Computing Geographically: Bridging Giscience and Geography [1 ed.] 1462553931, 9781462553938

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GUILFORD PRESS e-book

COMPUTING GEOGRAPHICALLY Bridging Giscience and Geography David O’Sullivan

THE GUILFORD PRESS New York London

Copyright © 2024 David O’Sullivan Published by The Guilford Press A Division of Guilford Publications, Inc. 370 Seventh Avenue, Suite 1200, New York, NY 10001 www.guilford.com All rights reserved No part of this book may be reproduced, translated, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the publisher. Printed in the United States of America This book is printed on acid-free paper. Last digit is print number: 9 8 7 6 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data Names: O’Sullivan, David, 1966- author. Title: Computing geographically : bridging giscience and geography / by David O’Sullivan. Description: New York : The Guilford Press, 2024. | Includes bibliographical references and index. Identifiers: LCCN 2023048057 | ISBN 9781462553938 (hardcover) Subjects: LCSH: Geographic information science. | Geographic information systems. | Geography–Methodology. | BISAC: SOCIAL SCIENCE / Human Geography | SCIENCE / Earth Sciences / Geography Classification: LCC G70 .O85 2024 | DDC 910.285–dc23/eng/20231106 LC record available at https://lccn.loc.gov/2023048057

For Doreen and Waldo

Preface Writing this book has taken a lot longer than I had hoped. It turns out that moving countries, starting a new job, and a global pandemic are not conducive to writing. When you are assembling your thoughts through writing, so much the worse. Writing has been difficult for other reasons too. I have spent a long enough period of time bridging the worlds of giscience and geography to know that while there have been signs of greater sympathy between the camps of late, antagonisms, especially with human geography, remain. This is still narrow, contested ground. For every sign of a greater commitment to pluralism and understanding (Barnes, 2009), there is a suggestion that ultimately the two camps inhabit different philosophical worlds (Leszczynski, 2009), limiting the possibilities for productive exchange. This is to say nothing of the relationship of physical geography to either human geography or giscience, although, perhaps surprisingly, some of the more promising possibilities for conversation across divides have happened there (Massey, 1999, 2001; Raper & Livingstone, 2001; Lave et al., 2014; Lane, 2017). In any case, the terrain between giscience and theoretical work in geography is extensive, yet underexplored. This has bothered me for a long time, so this book is an attempt to map this terrain, to advance both geographical theory and giscience, in v

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the hope of making each more attuned to the other. There are many ways to approach this. A historical account, or a science and technology studies inquiry into geographic information systems (GIS), are possibilities. There is still relatively little work in either of these styles on GIS (Chrisman, 2006, and Wilson, 2017, are recent exceptions), by contrast with the rich literature on the history of cartography (see Harley et al., 1987-[2023]). But I have not attempted such an account. Instead, I consider key geographical concepts and explore how these have developed in recent (anglophone1 ) geographical thought, and how they manifest—or fail to—as concepts and representations in giscience, and are deployed—or not—in GIS. I hope it is clear that I am doing all this from a position of “care of the subject” (Schuurman & Pratt, 2002). The book is not an extended critique of giscience, although I am sometimes underwhelmed by actually existing geographical computing. Instead, it is an attempt to expand the thinking from geography that giscience draws on, in the hope that this will yield new and exciting kinds of geographical computing. I further hope this book can be read by any geographer—regardless of subdiscipline, or level of study; whatever their level of engagement with GIS and giscience; and considering geographer to include anyone trying to think geographically with computers.

ACKNOWLEDGMENTS The impetus to write this book was my move in 2013 from Auckland to Berkeley, where I was expected for the first time to teach an introductory class in GIS. Many will consider the material here singularly ill-suited to an introductory class.2 But the idea of presenting key geographical concepts—space, place, scale, and so on—via their GIS avatars, and reflecting on how well or badly those concepts were represented by 1 2

That my focus is on anglophone geography is an important limitation of this work and I would be interested to know if similar concerns apply in other geographical traditions. Although if spatial thinking is widely accepted as an appropriate topic in introductory classes, it is unclear why geographical thinking is not!

