applet, the GIS front end can be embedded in a web page and viewed with a browser. Choices made using the client interface can be sent within an HTTP universal resource locator (URL) to a server process such as a java servlet, which then can process the user queries. The resulting geo-representation or document can then be returned to the browser for viewing. This architecture makes it possible to develop a multidimensional hypermedia semantic network based on hyperlinks, where individual nodes can be documents or geo-representations that are customised in real time by calls to the server from the client. This kind of hybrid hypermedia and GIS architecture is a suitable platform for delivery of information within organisations via an intranet, or to the public via the Internet. Panoramap hypermedia environment Panoramap, developed for the Virtual Field Course (VFC) project in the cross-platform TCL/TK development environment, can be described as a georeferenced browser of multimedia geo-representations (Dykes 2000). Panoramap allows the user to place geometric features on a georeferenced base (e.g. map or imagery) which are linked to multimedia geo-representations stored locally or in a remote database accessed via the

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‘hubserver’ metadatabase (Dykes, Moore and Wood 1999). Each link to a georepresentation on the mapbase has a (user)-defined application for viewing it e.g. text, HTML or video. Panoramap itself displays panoramic imagery, vector polygons and GPS track data and provides interaction tools for each of these data types. In the case of panoramic imagery, the view direction and the field of view are drawn on the map base and updated as the panorama is scrolled either to the left or right. As multiple panoramas can be opened it is possible to choose panoramas that can be turned towards each other. The Panoramap georeferenced map base has a hypermap function allowing users to click on footprints placed on the map base, which link to new larger scale map bases. In plate 6.3 the 1:50,000 scale Ordnance Survey topographic map of the North Norfolk coast around Brancaster (as shown in plate 6.1) has been loaded into Panoramap and overlaid with aerial photograph footprints. The points are linked to panoramic photographic images, two of which are displayed along with their field of view. The vertical arrowheads within the images represent the positions of other panoramic images; their lengths are proportional to their distance from the current panorama location. By clicking on the arrows in the panorama, it is possible to highlight the corresponding symbol on the mapbase. When double-clicking on a selected arrowhead the target panorama opens making it possible to move step-by-step across the area of the base map. This allows the user to build up an allocentric virtual environment from multiple egocentric panoramic views (see chapter 2). Panoramap is a novel and rich form of hypermedia interface to geo-representations that has many potential applications in coastal data management and exploration. The open nature of its architecture and the cartographic design of its user interface makes it a powerful geo-representation browser. The ability to control the symbolisation of points and to shade polygons by values in attribute data files makes Panoramap a useful data integration tool. Its integration with the VFC ‘hubserver’ metadatabase also makes it a potential ‘geolibrary front end’ to stored multidimensional geo-representations.

POTENTIAL These three experiments in hypermedia using coastal management data illustrate the potential of hypermedia techniques in the structuring and exploration of georepresentations. While these applications are suited to browsing through semantic networks, there can be a poor cognitive fit between the functionality available for the exploration of hypermedia geo-representations, and therefore the user’s efficient and effective completion of any associated information tasks (Gluck and Fraser 1997). Effective task-oriented information seeking requires an understanding of the cognitive setting of the user (Dervin 1983) and appropriate information system design based on task-related information analysis (Sutcliffe 1997). These elements have been brought together in information design (Jacobson 1999). There have been few attempts to develop cognitive settings, information analyses or designs for the exploration of multidimensional geo-representations. Progress on these objectives will ensure that MacEachren’s (1995) GVIS ‘thinking-knowledge construction process’ is contextualised and underpinned by new methodologies. The most critical

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elements of this new methodology are new ontologies for multidimensional geophenomena.

CHAPTER 7 Geo-representation of dynamic coastal geophenomena CONTEXT The high rates of change in geo-phenomena at the coastline demand the use of dynamic geo-representations for their exploration using multimedia techniques. Multimedia data types offer new approaches to dynamic geo-representation through video, sound, animation and real-time monitoring systems. These systems can be termed ‘dynamic’ due to their high rates of sampling relative to the increments of change. Such high rates of sampling ensure that there is a very low probability of an unmeasured event between any two samples. Examples of dynamic geo-phenomena at the coastline are windblown dust particles or smoke, water flows and waves, vegetation growth and shifting landforms in declining order of rates of change. Human movement patterns also exhibit spatiotemporal behaviour, and can be regarded as a special case of dynamic change. The goal of dynamic geo-representation is to model continuous multidimensional identity using discrete dynamic systems so that the available concepts of change can be enriched. Dynamic geo-representation must though operate under certain representational constraints. Change must be made discrete by sampling at a specified spatial and temporal resolution. Dynamic geo-representations require a correspondence to be established between the world time of their origin and the playback time defined by the user. When dynamic geo-representation ‘filters’ the world using multimedia techniques (see chapter 5), then there can be no implicit index to the content, and queries will depend on knowledge-driven content-based indexing. When dynamic geo-representation animates geometric reconstructions using maps or models, then queries depend on the indexing of represented objects, their inter-relationships, the viewpoint and the qualitative aspects of display. The nature of change captured by ‘filtering’ and ‘reconstruction’ is subtly different in these two representational contexts.

EXPERIMENTS IN GEO-REPRESENTATION OF DYNAMIC COASTAL PHENOMENA These experiments exemplify some of the forms of dynamic geo-representation discussed above and in chapter 5. These case studies refer to Scolt Head Island or other sites in eastern England, where attempts have been made to explore the dynamic nature of coastal change using new representational forms, over a variety of timescales.

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Videometric measurement of processes Raper, McCarthy and Williams (1998) defined the term ‘videometry’ in the context of geo-representation as ‘procedures used to extract robust georeferenced measurements of the position of phenomena visible in video imagery using orientation parameters recorded at the time of acquisition’. The simplest form of this general case is orthogonal or pseudo-orthogonal viewing of a scene by a video camera. Raper and McCarthy (1994a) outlined techniques for the vertical case from aerial platforms while Foote and Horn (1999) discuss the requirements of the horizontal case for beach and flume studies of swash wave run-up behaviour. The more complex cases involve oblique viewing such as those used for coastal monitoring by Holland and Holman (1997) and Eleveld, Blok and Bakx (2000), and for target positioning (McCarthy 1999).

Figure 7.1 Wave orthogonal mapping at Far Point on Scolt Head Island

Wave processes are the most important dynamic processes in the coastal environment as they have an important influence on landform evolution. Figure 7.1 shows a digital camera image taken on November 1997 for Far Point of Scolt Head Island, showing waves breaking on the very end of the spit landform. The image was imported into the SMPviewer application (Raper and Livingstone 1995b) (see chapter 6) and annotations were made on the image to indicate the outline of the spit and to mark wave crest orthogonals close to the bar. The wave crest orthogonals clearly show the wave refraction around the end of the spit. However, this is a static analysis: using video georepresentations it is possible to record the movement of the waves as they break. Plate 7.1 shows four sequential video frames of breaking waves filmed from the air. Between frames timed at 09:06:51 and 09:06:54 the large bow shaped breaking wave in the centre moves across the frames to the right as the aircraft moves. However, the wave also

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advances on the shoreline and changes shape sufficiently to see that it is a spilling wave and not a plunging one. Such insights can only be gained from the analysis of dynamic imagery if there are no observers on the shoreline. Video imagery of dynamic environments can also be made into a strip map by playing the video through a frame matching system. Frame matching finds the overlap between successive frames, orients them together, and then adds the frames into the strip map. Plate 7.2 shows a strip map made from aerial video imagery for the mouth of the Ore River at Shingle Street in Suffolk. The way that the waves are blocked by the small intertidal swash bars is clearly seen in the static image. However, in the live video sequence the flow of the Ore River in two distinct channels can be distinguished by the interference patterns between river and waves, and approximate speeds of movement calculated. Such methods can be used to update marine charts in places where the landforms change very rapidly. Animating multidimensional landform behaviour The rapid change that occurs in coastal landforms can be captured by high rates of mapping or imaging. If the individual map/images are comparable samples of the geophenomena through time, then the geo-representations can be animated to reproduce the change. Such animations of geo-representational scenes allow the user to replay the events either forwards or backwards and at any chosen speed. In a sequence of scenes shown rapidly there is a tendency to interpolate between them. Surveys over 8 years of the rapidly changing spits on Scolt Head Island have produced over 20 separate maps of the terrain at Far Point (Raper et al. 1999). Terrain elevation and surface sedimentary composition data for the currently active Far Point spits was captured at six-monthly intervals between April 1992 and September 1995, then at monthly intervals during the winters of 1995–6 and 1996–7 and then again at six-monthly intervals subsequently. These surveys were conducted using a total station surveying instrument with sampling points at approximately 10m horizontal resolution, and were based on a set of ground control monuments used to define a local coordinate system (Raper et al. 1999). The surveys of elevation since 1993 (plate 7.3) show that the spit develops through a process of longshore transport. Sediment eroded from the shoreface close to the end of the barrier beach becomes deposited at the very end of the spit. Washover appears not to be important on the spits at Far Point except in high-magnitude storm events. After a period of several years, a new spit is formed (as in 1994), which initially extends from the beach of the main barrier. The new spit then follows a similar path to the old spit further to the west, becoming elongated and progressively recurved (as in late 1995). The extension of a new spit appears to coincide with the gradual degradation of the older spit. This is interpreted to indicate that the new spit is capturing sediment that might otherwise have been supplied to the older spit. The processes that lead to the degradation of the older spit are largely attributed to tidal currents that trim the end of the spit and create breakthroughs. This is the most common cycle of spit development and degradation in (almost) a decade of observations. The net result is a gradual accretion process, where the net deposition volume is much less than the sum of each of the recurved spits.

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Two alternative animations have been made to study the change that takes place in these landforms. Firstly, an animation of the coloured contour maps in plate 7.3 was produced using animated GIF file techniques, using frame rates that echo the intervals at which the surveys were carried out. The resulting animation conveys several forms of behaviour that cannot be elicited from the static maps: firstly, there appear to be ‘pulses’ of sediment which move along the spits from the barrier island; secondly the whole landform complex rotates while moving; and thirdly, as the spits grow out to the west, the whole complex moves to the east, as a whole. Hence, the spit elongation that appear to occur as the spit grows is not actually making any forward progress, except at certain points when the angle of the spit to the barrier island increases to the point that a new spit can develop. An alternative animation was made using VRML models of the spits at Far Point for the same set of surveys. Each model was turned to the same viewing perspective, captured as a screen shot and animated in the same way as the maps. However, the visual impression is not as striking as in the case of the animated maps since many more aspects of change can now be seen, making it difficult to grasp them all simultaneously. Smith, Spencer, and Möller (2000) animated three late summer CASI aerial remote sensing images of the Far Point spits for the period 1994–96. The animation shows a single growth phase of the main spit in which it enlarges while earlier spit shrinks as its sediment supply is cut off. Human spatio-temporal behaviour The availability of hand-held Global Positioning System (GPS) receivers has made it possible to map personal movement paths more easily than ever before. Such paths through space-time can be stored in real-time GIS (see chapter 5), although they pose new problems for structured spatio-temporal database storage. Such space-time paths are a novel form of dynamic geo-representation, capturing instantaneous position, speed and heading. Figure 7.2 shows the space-time path for the two days used to survey one of the maps shown in plate 7.3, showing: the activity at the field site; the use of a store in the survey area (centre of the western path cluster); return journeys to the field centre accommodation (origin of journeys to the east); and the arrival/departure from the field site. Various derivative geo-representations can be envisaged such as daily envelopes of movement and self-contained periods of activity in certain locations. With the move to include this geolocation technology in mobile phones over the next few years such dynamic geo-representations may become widely available (Mountain and Raper 2000).

Figure 7.2 Space-time path for two days surveying the Far Points spits on Scolt Head Island in March 2000

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POTENTIAL A range of different dynamic geo-representations have been surveyed from high frequency process monitoring and low frequency landform change, to human movement mapping. Since multimedia and geolocation technologies permitting the collection of dynamic geo-representation data have rapidly grown during the last few years, this kind of multidimensional application is likely to become much more common. Currently, the databases and analyses needed for multidimensional datasets of this kind are still poorly developed and there is considerable scope for further development.

CHAPTER 8 Geo-representations of coastal change using virtual environments CONTEXT The inaccessibility of the coastal environment and the limited number of people who experience the extraordinarily dynamic change that takes place there, are two important reasons to develop virtual geo-representations of the (Norfolk) coast. Limited time and the arduous nature of the walk to the Scolt Head island National Nature Reserve means that many tourists, visitors and field trip students do not ever experience first hand one of the few natural and unmanaged parts of England’s lowland coastline. While a virtual environment is a poor substitute for that personal experience it is arguably better than no substitute at all, and, when combined with interpretive material it can be valuable, as Dykes, Moore and Wood (1999) have argued. While the author has seen over 20 years of change at the Far Point spits on Scolt Head Island, few others can have witnessed this dynamic behaviour. A virtual geo-representation allows a wider audience to explore the geomorphological change from user-defined perspectives within the model. These two scenarios correspond to the ‘here’ (the current landscape) and the ‘elsewhere’ (a simulacrum of landform change) respectively, of the Pimentel and Teixeira (1993) virtual environment representational scheme (see chapter 5). Most of the work done so far on virtual geo-representation has focussed on realism and reconstruction. Yet this representational form also allows other perspectives to be explored, ones that cannot and will not ever be seen directly, but ones that could be constitutive of multidimensional change. Hence, this chapter will also explore new analytical and exploratory virtual geo-representations in an attempt to ‘see’ change in geo-phenomena multidimensionally. A new 3.5D visualisation approach was developed using analytical drapes over virtual geo-representations. These representations are much more complex that those used traditionally. Note that Shneiderman (1997) has argued that the human cognitive system can cope with more information than usually presented in current user interfaces, if they are well designed.

VIRTUAL GEO-REPRESENTATION OF COASTAL CHANGE These experiments explore the possibilities of virtual geo-representation in both realistic and analytical environments. These perspectives are used to situate the user in an environment (the realistic model) and then to allow the exploration of multidimensional representations of coastal change.

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Interfaces to virtual geo-representations Modern virtual environments offer a powerful visual experience: on coming face-to-face with the real place, one of the author’s own students, having earlier explored a model of that location, commented immortally ‘it looks just like the virtual world’! Plates 8.1 and 8.2 (similar to the ones the student saw) show the hilltop view over the coastal plain and the equivalent ‘virtual view’ of the virtual geo-representation, which is a terrain model draped with a satellite image. Although the virtual view lacks buildings, colour and people it is recognisably the same place, especially wihen viewed dynamically. More sophisticated virtual reality systems can produce much more realistic geo-representations. The virtual geo-representation shown in plate 8.2 can be explored by the user through the standard PC interface, using the mouse and its buttons to move around. However, without pre-existing knowledge of the location it is difficult for users to orient themselves in the virtual geo-representation. This led to the development of the VRGIS system (Raper, McCarthy and Williams 1998) which added a map interface alongside the virtual geo-representation. The VRGIS 1.0 system illustrated in plate 8.3 is made up of two main windows: virtual reality (right) and GIS (left). In the application illustrated in plate 8.3 there is a dynamic element in the virtual world viz. an aerial survey plane that moves around. The terrain model grid cell in the VR window vertically below the survey plane is highlighted as it moves over the terrain. The yellow rectangle in the GIS window displays the current aircraft position on the map, and the black stars show the previous positions of the aircraft since it began to move. As the plane flies around in the virtual world, the map scrolls to keep up with the plane. In VRGIS 2.0 constructed as part of the Virtual Field Course (Dykes, Moore and Wood 1999), the ability to change the map and the VR surface drape were added to the interface (plate 8.4). Users were given greater control over the movement in the virtual world with options to specify a height of movement or to enter terrain-following mode. By clicking on the map users could also query features on the map and receive a report of all the attributes attached to the vector or raster data at that point. The ability to read source data from the Virtual Field Course hubserver was added so that the system could read metadata and import data from remote sources. Analysing coastal change using virtual worlds The challenge of showing change in a three-dimensional geo-representation, such as the evolution of a landform, are considerable. On Scolt Head Island the spits at Far Point grow, move and change shape, all at the same time, making it difficult to track their evolution. Since the spit landforms are only represented in a 2.5D surface model, visualising their dynamic behaviour can be termed a ‘3.5D problem’. One attempt to present this information was to use the Virtual GIS room developed by Neves et al. (1999) to view the terrain models in an exhibition. Each model in turn could be selected from the ‘wall’ display and placed on the ‘table’ in the Virtual GIS Room and examined by the user from any angle or resolution (figure 8.1). While this approach was useful, it did not meet the need to visualise and analyse the full dynamic behaviour of the landform morphologies as it was not possible to see the changes that occurred between models.

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Figure 8.1 Scolt Head Island Far Point spits in a gallery in the Virtual GIS Room with the currently selected model displayed on the viewing table

A 3.5D geo-representation requires comparable surface models, an analysis of the change that has occurred and a visualisation of the dynamic behaviour as it occurs. In this experiment the surface models were produced using TIN methods as there were a large number of surface elevation point samples in each time period, and from field experience, these were known to capture terrain shape well. For analysis of the evolution of the spit geo-phenomena two potential methodologies can be identified: ‘window of comparison’ methods; and ‘regions on surface’ methods. Each of these methodologies can be implemented for both TIN and grid raster surface modelling approaches. The ‘window of comparison’ methods are based on the assumption that successive surface models constructed from point sampled data can be compared within the same georeferenced frame. Various possible frames of comparison can be defined depending on overlap and the type of surfaces to be evaluated. Firstly, all surfaces can be compared

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using a mimimal fixed frame such as the unique area of overlap between all the surfaces in a set. This approach has the advantage of strict comparability as it compares the character of the surface at the same location, but has the disadvantage of ignoring the information from the surfaces lying outside the minimal fixed frame. Secondly, all surfaces can be compared using a maximal fixed frame where the surfaces are compared against an area containing all the data points from all the surfaces. This approach has the advantage of having no redundancy as all the data points are used in comparisons. However, many of the surfaces will be compared against ‘no data’ areas for other surfaces. Sometimes the area of actual overlap may be quite small (or even non-existent) for surfaces created from samples that are far away from each other in time and where the geo-phenomena moves rapidly (e.g. a cyclone) Other ‘window of comparison’ methods may be defined which use the overlap of each pair of surfaces. A logical AND comparison between two surfaces will give results for the unique area of overlap and will ignore areas where only one surface has data. The disadvantage of this approach is that the surfaces are compared against a ‘local’ overlap zone, specific to the two surfaces, and are not compared against any ‘global’ comparison frame that is of significance to the whole set of surfaces. Comparisons can also be made by using externally defined zones in two dimensions to define ‘windows of comparison’: examples would include low tide or mean atmospheric pressure lines. Comparisons between surfaces can also be made by ‘regions on surface’ methods which identify parts of both surfaces to be compared. Firstly, the surface can be regionalised by a partition of the z attribute (e.g. elevation) and the area of the zones enclosed by these regions can then be compared for overlap and area. These methods have the advantage of using a ‘global’ criterion for comparison that can be used for any pairs of surfaces, but the disadvantage that the ‘region’ frame of comparison is fixed through time. Secondly, the surface can be regionalised by overlaying a secondary map with zones of significance for the comparison e.g. sediment type in geomorphology or areas of rainfall in meteorology. In this case, the surfaces are compared in terms of the correspondences of the z attribute within the ‘significance’ zones defined. This method has the advantage of using a physically based zone of comparison but the disadvantage of using a comparison method employing secondary rather than primary attributes of the surface. The pairwise surface to surface comparisons produced by ‘window of comparison’ or ‘regions on the surface’ methods can be used to generate a third surface showing the change. These change surfaces have both positive and negative values reflecting the surface differences and are amenable to further analysis. Change surfaces can be calculated for raster grids by simple subtraction. For TIN’s the value of the change is determined by interpolating the value of the point in the second surface at the x, y location of the point in the first surface. Positive values indicate accumulation or increase in the z attribute while negative values indicate removal or decrease in the z attribute. The positive and negative zones can be delineated by a zero change line, which can be mapped through time. The identified changes can be ‘balanced’ by a comparison of volumes between positive and negative areas, if it is clear that no net gain/loss over the external boundaries of the models takes place. Note, however, that these changes could either be indicative of change in situ through time, or of the movement of a phenomenon