ACKNOWLEDGMENTS

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those avatars, if it started anywhere, started in developing the materials for Geog 80 Digital Worlds. Far from rebelling at spending time on concepts and ideas rather than learning how to “do GIS,” students in that class got a lot from the approach. Unfortunately, I’ve not been in a position to teach a similar class since 2018, but the experience convinced me that GIS or giscience or whatever we call this thing we do3 should be introduced in conversation with big ideas in geography. I thank my students from that class for their forbearance and for that insight, particularly the graduate student instructors along the way, John Elrick, Dana Rubin, Alexander Arroyo, Will Payne, Eve McGlynn, and Xiaowei Wang, and especially the brave souls who taught the class in summer sessions and in the Fall of 2018 when I rather abruptly departed Trump’s America. Alexander, Will, and Eve were also among the students in Geog 254 Seeing Geographically, a seminar where we explored many of the obscure intersections between art, cartography, giscience, mathematics, and the digital humanities that show up in these pages (and many more that unfortunately don’t). I don’t expect any of them to be impressed by my still naïve takes on critical theory as it manifests in the geography literature, but they along with other students at Berkeley—John Stehlin, Alex Tarr, Adam Jadhav—bear some responsibility for me thinking a book like this just might work, if none of the blame for how it has turned out. While my time at Berkeley inspired me to start writing, I owe a debt of gratitude to so many others. First and foremost this book would not exist but for the unstinting support of Gill. Even her enthusiastic but awkward—for me—prompting to pitch the book’s message to many hapless civilians (who naïvely thought they’d come over for dinner) worked out for the best, as rambling lectures attempting to explain what I was doing clarified my thinking. Fintan and Malachy have been similarly supportive, not least by just getting on with life on the complicated space-time trajectory we’ve put them through. While thinking through these ideas, I’ve been helped along the way by numerous colleagues and students, over several years. Most of them 3

Maybe a little more than half in jest Mike Goodchild recently suggested “geospatial. . . er. . . stuff” (2015).

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appear at some point in the extensive references. Colleagues at University College London, Penn State, Auckland, Berkeley, and Te Herenga Waka Wellington have at various times, in various ways, influenced my thinking, knowingly or not. It is particularly important that I thank my PhD advisor Mike Batty to allay any impression that my time at UCL in the Centre for Advanced Spatial Analysis was intellectually narrow, which my comments in the first chapter might imply. Mike was (and is) a tremendously broad thinker. He might disavow many of the things I discuss in this book, but his openness to intellectual exploration is ultimately where this book comes from. A book like this cannot help but owe a great deal to academic inspirations, among them Bill Bunge, Helen Couclelis, Danny Dorling, Pip Forer, Mark Gahegan, Doreen Massey, Gunnar Olsson, Waldo Tobler, and Dave Unwin. Among colleagues and friends who I flatter myself are my peers in denial of their brilliance, I owe particular thanks to regular correspondents Luke Bergmann, Nick Lally, and Jim Thatcher, and also to Wokje Abrahamse, Ben Adams, Brendon Blue, Carolyn Boulton, Cathryn Carson, Ralph Chapman, Brett Christophers, Alicia Cowart, Mairéad de Róiste, Igor Drecki, Matt Duckham, Dan Exeter, Rachel Franklin, Gina Hochstein, Sara Kindon, Laurel Larsen, Jane Martin, James McCarthy, Chris McDowall, Tony Moore, Fraser Morgan, Warwick Murray, George Perry, Nathan Sayre, Mirjam Schindler, Renée Sieber, Seth Spielman, and Amanda Thomas. I am especially grateful to Eric Sheppard and May Yuan, who provided constructive commentary on an unsolicited draft, and also to John Kostelnick, Steve Manson, and Matt Wilson, whose suggestions, along with those of one anonymous reviewer, were clarifying. Thanks also to my editor, C. Deborah Laughton, who remained enthusiastic even after 2 years of radio silence, as well as to Liz Geller, Paul Gordon, and the rest of the Guilford team. Finally, Rosa (the cat) has surely contributed something. Writing alone is harder than I thought, and Rosa’s quiet omnipresence has ensured I was never entirely alone. If nothing else, she has put in the hours. David O’Sullivan ∼ Te Whanganui-a-Tara ∼ September 2023

Contents

Preface Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . List of Figures

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1 Building Bridges A History of My Spaces . . . . . . . . . . . Becoming a GISer (1996–2000) . . . . . Becoming a Geographer (2000–2004) . . Becoming a Bridge (2004–) . . . . . . . . Reflections . . . . . . . . . . . . . . . . . Plan of the Book . . . . . . . . . . . . . . . On the Imperfectibility of Representations How to Read the Book . . . . . . . . . . .