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through space over time: the change identified must be physically explored and justified in itself. In this experiment the data availability and the dynamic behaviour was such that a ‘maximal fixed’ frame approach produced the most useful surface to surface comparisons. Areas in one model compared to ‘no data’ areas in the other were unchanging and have been ignored. Since each ‘change surface’ spans two time periods, each survey surface also belongs to two change periods, i.e. ‘change up to this point’ (past); and, ‘change from this point on’ (future). Plate 8.5 shows two surface models (with different data coverage) of the Far Point spits for September 1993 and March 1994 shaded by elevation. To visualise the change of elevation between these two surfaces the differences between them were calculated by TIN techniques and visualised using a dichromatic legend palette from red (deposition) to blue (erosion). This change surface was then draped over the earlier survey surface i.e. September 1993 (plate 8.6). The model in plate 8.6 shows where the deposition that will take place in the next six months will occur in a ‘change from this point on’ type representation. Positive redorange-yellow changes are located in the prominent east-west trending intertidal bar north of the spits and at the end of the ‘current’ spit. Negative blue-purple changes are located along the northerly edge of the spit and at the southern end of the ‘inner spit’. As it is difficult to find any one position within the virtual world where all the change can be seen at once, the model has been built using VRML so that the user can move around within the change-draped-surface model. This geo-representation gives an analytical view of the change allowing the exploration of the differences between the survey maps. As the VRML model allows the surface draped over the model to be changed quickly, the ‘change up to this point’ surface can also be displayed to explore the change prior to the current time period. These geo-representations are good examples of ‘simulacra’ type defined in the Pimentel and Teixeira (1993) classification of virtual environments. Time-dependent display of virtual worlds Virtual environments can also be used to display time-dependent behaviour. In the coastal environment the diurnal tidal cycle changes the processes operating on the spits and strongly influences accessibility to the island. Visualising this behaviour involves calculating the height of a given tide in metres and ‘flooding’ the model to that depth by inserting a tide water object. Plate 8.7 shows a surface model of the sea wall and marsh south of Scolt Head Island captured using laser surface-profiling LIDAR techniques and shaded for elevation. Since LIDAR has a footprint of 2m and is accurate to a few centimetres, every building, tree, yacht mast and telegraph pole is shown. The model has a ‘spiky’ appearance due to the vertical exaggeration of these features. Both high and low tide states of the tidal model as calculated in the Arcview GIS are displayed using 3D Analyst. An automatically updating display could be calculated if the tide water object was given temporal attributes.

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POTENTIAL The use of virtual environments has huge potential to represent the inaccessible reality and ‘unseeable’ phenomena of geo-phenomena. These experiments show some examples of multidimensional geo-representations showing how they can extend the scope of current representation. In particular, virtual environments make it possible to develop 3.5D representations to allow the analytical exploration of multidimensional change.

CHAPTER 9 Three-dimensional modelling of coastal landforms CONTEXT Understanding the genesis and evolution of sedimentary landforms requires knowledge of their internal structure and sedimentary facies composition so that the depositional environment of formation can be reconstructed. Such knowledge can come from natural field exposure, destructive sampling such as boreholes or non-destructive sensing such as geophysical surveys. In the absence of natural exposures, representational techniques are needed to reconstruct the structure and composition of landforms. The simplest georepresentation that can be created is a cross section, which can be produced by linking together boreholes or interpreting the plot produced by a geophysical survey. These cross sections can be used directly or, by picking sedimentary strata of interest from all available cross sections and interpolating their elevation values, it is possible to form single-valued surface models. Surfaces can be stacked together and intersected where necessary to form pseudo three-dimensional geo-representations, which divide but don’t enclose space (see chapter 4). While sedimentologists have developed many significant sedimentary facies models based on such information (Miall 1983, Anderton 1988), it is accepted by many that where depositional environments are complex it is difficult to resolve some problems of interpretation (Kelk 1992). Accordingly, sedimentologists have looked to new threedimensional representational tools to make models of complex sedimentary environments (e.g. Orlic and Rösingh 1995). Solid three-dimensional geo-representations allow the reconstruction of sedimentary architectures and permit the interpolation of volumetric property variation. The insights gained from such new geo-representations have advanced the science and practice of sedimentology in the last few years and offer further new opportunities for research when suitable datasets are collected. In coastal sedimentology and geomorphology, barrier island and tidal inlet landforms and processes pose considerable scientific and management problems due their highly dynamic behaviour (Biegel and Hoekstra 1995). One element of the landform assemblage in this environment is the spit landform: ‘a detached beach that is tied to the coast at one end and free at the other, with a free end that often terminates in a hook or recurve’ (Raper et al. 1999). Spits are usually produced by longshore movement of sand and gravel across inlets where wave and tidal processes interrupt the shore parallel movement of sediment and recurve the landform into the inlet. Since spits are highly mobile they often require active management (Bradbury and Kidd 1998), which depends on their monitoring (Zuhar et al. 1997) and analysis of their mobility (Riddell and Fuller 1995). Spits can also be regarded as barometers of contemporary sea level change and

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they serve as useful analogues for the coastal environments reflected in the many sedimentary basins of economic importance. On Scolt Head Island Steers (1960) suggested that the main east-west trending barrier and the spits recurving to the south were composed of ‘shingle’ (gravel and cobbles), which formed a platform extending under the salt marsh muds. The widespread existence of shingle was confirmed in a comprehensive study by Allison (1985), who augered 42 boreholes in locations across the island, encountering shingle at depth in 21 holes. However, the work by Allison concentrated on the stratigraphy and did not make any detailed investigation of the relationship between the spits, the salt marsh muds and any underlying ‘platform’. The question of the formation of the spits has remained unexplored. A project to drill boreholes into a small segment of a spit on Scolt Head Island was undertaken to develop a three-dimensional geo-representation of its composition and sedimentary architecture. Such reconstructions allow the linkage of form and process to composition and structure. Two alternative three-dimensional modelling approaches were used to create the geo-representation of the spit segment: firstly the Earthvision minimum tension approach, and secondly the tetrahedron modelling approach developed by Lattuada (1998). The geo-representations produced by these two systems are compared to assess their relative merits for sedimentological explanation.

EXPERIMENTS IN THREE-DIMENSIONAL MODELLING OF COASTAL LANDFORMS The set of borehole data used in these experiments into the three-dimensional georepresentation of spit sedimentary architecture came from the south Privet Hill field site on Scolt Head Island (figure II.2). The Privet Hill relict spit runs 500m NNW to SSE from Privet Hill (a relict sand dune) to Norton Creek, separating two marshes. The crest of the Privet Hill spit lies 3.8–3.9m above Ordnance Datum (OD), while the marshes are now only 1m lower at 2.8m on the younger, west side, and 3.0m on older, east side. The tidal range in this area extends from around 1.3m OD to 4.0m and closely mirrors the height of the spit. In cross section the bar is asymmetrical, being steeper on the eastern (formerly inner, sheltered) side. At the south Privet Hill field site 26 holes were bored in a 52m by 32m rectangle placed across the bar, and are distributed within the site at approximately 10m spacing (figure 9.1). The positions of these holes were surveyed onto a local grid oriented to magnetic north, and tied to a benchmark on the crest of the bar. The holes were bored to a maximum of 5m depth using percussion coring techniques. A full sedimentological log was compiled from the core at the time of recovery, and samples were taken every 25cm. These samples were analysed to determine their particle size distribution (PSD), that is the percentage of the sample falling in a range of particle size classes ranging from gravel to clay. To determine the PSD the samples recovered from the 20 holes were: • sieved using the aperture sizes shown in table 9.1, with samples having substantial fine fractions below 4 (63 microns) being further analysed analytically in a sedigraph machine (128 samples, 12 holes); and

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• processed in a laser granulometer device (119 samples, 8 holes)

Figure 9.1 The sedimentary logs of the recovered core for the south Privet Hill site

Table 9.1 Sieve aperture sizes used in mm (upper row) and phi ( ) (lower row) 16

8

4

2

1

0.71

.5

.355

.25

.18

.125

.09

.063

.045

.038

−4

−3

−2

−1

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

4.75

The statistical parameters that were chosen to describe the samples’ grain-size distributions were the mean, standard deviation (sorting), skewness and kurtosis. The method of calculation was based upon the experiments by Swan et al. (1979) who indicated that the errors due to grouping the grain sizes within an interval of one central measure were small as long as the interval was also small: ie 1 or smaller. Swan et al. (1979) also concluded that lumping the unanalysed sediments (finer than the smallest sieve aperture) into one lower fraction gave statistically valid results if the unanalysed percentage was less than about 12%, but above 12% the mean becomes less accurate. For most sediments, Swan et al. suggested a bounding measurement value of 10 or 14 , however, 5 is sufficient for sands and gravels. Since samples with more than 30%

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unanalysed sediment may have a mean that does not fall within 0.5 of the real value these values were treated with caution, although in most cases these samples have a clay size mean which the missing data would not change. In this study only the mean particle size in phi units ( ) were modelled. In three dimensions this is equivalent to a set of 247 mean particle sizes arranged in 20 vertical sequences at 25cm vertical intervals. The objective of the modeling process was to develop a three dimensional georepresentation of the sedimentary architecture using sample data, which was consistent with the sedimentary log of the recovered core (figure 9.1). This model could then be compared with the hypothesis that these relict spit bars are composed of ‘shingle’ (gravel and cobbles) connected directly to an underlying platform composed of the same sediments. It may also provide an insight into the processes of spit formation and development. Minimum tension isosurface modelling The Earthvision system was used to interpolate from scattered data to a 3D grid using minimum tension isosurface modelling, and, to create isosurfaces from the 3D grid. However, the selection of interpolation options strongly influences the characteristics of the model. This is primarily because a deterministic three-dimensional interpolator is highly dependent on the input options. It is necessary to control inputs and evaluate outputs carefully to avoid the generation of models with artifacts. In most cases this involves the creation of several generations of models with quality assessments of each. The most important inputs to the Earthvision modelling of sedimentary architecture are appropriate structural constraints. In this case examination of the sedimentary logs showed that 21 out of 26 holes contained a single or double layer of mud (similar in consistency and grading to marsh mud) which appears to pass right through the spit below the level of the modern marsh surface. Since this is an important structural feature of the sedimentary architecture it was decided to divide the data points into three zones using the upper and lower surfaces of this ‘mud’ zone as boundaries. These surfaces were created separately in Earthvision by using the 18 data points with ‘mud’ depths in an area 5% larger than the bounding box containing the 20 boreholes with the completed sample analysis. A mean grain size property model was made for each of the ‘lower’, ‘mud’ and ‘upper’ structural zones. The top of the model was clipped using ground elevation data, while the deepest point reached in boring was used as a clip for the base. In forming the model the following Earthvision interpolation settings were selected: • Conformality: all three grids were interpolated such that each was both top-and bottomconformal. This option was selected since it was considered likely that sedimentation had been influenced by the palaeo-topography of the mud unit and by the surface topography of the bar itself. • Zone expansion: a zero ‘zone expansion value’ was used to prohibit interpolation using values outside, but adjacent to, each zone grid, since inspection of the sedimentary logs indicated that the mud layer represented a sharp hiatus in sedimentation. • Property value range: after experimentation it was decided to restrict grid values to the exact range of data values in the scattered data within each bounded zone. Without this

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constraint it was found that some improbably high and low values were generated by the interpolation process, probably due to the rapid changes in mean grain size over short vertical distances. • Z-influence factor: the default value of the ‘Z-influence’ factor was used because experimentation showed little difference in the resultant grids, even if a factor of 0.5 was used to introduce greater horizontal influence in interpolation. The final model shaded by mean grain size in units is shown in plate 9.1. Model quality was assessed by checking the model against the sedimentary logs, and by evaluating the residuals between the input data points and values calculated from the grid at those locations (‘back interpolation’). The upper and mud zones have a wide distribution of residuals indicating that in some locations the grid has generated some spurious values. However, the lower zone has a very narrow range of residuals suggesting that the grid approximates the mean values of the samples well. In order to produce the best possible grids for three dimensional geo-representation, the grid of residual values was added to the first grid to create a ‘corrected’ grid in which all mean grain size values from the samples match the values in the grid. Two main theoretical problems arise which cannot be precisely resolved. The first problem concerns the use of the mean as a one-dimensional summary of the grain size distribution. Swan et al. (1979) pointed out the conditions in which a mean was an acceptable estimate of the population given standard calculation procedures and assumptions. Ultimately, the mean best summarizes uni-modal, well-sorted sediments. This was a condition that seemed to be acceptably met in the present case. A second theoretical problem concerns the widely differing sampling interval between x-y (10– 20m) and z direction (mostly 25cm). This clearly poses problems for an interpolation algorithm, although the problem is partly alleviated by using a different number of grid cells in the horizontal and vertical axes. In this study the horizontal grid cells were 1m square, but 0.1m thick in the vertical direction: a ratio of 10:1. Despite the qualifications noted above, much can be learned about the sedimentary architecture of the spits. The three zones are now examined in turn and compared with the generally accepted hypothesis of bar formation. The crest of the bar viewed in plate 9.1 can clearly be seen crossing the model diagonally runs SENE: the base of the ‘upper’ zone is delineated by the thin blue coloured ‘mud’ zone. At the surface of the ‘upper’ zone the west (left) side of the bar is made up of muds from the modern salt marsh while on the east (right) side the model is composed of coarse, largely gravel sized sediments. Viewing the model from the SE it can be seen that there is an extremely sharp gradient between the west side muds and the east side gravels, and little sign of a ‘core’ is evident. Sedimentary logs suggest that there are ‘accretionary’ layers of medium sands and fine gravel in the core of the bar that are characteristic of a beach. However, little structure can be determined for the core of the bar in the model due to the high variability of the sediments relative to the frequency of vertical sampling. The ‘lee side’ gravels on the east side (which can clearly be seen in the sedimentary logs) are inferred to be a wedge of washover sediments associated with the active development of the bar, probably indicating that storm tides overtopped the bar from left to right as viewed. The mud zone can be seen to pass right under the bar and under the modern salt marshes. From the sedimentary logs it is known that this actually occurs, but it is not clear

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whether the two zone merge or whether the more recent marsh muds always overlie the mud zone in the spit. At present it is suggested that the mud zone is the remnant of a marsh which was developing in the lee of the developing bar, and that the whole bar has migrated over the mud by a process of overwashing. This has preserved what was originally a lee side salt marsh under the spit itself. It is also likely that on the side of the bar exposed to wave attack, the mud was progressively removed as the bar migrated east. The composition of the lower zone can be seen as a fining up sequence, perhaps indicating a reduction in energy as the spit developed here. Tetrahedron-based modelling The tetrahedron-based approach of Lattuada (1998) was used to produce a different georepresentation of the spit sedimentary architecture using the same boreholes and samples (see chapter 4). Tetrahedra-based modelling algorithms structure the data points directly by triangulating them in three dimensions to form solids; there are few parameters to influence the outcome. In this case the data points are close to each other in the z dimension and more widely spaced in x, y meaning that the tetrahedra formed are very thin. In order to improve the performance of display and analysis, the tetrahedra were subdivided using data points added inside the tetrahedra produced from the original data (Lattuada and Raper 1995). The completed model is shown in plate 9.2, viewed from the east, and showing the NNW to SSE trending ridge (shaded orange). In tetrahedra models a method is needed to assign attributes from data points to tetrahedra. Starting with the base triangulation the ‘added data points’ are assigned attributes based upon the influence vertices in the surrounding Voronoi region. Where constraints have been added to the tetrahedra then limits are placed on interpolation in certain directions. If the attributes are assigned discretely to tetrahedra then points on the boundary may have different attribute values depending on the direction from which they are approached, i.e. the tetrahedron through which they are approached. Once all the original and ‘added’ data points have attributes, then normals are computed for triangles to determine tetrahedron membership of triangles. Attributes can be calculated for each tetrahedron depending on the attribute values calculated for its four triangular faces. The resulting attribute shaded tetrahedra in plate 9.2 are a function of data point weighting. The model is shaded by particle size such that the coarser sand and gravel of the spit picks out the line of the ridge, while the muds of the marsh extend out to the west. The sands of the underlying sedimentary platform are visible at the base of the model. The geo-representation can be broken down into attribute zones or individual tetrahedra by simple boolean operations.

POTENTIAL Both of these geo-representations suggest that the spit is not made of gravel nor is it connected to a coarse underlying deposit as Steers (1960) and Allison (1985) suggested. The models offer support for the view that the spit was being forced back to the east as it recurved to the south since the mud layer cannot have formed in situ, and must have once

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formed a lee-side mudflat/salt marsh. These insights can be gleaned from figure 9.1 but visualisations of sedimentary logs such as this are hard to place in any elevational framework. The two models have distinct advantages and disadvantages as geo-representations. The Earthvision model is easier to view and explore as it is made up of smoother geometric elements than the tetrahedra approach of Lattuada (1998). However, the tetrahedra are a more conservative form of geo-representation since they only display tetrahedra bounded by data points or subdivisions of them unlike Earthvision, which has transformed the original data points into a grid. The grid base of Earthvision also promotes interoperability and error quantification through ‘back interpolation’ methods. The experience of making geo-representations using these two systems reinforces the need to carefully specify three-dimensional data modelling so that appropriate selections can be made during the modelling process.

CHAPTER 10 Multidimensional geo-representation in coastal environments CONTEXT One of the greatest challenges for geo-representation is the multidimensional process modelling of geo-phenomena. This is a definitively four-dimensional problem, where process and forms must be fused in a structural and functional representation. The goal of multidimensional process modelling is the simulation of geo-phenomena using boundary conditions and mechanisms derived from empirical investigation. It is accepted that the outcome will not be and can not be ‘realistic’ in the metaphysical sense. The aim is rather to make a projection from a known starting point and then to compare the model outcome with independent observed outcomes. The comparison should pose further epistemological questions and generate new ontological concepts to motivate the rethinking of multidimensional identity and evolution. Developing multidimensional process modelling for the coastal environment is challenging because the processes change forms and the forms change processes in a reflexive cycle that operates at high frequency. In the case of coastal spits there is evidence from the elevation surveys (chapter 7) and from the theory of May and Tanner (1976), that the movement of sediment along the shoreline by waves is controlled by shoreline cells formed out of the incoming incident wave field by infragravity waves (oscillations at right angles to incident waves). Waves focus within shoreline cells, i.e. wave crests become slightly concave shoreward when viewed from above, so that waves are larger at the centre of the cell (which can be 100–300m across). This means that sediment transport along the shoreline is highest where the waves are highest (cell centre), and lowest at the cell margins, with transport being driven overall in the direction of the wave approach. Sediment movement speeds up and slows down as it is ‘handed on’ from cell to cell, which is consistent with some features of the animation discussed in chapter 7. Wave refraction and diffraction recurve the cell shape to produce the typical spit morphology. When trying to develop multidimensional process models for coastal spits a number of representational problems emerge. Firstly, it is clear that much of the sediment transport goes on in the narrow swash zone as it moves up and down with the tide, yet almost all computational designs use the same spatial resolution close to the shore as elsewhere. Secondly, it is difficult to develop shoreline cell implementations with the ability to self modify under variable wave direction inputs. Thirdly, most models do not simulate ‘storm reconfiguration’ which may push the spit out of position and enable an intertidal shore-parallel bar to extend into the newly vacated space. Despite these limitations a multidimensional process model based on the SEDSIM system has produced results that

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raise further questions about coastal behaviour. Multidimensional exploration of geo-phenomena can also be envisaged when large amounts of spatially and temporally referenced data have been recorded. The ability to carry out four-dimensional range queries on multidimensional datasets poses new representational and analytical challenges. This research aims to identify ‘emergent’ behaviour by exploring the space-time structure of the geo-phenomena.

MULTIDIMENSIONAL COASTAL GEO-REPRESENTATION EXPERIMENTS Simulation of spit morphodynamic behaviour The SEDSIM model was developed by Tzetlaff and Harbaugh (1989) to simulate the erosion, transport and deposition of sediments in three dimensions over geologic timescales. SEDSIM was originally developed to simulate unidirectional unsteady flow in rivers, but has since been modified by the addition of the WAVE module (Martinez and Harbaugh 1993), which allows the simulation of coastal and nearshore environments affected by wave-induced erosion, transport and deposition. SEDSIM/WAVE is a hybrid four-dimensional finite-difference/finite element model that simulates wave-induced nearshore currents and is linked to algorithms that redistribute sediments in response to these currents. The model simulates incident waves, wave breaking, surf zone radiation stress, longshore currents, wave-current interaction and nearshore sediment transport over three dimensional deformable sea bed surfaces. Modifications to the operation of the model have been made by Livingstone and Raper (1999) and Raper et al. (1999) to optimise SEDSIM for spit evolution modelling over engineering spatial and temporal scales. Thus, the model was run for periods of months and years over a grid of (variously) 500m to 1500m in dimension. The three-dimensional modelling in SEDSIM/WAVE uses simplified assumptions for calculating longshore transport within the surf zone but a complex morphological representation of that transport, which feeds back into morphological change into the model at each time step. The three-dimensional model provides incident wave control, wave breaking over input sea bed topographies, variable sediment transport across the breaker zone, differential movement of four grain sizes, onshore-offshore sorting of sediment and a mobile bed of sediment. SEDSIM/WAVE determines which cells are in the breaker zone by comparing their current elevation with the input wave base. The empirically determined sediment transport rate is distributed over this breaker zone area according to the approximation of cross-shore and longshore transport. Since most radiation stress is dissipated within the surf zone as longshore and onshore-offshore currents the momentum from the wave field is dissipated among the cells in the breaker zone. This is achieved using a non-linear cross-shore function for each shore-normal column of grid cells, which is at a maximum just shorewards of the breakers, falling off to a minimum offshore and at the shoreface. This approach simulates cross-shore variation in bed shear stress on a time and depthaveraged basis as real onshore-offshore processes oscillate with each passing wave.