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2 Location and Space The Nature of Space Absolute Space . . Relative Space . . Relational Space .

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Space in Giscience . . . . . . . . . . . . . Absolute Space in GIS . . . . . . . . . . Relative Space in Quantitative Geography Prospects for Relative/Relational Giscience Data Structures That Include Adjacency . The Voronoi Model of Space . . . . . . . Object Fields . . . . . . . . . . . . . . . Graph Databases . . . . . . . . . . . . . Spatial Analysis and Spatial Models . . . From Space to Everything Else . . . . . .

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3 Scale and Projection Scale in Geographical Theory . . . . . . . . . . . . . Scale as Size or Scope . . . . . . . . . . . . . . . . Scale as Hierarchy . . . . . . . . . . . . . . . . . . Scale as Socially Constructed . . . . . . . . . . . . . The End of Scale? . . . . . . . . . . . . . . . . . . Scale in Giscience . . . . . . . . . . . . . . . . . . . . Scale and the Web Map . . . . . . . . . . . . . . . Scale and Map Projection . . . . . . . . . . . . . . Scale-Dependencies: Resolution and Generalization The Salience of Scale . . . . . . . . . . . . . . . . . .

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4 Place and Meaning in Space From Space to Place . . . . . . . . . . . . . . . . . Making Space Legible: Addressing the World . . . Place: The Intersection of Space With Experience Everything in Its Place . . . . . . . . . . . . . . . Place in Relational Space . . . . . . . . . . . . . . Place in Giscience . . . . . . . . . . . . . . . . . . Place as Vague Location: Gazetteers . . . . . . . . Place as Geographical Context . . . . . . . . . . . Place and Meaning . . . . . . . . . . . . . . . . . Place in Mind: Cognitive Maps . . . . . . . . . . . Toward Computable Place? . . . . . . . . . . . . .

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5 Lines and Areas Drawing Lines: The Originary Power of Maps . . . The Map and the State . . . . . . . . . . . . . . . New Lines and Countermapping . . . . . . . . . . Territory and Territoriality . . . . . . . . . . . . . . Escaping the Territorial Trap . . . . . . . . . . . . Fiat and Bona Fide Boundaries and Objects . . . . When the Map Is and Is Not the Territory . . . . . Exclaves: Territory Interruptus . . . . . . . . . . . Territory, Borders, and Movement . . . . . . . . . Territory and Property: Cadastral Data . . . . . . Territory and Governance: Statistical Aggregations The Arbitrariness of Boundaries . . . . . . . . . . . The Modifiable Areal Unit Problem . . . . . . . . Regionalizing Space . . . . . . . . . . . . . . . . Moving On From Geometry . . . . . . . . . . . . .

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6 Relations, Networks, Flows Relations, Space, and Place . . . . . . . . . . . . Mathematical Graphs . . . . . . . . . . . . . . Relations Do Not a Network Make . . . . . . . Network Science . . . . . . . . . . . . . . . . . Local Properties . . . . . . . . . . . . . . . . Network Distance and Path Lengths . . . . . . Centrality . . . . . . . . . . . . . . . . . . . . Connection, Disconnection, and Communities Functional Roles and Blockmodels . . . . . . . Small Worlds . . . . . . . . . . . . . . . . . . Graph Drawings as (Possible) Projections . . . . Networks Are Flows Frozen in Place . . . . . . .

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7 Time and Dynamics 181 Time and Space: A Coin With Two Sides . . . . . . . . . . . 182 Cartography and Giscience’s Problem With Time . . . . . 184 The Trouble With Snapshots . . . . . . . . . . . . . . . . 190

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Hägerstrand’s Time Geography . . . . . . . . . . The Space-Time Aquarium . . . . . . . . . . . Limits to Time Geography . . . . . . . . . . . . . Beyond Time Geography: Mobilities and Human Dynamics . . . . . . . . . . . . . . . . . . . . . From Time to Dynamic Processes . . . . . . . . .

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8 Process and Pattern Process Philosophies . . . . . . . . . . . . . . . . . . . Process, Space, Place, and Pattern . . . . . . . . . . . Related Strands in Geographical Thought . . . . . . . Postscript: Process in General and Process in Particular The Place of Complexity Theory . . . . . . . . . . . . Getting to Grips With Complexity . . . . . . . . . . . Reflecting on Complexity . . . . . . . . . . . . . . . Simulation Models . . . . . . . . . . . . . . . . . . . . Cellular Automata . . . . . . . . . . . . . . . . . . . Agent-Based Models . . . . . . . . . . . . . . . . . . CA and ABMs as Geographical Process Models . . . . Process and Pattern Revisited . . . . . . . . . . . . . .

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9 Doing Giscience Doing Geography Common Ground: A Space to Think . . . . . . . . . . Doing Giscience: Representation as Process and Practice Toward Doing Differently . . . . . . . . . . . . . . . . Finally. . . . . . . . . . . . . . . . . . . . . . . . . . . .

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References Index About the Author

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The companion website at www.guilford.com/osullivan-materials provides the figures, code to produce versions of selected figures, updated web links, and other resources.

List of Figures 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

A representation of an absolute space . . . . . . . . . . . Three views of Aotearoa New Zealand data . . . . . . . Cartogram deformation grid . . . . . . . . . . . . . . . Two point patterns in absolute space . . . . . . . . . . . The GeoJSON file format . . . . . . . . . . . . . . . . . . Slivers and gaps in a polygon layer . . . . . . . . . . . . Voronoi polygons associated with a set of point locations Voronoi polygons associated with lines and polygons . . A range of spatial weights applied to polygon data . . . .

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A nested hierarchy of scales . . . . . . . . A spatial hierarchy . . . . . . . . . . . . . Montello’s (1993) spatial scales . . . . . . Three levels of web map hierarchy . . . . Distances on tile 0/0/0 . . . . . . . . . . Latitude and longitude . . . . . . . . . . Two simple world projections . . . . . . . A loxodrome on the sphere and projected Equal area world in a square . . . . . . .

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3.10 Raster aggregation and disaggregation . . . . . . . . . . . . 3.11 Map generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Geohashes and hierarchical indexing . . . . Neighborhoods in Wellington, New Zealand Many Springfields . . . . . . . . . . . . . . Google maps of vague places . . . . . . . . Te Reo M¯aori toponyms in Aotearoa . . . . Distortions in cognitive maps . . . . . . . .

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The 9-intersection model of topological relations . . . The Cooch Behar enclave complex . . . . . . . . . . . The border–crossing dual . . . . . . . . . . . . . . . . Flint, Michigan municipal boundary and ZIP codes . . Maps of areas with widely varying populations . . . . . Simple illustration of the modifiable areal unit problem The MAUP aggregation effect . . . . . . . . . . . . . The zoning or gerrymandering effect in MAUP . . . . Zones designed to achieve equity . . . . . . . . . . . . Simple regionalization of San Francisco Bay Area . . .

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6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14

Levels of detail in representation of a street network . . Commutes into Upper Hutt Central . . . . . . . . . . Clustering coefficient of a vertex . . . . . . . . . . . . Paths in a network . . . . . . . . . . . . . . . . . . . . Reduced world city network data viewed conventionally Reduced world city network data viewed geographically World trade network communities . . . . . . . . . . . Group and bipartite structure in simple graphs . . . . . Another look at the trade network as a blockmodel . . The small world rewiring process . . . . . . . . . . . . The small world rewiring process in two dimensions . . A simple graph drawn nine different ways . . . . . . . World city network data viewed purely as a graph . . . Relative time map of the Santa Barbara street network

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7.1 7.2 7.3 7.4 7.5 7.6 7.7

Some ways a polygon can change . . . . . . . . . . . . . Simple space-time path for a day’s activity . . . . . . . . A meeting in the space-time aquarium . . . . . . . . . . Capability and coupling constraints in space-time . . . . Time geography prism in three-dimensional space-time Space-time paths for 100 Beijing taxis . . . . . . . . . . Coordination in space-time paths . . . . . . . . . . . . .