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SEDSIM/WAVE models sediment transport for four different user-specified grain sizes by using a transportation efficiency factor derived from the threshold shear stress required for entrainment. To approximate the net change in the elevation of the bed in the surf zone, SEDSIM/WAVE must model erosion and deposition of sediments under the specified sediment transport rate in the calculated breaker zone. SEDSIM/WAVE uses a series of ‘accounting procedures’ to manage the transportation of the sediment. SEDSIM/WAVE calculates the entrainment of sediments and the amount of each grain size that is removed. It then moves this sediment to the adjacent cell under continuity constraints and deposits it, leaving the remaining sediment in its existing grid cell. Grid cells are filled and emptied by deposition and erosion during a user-prescribed number of time steps, before the sequence of sediment types in the cell is ‘closed’ and recorded (it can still be eroded later). Finally, cross-shore sorting of grains are simulated by redistributing the proportions of different grain sizes without changing the elevation. The ‘topography generation’ program ‘Sedmodel’ was developed in Arcview GIS using the Avenue programming language so that controlled experiments can be created and converted to a format suitable for SEDSIM/WAVE. Sedmodel allows ‘basement’ topographies to be built from imported polygonal shapes to represent coastline configurations like headlands and bays. Sedmodel also allows the creation of ‘deposit’ layers of deformable sediment in conformance with the ‘basement’ topography. Wave inputs were specified as a transport rate in the surf zone, which were based upon the empirical expression developed by Komar and Inman (1970). These topographic and process inputs were scaled to the conditions on the North Norfolk coast based on field experience there. Since the fundamental objective was to ‘reverse engineer’ spit evolution a systematic trial and error approach was taken to the experimentation. Once the calibration had indicated the stable ranges for the input parameters both separately and in combination, a set of experiments was designed to promote spit growth. A number of experiments were run over a simulated three month period with a constant wave climate to study the influence of wave direction on spit development. An initial topography was selected that had proven stable in conjunction with a range of input parameters. The topography consisted of a 4m thick deposit of sediment draped over a predefined basement designed to simulate a simple headland with an acute angle with a constantly sloping beach at an angle of 1:15. Each experiment used the wave rate form to specify wave climate. The experiments can be visualised as surface models in plate 10.1. In the centre map of plate 10.1 waves were coming directly onto the beach from the south while other models showed waves coming increasingly from the east or west. The experiments clearly show the sensitivity of the model to changing wave direction. The growth of landforms with a spit-like morphology is more pronounced as waves swing round from south towards the south-west. The direction of wave approach that produced features with the most spit-like morphology was approximately in the range 20 to 40 degrees west of model south. Inspection of wave data for the North Norfolk coast indicates that the most frequent waves have a similar direction of approach. While the models are sensitive to input change and show moderate similarity with Scolt Head spit features, the real value of these models lies in their potential for investigating critical controls on spit-formation, such as angle of wave approach.

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The experiments have shown that the SEDSIM/WAVE model can simulate the longshore movement of sediment to form features like spits that develop in a similar way to those observed in morphodynamic monitoring. Using the inverse modelling approach of Cowell, Roy and Jones (1995) this work has shown how to stabilise the model parameters for engineering time and spatial scales and with appropriate wave energy and sediment transport values. The modelling reported here shows how spits evolve under steady state conditions in swell wave environments and bear a similarity to recorded change at Scolt Head Island. Three-dimensional models like SEDSIM/WAVE are potentially valuable tools for investigating the effect of nearshore topographies and wave approach angles on spit evolution and can show how sea bed elevation can feed back onto spit evolution. Currently the model is limited in its ability to handle variable wave approach, variable sediment transport rates, tides and wave tide interactions and nondepth-averaged radiation stress in the surf zone. In the future it is hoped to introduce real wave climates based upon wave measurements as well as tidal flows. Multidimensional exploration of coastal change A further challenge for multidimensional geo-representation is the ability to explore fourdimensional datasets for patterns or conjunctions that are constitutive of geo-phenomenon identity. The superset of all data points collected for elevation surveys at Scolt Head approaches 17,500 over eight years (plate 10.2). This dataset, where each point describes surface elevation at-a-time, can be explored multidimensionally to seek evidence for some of the behaviour conjectured for the evolution of spits. For example, this data can be searched for spit slope facets that are close in space-time to other spit slope facets where the angle has changed considerably. Such discoveries may shed light on the idea that sediment moves along spits in pulses, whose movement is often correlated with slope angle change.

Figure 10.1 Two spit cross sections at the same spatial location but one month apart

Plate 6.1 Reproduced by kind permission of Ordnance Survey © Crown Copyright NC/00/1136. The 1:50,000 scale topographic map of the North Norfolk coast around Brancaster in Arcview GIS overlaid with points representing aerial photograph locations.

Plate 6.2 An SQL connect operation using the Open Database Connectivity (ODBC) protocol in Arcview GIS, which links to a table in a Microsoft Access database containing geometric and attribute data for coastal landforms.

Plate 6.3 Reproduced by kind permission of Ordnance Survey © Crown Copyright NC/00/1136. The 1:50,000 scale topographic map of the North Norfolk coast around Brancaster in Panoramap, overlaid with orange points representing the location of photographic images, two of which are shown with their respective fields of view. Courtesy of Virtual Field Course (J.Dykes).

Plate 7.1 Four sequential video frames of breaking waves filmed from the air. Courtesy of Airborne Videography Ltd.

Plate 7.2 A strip map made from aerial video imagery for the mouth of the Ore River at Shingle Street in Suffolk. Courtesy of Airborne Videography Ltd.

Plate 7.3 Surveys of elevation at Scolt Head since 1993 (label gives month and year of survey). Spit landforms denoted by dark brown colour.

Plate 8.1 A hilltop view over the coastal plain showing Brancaster Staithe and Scolt Head Island (land on right hand side of the channel extending away from the viewer).

Plate 8.2 The equivalent virtual geo-representation of the view shown in plate 8.1 made by draping a terrain model with a satellite image in Sense8 WorldUp.

Plate 8.3 VRGIS 1.0. The virtual world is displayed on the right with a moving aircraft and the terrain grid cell vertically below it being highlighted as it moves. The map on the left shows the track of the aircraft and its current position inside the yellow rectangle.

Plate 8.4 VRGIS 2.0 with controls for viewing and querying the virtual world and the map. Courtesy of the Virtual Field Course (T.McCarthy).

Plate 8.5 Two surface models (with different geographical data coverage) of the Far Point spits on Scolt Head Island for September 1993 and March 1994, shaded by elevation. The orange colour corresponds to the dark brown colour of plate 7.3.

Plate 8.6 The change of elevation between September 1993 and March 1994 for the Far Point elevation surfaces calculated using TIN techniques and visualised using a dichromatic legend palette from red (deposition) to blue (erosion). The arrow shows a bright orange/yellow location in the VRML model where high deposition took place in this time interval.

Plate 8.7 Surface model of the sea wall and salt marsh south of Scolt Head Island, captured using laser surface-profiling LIDAR techniques and shaded for elevation. Data is copyright Environment Agency.

Plate 9.1 Three-dimensional minimum tension isosurface model of the spit section at the Privet Hill south site shaded by mean grain size phi ( ) units.

Plate 9.2 Three-dimensional tetrahedra model of the spit section at the Privet Hill south site shaded by attribute ranges. Courtesy of R.Lattuada.

Plate 10.1 Surface models showing coastal sedimentary landforms generated by SEDSIM experiments. Courtesy of D.Livingstone.

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Plate 10.2 The 17,500 superset of all data points collected for elevation surveys at Scolt Head over eight years between 1992 and 2000.

In the research at Scolt Head Island this kind of four dimensional query has been implemented experimentally. The experiment called for the creation of firstly, a database of morphology, composition and process information which was standardised in terms of coordinate system and spatial/temporal datum, and secondly, a multidimensional access tool allowing the user to specify spatio-temporal queries on this data. Data collected across space and time was stored in the Arc View GIS as a series of geometric layers. Arcview was used to measure distances and height differences between points at a similar position in absolute space for the two different times. In figure 10.1 the two cross sections show the profiles of the spit shoreface for two pairs of points that are very close to each other in space but one month away in time. Surveyed points represented ‘breaks of slope’ where slope angle changed sharply, suggesting that these observed differences reflect real changes in slope configuration. This multidimensional access tool allows the user to compare spatial locations at different times (for example, by the construction of time-difference maps) or to track the movement of spatial configurations through time. An improvement in efficiency can be expected if this access tool were to be implemented in a true four-dimensional GIS.

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POTENTIAL Multidimensional simulation and exploration are two new elements in an emerging multidimensional geographic information science. When space and time are fused into new representations new problems and opportunities for the reconstruction of multidimensional identity emerge. It seems likely that these new methodologies will open up new questions not previously attempted.