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The 32 symmetric one-dimensional cellular automata . The one-dimensional rule 110 CA . . . . . . . . . . . The game of life CA . . . . . . . . . . . . . . . . . . A voter model CA . . . . . . . . . . . . . . . . . . . . The Schelling-Sakoda segregation model . . . . . . .

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Chapter

Building Bridges ike everyone else, geographers have been using computers regularly for well over half a century. As elsewhere, in geography, the computer “became what various groups of people made of it” (Mahoney, 2005, p. 119). Perhaps more so than other academic disciplines, geography’s public identity has become bound to a whole genre of software platform, geographic information systems (GIS1 ) and an accompanying would-be science, geographic information science (giscience2 ), which aims to advance how computation can be applied in specifically geographical settings. But to a surprising extent these developments have occurred in isolation from developments in geographical

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Here and elsewhere, unless it is clear from the context, I intend GIS to stand in for the broad spectrum of geographical computing encompassing GIS, GPS, web-mapping, location-aware devices, and so on. I do not mean only desktop GIS. I am breaking with standard usage and not capitalizing the first three letters of giscience. This is partly for balance with geography, with which it is frequently paired in this book, and which—witness Bill Bunge’s “The Geography” (1973) —it feels absurdly portentous to capitalize; partly because the GIS in GIScience is itself an abbreviation, making it a bizarre portmanteau abbreviation anyway; and finally, because there seems no particular reason to adopt the unconventional use of mixed upper and lower case in that word alone. Written as giscience it amuses me to imagine it a kind of omniscience, pronounced accordingly. This choice is unrelated to Bergmann & Lally’s use of lowercase “gis” for their geographical imagination systems (2021), which I nevertheless fully endorse.

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thought and from the concepts used by geographers to describe, discuss, and explain the world. Perhaps this is because the widely held belief that geographers have had much to do with the development of GIS is wishful thinking: According to Paul Longley, “geography has never been central to the development of GIS” (2000, p. 39). Whatever the reason, giscience is not central to geography in the way that, for example, bioinformatics has become central to much of contemporary biology (Stein, 2008; Bartlett et al., 2017). This book aims to bridge the gap between giscience and geography to the benefit of both. More than that, I want to assert that giscience is geography, and also that geography and its disciplinary concerns belong at the heart of giscience, an argument that is particularly pressing with the rise of notions of data science unmoored from any disciplinary underpinnings. After all, if giscience has little or no connection with geography, why not leave it to the computer scientists, mathematicians, and physicists? I originally planned for this opening chapter to be a historical account of the relationship between giscience and geography. It would open on a couple of my intellectual heroes from early in geography’s quantitative revolution, showing how their work was deeply engaged with geography, and contrast that with how distanced from geography giscience and GIS have become. Then, somehow or other I was going to explain how this distance had grown. Perhaps due to GIS’s roots in automated cartography and the military? Or because of the uptake of GIS in contexts where its bureaucratic instrumentality obviates any need for it to be geographically interesting? Or was it an outcome of the academic science wars of the early 1990s? Or did the embrace of GIS in universities as a skill that geography degrees could promise students cause tensions between GIS and non-GIS colleagues? But that version of this chapter was failing to cohere, and instead was mutating into a mildly embarrassing paean to a couple of old geographers from way back when. I was also falling into the traps of presentism discussed by David Livingstone in The Geographical Tradition, and seeking “self-justification from the heroes of the past” (1993, p. 5). I think that some version of the story above remains to be told, by someone, but not

A HISTORY OF MY SPACES

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by me. Telling it will require trips to archives and interviews with any protagonists who are still around.3 Instead, I decided to present a story I know much better: my own experiences as student and educator in geography and giscience. This draws attention to the last of the hypothesized explanations above, the contradiction and tensions between separate distinctly geographical and giscience education pathways. It is those contradictions which this book aims to address as a step toward bridging giscience and geography. This involves some autobiography: I can only hope it’s not too self-indulgent, and offer that it’s been at least as hard for me to write as it will be for you to read. In any case, it’s important to know where I am coming from if you really want to know what this book is about, so here goes. . .