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Index

A A-series time, 104 abduction, 12, 200 absolute space, 34, 57, 66, 92, 101, 122, 126, 162 Access database, 212 Achilles, 86 ACIS volume model, 151 action-at-a-distance, 12 Adelard of Bath, 88 agents, 50, 193 agglomeration, 124 air photo interpretation, 79 Alberti, 53, 66 Alexandria Project, 195 algebraic topology, 125, 133 Al-Idrisi, 59, 64, 68 Al-Khwarizmi, 64, 68 allocentric, 38, 40, 42, 48, 82, 213 allometry, 130 Al-Mamun, 87 alpha shapes, 146 Alphaworld, 193 Analogue video, 176 animated GIF, 217 animation, 180, 191, 197, 198, 199, 201, 215, 217, 235 annotation structure, 208 anthropic, 8, 15 Anthropological, 4, 54, 56, 59, 109 antirealism, 14, 15, 16, 115 Apollonius, 90, 95 Arc/Info, 192, 198, 209 archaeology, 4 Archimedes, 95 architecture, 49, 54, 59 Archytas, 63 Arcview 3D Analyst, 155, 225 Arcview GIS, 212, 225 Aristotle, 6, 7, 32, 40, 63, 68, 86 arithmetic, 85 arrow of time, 108

Index artificial intelligence, 24, 36, 47, 49 astronomers, 125 attractors, 106, 127 attribute bundles, 163 audio, 177 autocorrelation, 127, 130 automata theory, 24 autopoesis, 24 avatars, 182, 193 axiomatisation, 105 Ayer, 11 B B-series time, 104 Babylon, 85, 126 back interpolation, 230, 232 Bacon, 11, 98 Baghdad, 88 Bartolomeu Dias, 69 basic-level categories, 51 Battle of the scales, 70 beach, 216 Beatus, 68 Bedolina petrograph, 67 Behavioural geography, 44, 47, 60 behavioural space, 73 Behavioural Time Sequence, 165 behaviourism, 16, 17, 18, 21, 23, 107, 110, 112 Berkeley, 7, 98 bifurcation, 106 big bang hypothesis, 100 binary trees, 146 binocular vision, 84 bintree, 170 Bohr, 101 Bolyai, 67, 97 bona fide boundaries, 41, 46 Boole, 106 boreholes, 227 Boundary Representation, 107, 145 Brancaster, 213 breaks of slope, 253 Brentano, 17 Broadbent’s rule, 111 Brunelleschi, 66, 90 B-spline, 144 Buache 70

294

Index C cancer cluster analysis, 201 Cantor, 24, 41, 95, 104, 105 CARIS GIS, 155 Carnap, 11, 15, 24, 102 cartesian scheme, 32 cartographic communication, 73, 75, 79 cartographic disinformation, 76 cartographic visualisation, 75 cartography, 4, 71 CASI, 218 Catastrophe Theory, 105, 126, 127 Cauchy, 96 causal chain, 166 causal relations, 38 causality, 12, 16, 28 Cave 3D, 155 caves, 179 cdv, 198 cell decomposition, 107 cells, 133 Cellular automata, 140 Centennia, 201 Central Place Theory, 110 centuriation, 68 Change Description Language, 163 change, 32 chaos, 86, 106, 119, 127 chaotic, 125 chat, 182 Chernoff, 182 Chinese and time, 85, 90 chora, 32 chorology, 34, 60 Christianity, 87 chronobiology, 108 chronos, 86 Chu Ssu Pen, 68 circadian clocks, 108 Clarke correspondence, 92 classification of spaces, 39 Classification Tree algorithm, 200 closed time, 103 closure, 132 coastal data management, 208 Coastal environments, 208 CoastMAP, 199, 212 cognitive collage, 44

295

Index

296

cognitive environment, 20 cognitive maps, 37, 40, 44, 48, 57, 58, 107 cognitive perception, 21 cognitive science, 5, 21, 23, 37, 76, 121 Collaborative Planning System, 189 collision detection, 180, 183 Columbus, 92 commodification, 27 common-sense psychology, 17, 23, 31 communicative action, 21 complementarity, 101 computational geometry, 49 computer science, 4 Comte, 8, 11, 16 conceptual schemes, 8, 10, 13, 18, 21 conditioned responses, 107 conditioning, 107 configurational knowledge, 47 Conformality, 230 conic sections, 66 conies, 90, 91 connectionist, 24 connotation, 27 connotative, 21 consciousness, 8, 12, 38 conservation laws, 98 consilience, 28 constant conjunction, 12 constructive modelling, 144 Constructive Solid Geometry, 107, 145 contagion, 32 Content Standard for Digital Geospatial Metadata, 195 content-based indexing, 215 contextualism, 33 contingency, 33, 81 contingent, 7, 9, 35, 121, 122, 123, 128 continuum hypothesis, 105 conventionalism, 102 convex hull, 146 convex spaces, 55 Cook, 93 coordinates, 65, 137, 140, 144, Copernicus, 6, 66, 69, 91 CORBA, 159 cosine rule, 141 cosmogenesis, 32 cosmogony, 32 cosmology, 84, 91, 95, 98, 101, 102, 116

Index CosmoPlayer, 192 Covering Law model, 12 critical rationalism, 11, 15, 110, 139 critical realist, 12, 15, 35, 113 critique of GIS, 80 cross section, 227 Cubists, 53 cultural milieu, 35 cultural universals, 51, 54, 57 CyberCity, 198 cycloids, 66 cyclone, 201, 224 D Daedalus, 156 daily envelopes of movement, 217 Data Information and Access Link, 196 data mining, 193, 199, 200 data warehouse, 200 database time, 165 decibel, 178 deconstruction, 76, 81, 113 deductivist, 12 deep structure, 121 deep syntax, 19 definition-limited, 136 Delauney Pyramid, 155 Democritus, 63 denotative, 21 depictive structure, 23 deposition, 236 depositional coasts, 208 depth cueing, 144 Descartes, 7, 11, 18, 40, 66, 91, 97, 98 Descartes system, 197, 200 desktop virtual reality, 174 determinism, 13, 16, 28, 59 deterministic, 8, 13, 23, 130, 138 developmental psychology, 47 Diderot, 33 différance, 34 differential equations, 125, 127 diffusion, 124 digital atlas, 197 digital camera, 216 digital elevation modelling, 142 digital library, 195 digital transition, 81

297

Index

298

digital video, 176 dimensional dominance, 162 Dionysius Exiguus, 87 direction of time, 101, 103 directionals in language, 52 discourse, 9 Discrete Surface Interpolation, 154 distanciation, 113 dogmatists, 11 Domesday System, 197 dualism, 7, 11, 18 Dublin Core, 195 dunes, 208 Dura Europa shield map, 68 durée, 33 dVISE virtual world, 183 dVS operating system, 183 DYNASED, 171 E Earth Observing System, 196 Earthvision, 157, 228, 230 Easter, 87 eclipse, 87 ecliptic, 93 ecology, 34 economic spaces, 60 economics, 137 edge detection, 49 edges, 146 egocentric, 38, 42, 48, 49, 82, 213 Egyptians, 85 Einstein, 14, 33, 67, 92, 95, 98, 99, 101, 102, 103, 105 electromagnetic fields, 95 electromagnetic spectrum, 176 ElevationGrid, 180 elliptic spaces, 67, 97 emancipatory, 17, 81 emergence, 22, 25, 36, 121, 131, 235 empiricism, 11, 14, 16, 26, 58 empty space, 32, 91, 101 Encarta, 197 encounter field, 56 Endurantism, 102, 123, 130, 136, 138, 165 engineering, 137 enough light and no fog, 180 enskifte, 61 entification, 34

Index

299

entrainment, 237 Enuma Elish, 32 environmental determinism, 60 environmental impact assessments, 204 environmental problems, 208 Epicurus, 63 epistemes, 111 epistemology, 5, 9, 10, 11, 16, 19, 28, 31, 58, 59, 60, 76, 98, 105, 115, 131 equations of state, 139 equifinality, 106, 123 equinox, 90 Eratosthenes, 64, 68 ergodic, 28, 47 erosion, 236 error, 131, 137 essence, 10, 126, 163 essential property attribute, 164, 320, 322 essentialism, 76, 121 ESTDM, 127 estuaries, 208 ETAK, 54 ether, 95, 99 ethics, 4, 5, 20, 80 Euclid, 11, 32, 39, 54, 63, 64, 67, 88, 91, 95, 96, 97 Euclidean geometry, 49, 71, 91, 97, 105, 106 Euler, 92, 94, 95, 96, 107, 146 Eulerian representation, 140, 170 European Spatial Metadata Infrastructure, 195 event horizons, 115 Event Pattern Language, 162 Event-based Spatio-Temporal Data Model, 164 experientialism, 10, 20 explanation, 3, 9, 12, 13, 16, 31, 32, 49, 60, 68, 75, 124, 130 exploration, 90, 92, 93, 119 Exploratory Data Analysis, 75, 200 Expo ‘98, 199 extended octree, 147 extended relational databases, 143, 183 Extensible Markup Language, 191 extension, 91 extrasignification, 74 F faces, 146 falsification, 110 fault, 135, 154 Federal Geographic Data Committee, 195 feedback, 195

Index

300

Fermat, 66, 91 fiat boundaries, 41, 46 Fibonacci, 65 field equations, 99, 100, 127 field trips, 140, 205 finite difference, 138, 140, 153 finite element, 137, 140, 153 flume, 216 formism, 33 four-dimensional GIS, 126, 253 fractal, 46, 49, 130 frame matching, 217 frames of reference, 129 Frege, 24, 106 Freud, 108 Fuzzy entities, 43 Fuzzy concepts, 103, 131 G gaia, 86 Galileo, 7, 91 Gauss, 11, 70, 97 gazeteers, 195, 197 geist, 8 gender, 167 General Geography, 59 General Systems Theory, 24, 139 General Theory of Relativity, 99 generalisation, 45 generative grammar, 19 geocellular, 156 geocentric reference systems, 51 GeoCid, 191 geocognostics, 50 geocomputation, 3 geodesic, 99 GeoExploratorium, 191 geographic individuals, 33, 46 geographic information bearing objects, 27, 196 geographic information retrieval, 196 geographic information science (GISc), 3, 10, 16, 19, 21, 23, 27, 28, 76, 84, 120, 125 geographic information systems (GIS), 3, 4, 76 geographic kinds, 40 geographic messaging services, 193 geographic metadata, 180, 195 geographic virtual environments, 174 geographic visualisation (GVIS), 75, 199 geographical entities, 41

Index geographical matrix, 111 geographical ontology, 40, 41, 44 geographical realism, 33 geography, 3, 4, 24 geolibraries, 194, 213 geolocation, 218 geology, 59 GeoMedia, 212 Geomesh, 153 Geominer, 200 geomorphological kinds, 121 geomorphology, 123, 128, 144 geo-phenomena, 81, 129 geophysical surveys, 227 geopolitical entities, 41 geo-representation, 4, 9, 81 geoscientific ontologies, 135 geostatistics, 130, 135 Geostore, 159 GeoToolKit, 159 GeoVRML, 180 Gestalt, 11, 19, 23, 107, 200 Giotto, 66, 90 Giraffe, 196 GIS-scape, 210 glacier, 171 Gläser, 69 Global Positioning System, 77, 217 God, 6, 7, 8, 11, 87, 91 Godel, 24 granularity, 37 Graph theory, 134 GRASS, 170, 194 gravitation, 91, 92, 99 Great Cities of Europe system, 189, 198 Greeks, 85 Gregorian calendar, 85 Ground Truth, 80 grounding, 5, 8, 29, 31, 82 Guide, 186, 193 GVIS, 213 Gyogi-Bosatu, 68 H Halley, 70, 73 hallucination, 183 handlebody, 107 haptic, 182

301

Index Harrison, 70, 93 Harun al-Rashid, 87 Heidegger, 10, 18, 33, 54 Heisenberg, 101 Helical Hyperspatial indexing, 170 heliocentrism, 91 Helmholtz, 97 Henry the Navigator, 68 Heraclitus, 33, 86 hermeneutic, 21, 112 Hermite, 144 Herschel, 95 Hesiod, 86 heterotopia, 33 hexagons, 142 hexahedral, 157 Hierarchical Data Format, 195, 196 Hilbert, 97, 102, 105, 106 Hipparcos, 68, 86, 90 hippocampus, 49 historicism, 26 Holocaust, 76 holon, 129 Homer, 84 Hopi, 57, 109 Hubble, 100 Hubserver, 196, 213, 222 human cartography, 81 human interests, 112 Humboldt, 33, 59 Hume, 12, 98 Husserl, 18, 33 Hutton, 95 Huygens, 93 hydrocarbon exploration, 156 hyperbolic spaces, 67, 97 Hypercard, 186, 189, 197, 198, 199 hypercubes, 170 hyperdocument, 186, 209 hypergeometry, 210 hypermap, 190, 195, 196, 198, 199, 209 hypermedia model, 186 Hypermedia spatial database for Kuwait, 198 hypermedia, 81, 186 Hypersnige, 198 hypertext abstract machine, 186 Hypertext Markup Language, 185, 320 hypertext nodes, 186

302

Index

303

hysteresis, 106 HyTime, 185 I idealism, 7, 8, 9, 11, 13, 14, 17, 28, 31, 112, 128 identity, 34, 39, 53, 100, 115, 117, 121, 129, 131, 137, 161, 163, 215, 235, 238 ideology, 16, 32 image schemas, 20, 21, 52, 72, 116 immanent, 123, 128 immersive virtual reality, 174 implicatures, 20 IMPORT/DOME, 194 incident wave, 235 indeterminism, 8, 9, 14, 31, 59, 62 IndexedFaceSet, 180, 192 indicatrix, 95 indiscernibility of individuals, 92 individual-based modelling, 193 induction, 12, 15, 20, 98 inertia, 91 inertial frame, 66, 91, 102 infinitesimals, 86 infinity, 86, 95, 100, 103, 105 informatics, 5, 28 information bearing object, 27, 196 information design, 21, 26, 188, 213 information flow, 4 information ontologies, 196 information representation, 201 information transfer, 129 information, 24 informational society, 26 informational structures, 185 informavores, 26 infragravity waves, 235 infra-red, 142, 175 Inquisition, 6, 91 intellectual property, 27 intentionality, 9, 17, 18 interior, 132 International Meridian Conference, 94 International Time Zone system, 69, 86, 94 Internet GIS for London, 191 interoperability, 233 Interpolation, 142 intrasignification, 74 intrinsic difference, 122 Intrinsic reference systems, 51

Index introspection, 107 inverse modelling, 170, 238 isoparametric, 146 isosurfaces, 157 J Java Database Connectivity (JDBC), 196 java, 180, 191, 192, 211 javascript, 197, 199 Judaism, 87 Julian calendar, 85, 90 Julius Caesar, 87 K Kant, 7, 11, 19, 22, 33, 49, 59, 67, 95 KARMA VI, 192 k-cell complexes, 169 Kepler, 6, 91, 100 kinaesthesia, 54 kinematics, 34 Klein, 67, 97, 98, 106 k-manifolds, 169 knowledge, 3, 15, 16, 17, 21, 24, 25, 26, 28, 36, 117 knowledge discovery in databases, 200 knowledge representation, 40, 47, 49 Kriging, 135, 157, 170 Kuhn, 5, 15 kurtosis, 229 L labile, 130 Lagrange, 92, 95, Lagrangian representation, 140, 170 Lambert, 70, 95 landforms, 121, 227 landmark knowledge, 47 lantern, 161 laser granulometer, 229 latency, 140, 182, 193 lattices, 142 laws of conservation, 95 leap years, 87 legal time, 93 Leibniz, 33, 58, 92, 99 Leonardo da Vinci, 33 level of detail, 159, 182 Lhuilier, 96 libraries, 26

304

Index Library indexing models, 195 LIDAR, 225 light-seconds, 125 linear octree encoding, 147 linguistic categories, 19 linguistics, 5, 17, 19, 21, 23 Lobachevski, 67, 97 local knowledge, 81 local time, 93, 114 locale, 113 Location Trends Extractor, 193 location-based services, 193 locative, 51 Locke, 33, 36, 98, 103 locomotion, 45 logical model, 130 Logical positivist, 110 logistic equation, 125, 171 Longitude Act, 93 longitude, 87, 92 longshore sediment transport, 235 Lorenz transformation, 99 lossless compression methods, 178 lossy compression methods, 178 LSD tree, 159 Lucretius, 33 lunar cycle, 85 lunar distance method, 92 Lynx, 153, 156 M Mach, 8, 11 macrosigns, 74 Magellan, 69, 92 Magic Tour, 190 magnitude/frequency, 129 Maimonides, 88 MapGrafix, 199 MapGuide, 212 MapInfo, 212 mapping, 31 57, 60, 63, 65, 68, 69, 80, 81, 117 MARC, 195 Marco Polo, 69 marine charts, 79, 217 markedness, 53 materialism, 7 mathematical function, 125 mathematics, 4, 24

305

Index

306

Matthew Paris, 68 May and Tanner theory, 235 Maya, 85 Mayer, 93 maze, 107 mean day, 91 mean tidal level, 77 mean times, 114 meaning, 19, 26, 74 Mecca, 88 mechanicism, 33 medial axis transforms, 49 Medusa 3D GIS, 152 MEGRIN, 195 Memex, 186 memory, 74, 108 mental maps, 43, 112 mentalese, 21, 23, 110 Mercator, 69 Mereological actualism, 41, 121 mereology, 9, 34, 41, 58 mereotopological, 41, 117 meridian, 92, 94 mesh, 153 mesoscopic, 41 metadata, 195 metadatabase, 212 metaphysical realists, 9, 31, 40, 121 metaphysics, 5, 10, 19, 22, 31, 34, 36, 40, 102, 110, 121, 131, 235 methodological individualism, 34 methodological realism, 123 metre, 125 Michelson-Morley experiment, 96, 99 microbrowsers, 189 Microcosm, 189 Middle Ages, 6, 87, 90 Middle Egyptian, 85 Mill, 7 Minkowski, 125 mobile phones, 218 Möbius, 96 modifiable areal unit problem (MAUP), 47 monster polyhedra, 96 morphological laws of space, 54 morphology, 34 movables, 43 Move-X, 198 MP3, 177

Index

307

MPEG, 178 multidimensional distance function, 184 multidimensional geo-representations, 114, 117, 121, 174, 235 multidimensional Hilbert spaces, 102 multidimensional phase spaces, 105 multidimensional representation, 31, 90 multidimensional scaling, 61 Multimedia and Hypermedia information encoding Experts Group, 185 multimedia geo-representations, 174, 205 Multimedia, 174 multiple representations, 44 Mursi, 109 N naïve geography, 35 naïve physics, 35, 36, 39, 102, 116 Napoleonic wars, 70 narrative logic, 135 National Geospatial Data Framework, 195 natural kinds, 9, 19, 121 natural numbers, 95 naturalism, 16, 19, 28 nature conservation, 205 Navaho, 110 navigation, 31, 38, 47, 54, 63, 77 neighbourhood, 45 nested in information, 25, 26, 28 Neurath, 11 New Grolier Multimedia Encyclopedia, 197 Newton, 33, 66, 91, 92, 95, 101, 102 Newtonian physics, 13, 57 Nile, 85 9-intersection model, 50 noise, 178 nominalists, 9 nomological, 9, 13, 26 non-Euclidean geometries, 39, 67, 97, 99, 102 non-orientable surfaces, 97 North Norfolk coast, 208 Notecards, 186 N-separation, 147 N-tree, 154 NURBS, 145, 152 O objectivism, 9, 16, 21, 115 Object-Oriented Geodata Model, 166 object-oriented programming, 143, 187

Index

308

observable, 26, 104, 130, 139 octal numbers, 147 octree, 147 Open Database Connectivity (ODBC), 196, 212 Odyssey, 85 OLAP, 200 Omar Khayyam, 90 OMT, 166 onshore-offshore processes, 236 ontogenesis, 58 ontological dependence, 41 ontology, 4, 5, 9, 18, 19, 22, 24, 28, 40, 58, 121, 122, 126, 135, 162 Oogeomorph, 127, 170 Open GIS, 159 OpenGL, 151 open hypermedia systems, 188 Open Inventor, 155, 159, 179 open time, 103 optic flow, 22 orbis terrarum, 68 Ordnance Survey, 212 organicism, 33 orientation, 44 Origin of the Species, 95 Ortelius, 69 ostension, 20 P Palegrave, 66 Panoramap, 212 paradigm, 3, 15, 29, 117 parallel plots, 201 parallel postulate, 97, 105 parametric equations, 144 PARCBIT, 199 Parmenides, 63 particle size distribution, 228 particulars, 9, 18 parts, 33, 41 Pascal, 91 Pavlov, 107 Peano, 106 perception, 12, 19, 22, 23, 57, 97, 108, 110 Perdurantism, 102, 123, 125, 130, 165 personal movement paths, 217 Phei Hsiu, 68 phenomenalism, 7, 8, 9, 11, 22 phenomenology, 8, 10, 18, 28, 32, 53, 60, 102, 108, 112, 115, 117, 121, 128, 174

Index

309

phi units, 229 philology, 90 photogrammetry of video, 175 photorealism, 182 physical field, 135 physicalist, 18, 19, 24 physics, 137 physiology, 34 place cells, 48 place, 32, 34, 43, 91, 112, 113 planar enforcement, 134, 141, 158 Planck, 101 planning, 137 Plato, 7, 9, 11, 32, 63, 86, 87, 88, 96 Platonic solids, 88 playback time, 175 Playfair, 97 Plotinius, 87 Poincaré, 99, 102, 106 Poinsot, 96 pointset topology, 50, 132 political economy of informatics, 81 Polybius, 87 polygon decimation, 182 polyhedra, 88, 96, 97, 106, 146 polynomials, 91, 105, 144 polytopes, 170 polytree, 147 Pope, 87, 90 Popper, 12, 15, 26, 111 portolan charts, 69 Portugal Interactive, 191 Portuguese National Geographic Information System, 195 positivism, 4, 11, 14, 16, 22, 58, 110, 130 possibilism, 60 Postgres, 159, 183, 190 Postmodernism, 8, 61, 113, 174 post-positivism, 58, 81 Poststructuralist, 35 potential path areas, 167 pragmatism, 14, 15, 26 present at hand, 18, 121 PResentation Environment for Multimedia Objects, 185 primal sketch, 23, 108 primal spatial experiences, 53 primary theory, 56 Prime meridian, 70 primitive instancing, 107, 145

Index principle of cohesion, 48 principle of contact, 48 principle of continuity, 48 principle of selection, 46 Privet Hill spit, 228 privileged frame, 58 probabilist, 12 probability, 13 process modelling, 127, 130, 235 production of space, 35 professional language for space, 77 propaganda, 74, 76 Property Management System, 155 propositional attitudes, 17, 19, 116, 121 propositional structure, 23 propositions, 8, 10, 115 protophysics, 102 Psychologists, 38 psychology, 4, 12, 97, 137 Ptolomy, 32, 59, 65, 68, 87, 90 public enquiries, 205 Public Land Survey System, 59 public participation, 81 Puluwatan, 54, 57 Pygmies, 109 Pyramid, 165 Pythagoras, 63, 86 Pythagoras’ theorem, 141 Q quadtree, 182 qualia, 18 qualitative spatial reasoning, 50 qualitative, 126 Quantitative Revolution, 60 quantum mechanics, 16 quantum physics, 8, 13, 62, 101, 103, 105, 115 Qusta ibn Luqu, 88 R raster, 142 rationalism, 11, 26, 28, 58, 103, 107 rationality, 14, 15, 16, 28, 80 Raymond of Marseilles, 69 real numbers, 95 realism, 8, 9, 14, 16, 20, 28, 129, 138 reasoning, 120, 129 Recorde, 66

310

Index reductionism, 18, 36, 131 reference frame, 126 REGARD, 200 Region Connection Calculus, 50 regions on surface methods, 224 relational database management system, 142 relational, 101, 122 relationalism, 92 relationism, 100 relationist, 58 relative space, 34, 57, 92, 99, 101, 126, 162 relative time, 176 relativism, 15, 21 relativity, 14, 16, 92, 98, 99, 102, 105, 115 relevance, 28 Renaissance, 11, 53, 65, 69, 90, 91 representation, 4, 31 Representational art, 52 representational process, 82 representational theory of mind, 17 res cognitans, 7 res extensa, 7 reservoir management, 156 residuals, 231 resolution, 129 return period, 129 Riemann, 67, 97, 104 right-handed coordinate system, 179 Ritter, 59 Rock-CAD, 151 Roemer, 91 Roman Empire, 87 rough sets, 43 routes, 48 RTM, 17, 18, 19, 21, 22, 23, 28 R-tree, 159, 164, 190 rule-based models, 137 S Sacrobosco, 66 salience, 36, 57, 82, 116, 121, 129 salt dome, 154 salt marsh, 205, 208 sampling-limited, 135 Sargasso Sea, 42 satellite imagery, 77 Saultaux, 109 Savoy Cadastre, 70

311

Index scale, 44, 128 Scaleable Vector Graphics, 191 scene graph, 179, 180, 183 scepticism, 11, 15 Schlick, 11 science, 3, 8, 13, 21, 22, 26, 28 scientism, 59 Scolt Head Island, 204, 215, 221, 228 Scolt Multimedia Project, 189, 209 sea level change, 227 sea level rise, 205, 208 Second Law of Thermodynamics, 101 sedigraph machine, 228 sedimentary architecture, 228, 229, 231 sedimentary facies, 227 sedimentological log, 228 SEDSIM, 171, 235 semantic bleaching, 53 Semantic Hypermedia Architecture, 189 semantic nets, 184, 213 semantic proximity, 186 Semantics, 19, 24, 26 semiology, 73, 200 semiotics, 20 semivariogram, 135, 157, 170 sense perception, 22 sense-making, 49 sensorimotor skills, 35, 39, 84 Sequoia 2000, 196 servlet architecture, 211 sexagismal system of numbers, 85 shadow, 86 shape grammars, 49 shape, 49 shoreline cells, 235 Shoreline Management Plans, 208 shortest path algorithm, 160 simplices, 133 Simplicius, 63, 90 simply connected, 133 simulacrum, 183, 221 skewness, 229 slope facets, 238 SMPviewer, 199, 210, 216 social constructivism, 16 social theory, 4, 34 Socrates, 11 sonification, 200

312

Index Sophists, 33 Sothic calendar, 85 Sound, 125, 177, 215 space as difference, 34 space as territory, 59 space curves, 91 space graph, 164 Space Syntax, 54 space-time composites, 163 space-time prism, 167 space-time structures, 126 space-time, 33, 99, 122, 125 SPANSmap, 191, 199 spatial agent, 140 spatial behaviour, 82 spatial data modelling, 130 spatial elasticity, 113 spatial inference rules, 48 spatial occupancy enumeration, 147 spatial reasoning, 49 spatial representation, 4 Spatial Semantic Hierarchy, 49 spatial thinking, 38 spatiality, 35, 80, 113, 179 Spatio-Temporal Data Model, 165 spatio-temporal data modelling, 136 Spatio-Temporal Entity-Relationship, 166 spatio-temporal projection, 115 Spatio-Time Environmental Mapper, 164 Special Geography, 59 Special Theory of Relativity, 98 speed of light, 91, 96, 99 spheroid, 70 spit, 72, 205, 216, 227 SQL/multimedia, 164, 183 St Augustine, 86, 87 St Sever, 68 St Thomas Aquinas, 64, 87 standard deviation, 229 star constellations, 85 states of affairs, 9, 21, 27, 31, 115 Statutes (Definition of Time) Act, 93 stereometry, 88 ST-objects, 165 stochastic models, 137 storm surges, 206 Strabo, 59 Stratamodel, 156

313

Index

314

structuralism, 16, 60, 112 structuration, 113, 114 Structured Query Language, 158 Su Sung, 90 substantivalist, 57, 92, 100 sundials, 85 Supercard, 199 Superstring, 102, 105 surf zone radiation stress, 235 surface models, 135, 222, 227 surveillance, 178 survey knowledge, 47 surveying, 4, 77, 125 swash, 216 sweep models, 145 sweeping, 107 Synthetic Environment Data Representation and Interchange Specification, 180 system theory, 111 T taxel, 168 taxonomy, 34 TCL/TK, 212 TCObject, 166 telegeomonitoring, 193 teleological beliefs, 87 Temne, 54, 57 TEMPEST, 164 Temporal GIS, 163 temporal ontologies, 103 Terraserver, 196 tesselations, 136, 141 tetrahedral network, 153 tetrahedron modelling, 228 tetrahedron, 136, 232 Thales, 63 theatre, 183 Theogony, 86 theories of modelling, 138 Theory of communication, 19, 25, 73 Theory of computation, 23 Theory of the Earth, 95 thermodynamics, 125 thesauri, 195 thing-moment, 102 3.5D visualisation, 221 3-manifolds, 106 three-dimensional discrete topology, 147

Index three-dimensional interpolation, 230 threshold, 230 thrownness, 18 tides, 85, 87, 204, 225 time geography, 167 time lapse analysis, 175 time models, 175 time/space zones, 209 timekeeping, 90, 94 timepath, 185 TIN, 222 Tioga, 196 Tissot, 95 T-O maps, 68 Toolbook, 189, 197, 198, 201 topogenesis, 32 topographic maps, 73 topological, 37, 47, 50, 126, 132 tortoise paradox, 86 total station, 217 TOUR model, 49 toxels, 170 transcendental realism, 113 transformations, 131 transperceptual space, 181 traVelleR, 192 Treaty of Tordesillas, 92 TRIAD, 124, 163, 190 triangulated irregular networks, 143 triangulation, 69 trivariate parametric equations, 144 truth in labelling, 196 truth, 9, 10, 14, 15, 16 TSQL2, 164 tuple, 136 Turing, 24 U Uccello, 90 Ukiyoe, 53 ultra-violet, 142 uncertainty principle, 14 underdetermined theories, 15 underdetermined, 123 universal server, 184 Universal Time, 95 universalism, 33 universals, 7, 9

315

Index

316

universe, 8, 9, 13, 14, 27, 100, 102 Urban modeller, 192 utility companies, 77 V V0 interoperability protocol, 196 vacuum, 91 Varenius project, 4 Varenius, 33, 59 Vasco da Gama, 68 Vector Product Format, 154 vector, 140 vectorised octree, 147 Venerable Bede, 87, 90 verb tenses, 85 verge-and-foliot clocks, 90 verification, 110 Vertical Line Interval, 177 Vidal de la Blache, 60 video, 142, 175, 215 Video algebra, 184 video strip map, 217 videometry, 216 Vienna Circle, 8, 11 virtual environments, 179 Virtual Field Course, 221 virtual geo-representations, 175 Virtual GIS Room, 181, 191, 221 Virtual Reality Modelling Language (VRML), 154, 179, 225 virtual reality systems, 221 Virtual Reality User Interface, 192 virtualisation, 175 virtuality, 175, 179 VirtualPark, 193 VL database, 183 Voltaire, 33 volumetric components, 153 Von Thunen’s theory, 110 Voronoi region, 232 Voxel Analyst, 156 voxels, 136 VRGIS, 192, 222 Vulcan, 161 W Waghenaer, 69 Warburton, 70 warranted assertion, 14

Index washover, 231 water clocks, 90 Wave refraction, 235 WAVE, 235 wave-current interaction, 235 wavelet, 183 wayfinding, 36, 48, 58, 181, 188 web GIS, 190, 212 Web3D Consortium, 179 Wellington, 70 Werner, 92 West Indies, 92, 93 Wheatstone’s Electric telegraph, 94 wholes, 33, 41 Whorf s hypotheses, 21, 57, 116 window of comparison method, 222 Wired Whitehall, 193 wireframes, 107 Wittgenstein, 11 world history model, 124 world line, 114 world time, 165, 175, 215 World Toolkit/WorldUp, 155, 179, 192 World Wide Web, 185 worldview, 5, 10, 31, 33 Wundt, 97 X Xanadu, 186 XML, 192 Y yon clipping, 181 Z z39.2, 194 z39.50, 195 Zenith, 166 Zeno, 86, 104 Z-influence factor, 230 Zodiac, 85

317