A HISTORY OF MY SPACES4 Becoming a GISer5 (1996–2000) I first ran into GIS as an engineer, at a trade show. One thing led to another, and I ended up with a Masters in Cartography and Geographic Information Technology. I went on to do a PhD at University College London (UCL), inspired by the director Michael Batty’s Fractal Cities (Batty & Longley, 1994) and other work at his Centre for Advanced Spatial Analysis (CASA) applying ideas from chaos, complexity, and computation to cities. CASA was an amazing place to do research in the late 1990s. The complexity “vibe” combined with the newness of the internet at that time as the first dotcom bubble blew up and burst was a heady mix. 3

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Trevor Barnes has done archive work and interviews (Barnes, 2001, 2003, 2004, 2006, 2008, 2014; Barnes & Wilson, 2014) ; and there are insider histories (Chrisman, 2006; Foresman, 1997), and the beginnings of more critical histories (Wilson, 2017), but much remains to be done. With apologies to John Pickles (2004). I use the term “GISer” with affection—and consider myself one. I consider a GISer to be fully the equivalent of a giscientist without the superior tone of the latter. Many people, not only geographers, use GIS and other geospatial technologies at a high level without ever becoming, wishing to become, or identifying as giscientists.

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What was nevertheless strange, in an ostensibly interdisciplinary center combining geography, architecture, planning, and computing, was the disconnect from geography, both locally from the UCL department, and more generally. There was also a book, Ground Truth (Pickles, 1995), hovering around in the background, and mutterings at conferences like GISRUK and GeoComputation where older GISers would complain or joke about the latest allegedly crazy work of their human geographer colleagues, over morning coffees or evening beers. Given my research topic, which I self-importantly thought was grappling with the very nature of space, I was reading work apparently deemed crazy by many of my peers.6 Yet, much more puzzling to me than any geographical musings on the nature of space was the apparent indifference to such matters among other GISers.

Becoming a Geographer (2000–2004) Academic dues paid, I hit the job market and was lucky to get a tenure track job in geography at Penn State. I arrived amid a generational changing of the guard as one of six new hires,7 and mutual commiseration about the tenure process made for a tight-knit group. Not a GISer among them, and all of them doing brilliant, fascinating research! After the all-digitalonly-digital-all-the-time hothouse of CASA it was eye-opening: There was nothing crazy about their research, which was much more attuned to things I cared about than most giscience. It was conversations about geography, politics, and life in general with my Penn State cohort that led me to write more thoughtfully about complexity theory (O’Sullivan, 2004) in a broader context of geographical thought than I otherwise would have, based on my graduate training.

6 7

My unconvincing conclusions are in Chapter 2 of the thesis, available at https:// southosullivan.com/phd/. Lorraine Dowler, Colin Flint, James McCarthy, Melissa Wright, Chris Benner, and me. There were many other brilliant colleagues in the department, but if I list everyone, this book will never end.

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Meanwhile, it was increasingly apparent how far apart giscience and geography were, especially in the oral “comps” exams for graduate students, who were expected to cover all of geography. I was a popular exam commitee pick for human or physical geography candidates keen to avoid a grilling on cartographic theory; meanwhile other colleagues served similar roles in their respective subfields for the giscience students! Parallel to this pragmatic acknowledgment of geography’s lack of breadth, the all-year orientation to geographical research for graduate students was not infrequently staged as a standoff between quantitatively and qualitatively oriented students. It was hard to make any sense— in a discipline pretending to breadth—of such deliberate siloing into subdisciplines.

Becoming a Bridge (2004–) State College was a bad place for my partner’s career, so we decided to move on, this time to T¯amaki Makaurau Auckland. I wrote three giscience progress reports in the years after the move (O’Sullivan, 2005, 2006, 2008), and again, I adopted an openness to wider currents in geography in reviews of time, critical GIS, and agent models. It was the middle one of those reviews that had the biggest impact on what happened next (and on this book). It led to an invitation to a panel discussion “Straddling the Fence: Critical GIS” at the Association of American Geographers (Wilson & Poore, 2009), and made me part of ongoing critical GIS conversations, which almost certainly played a part in my getting a job at Berkeley in 2013. There had not previously been a (permanent) GIS position in geography at Berkeley, and rumors of a department dominated by critical human geographers, hostile to giscience, must be why some giscience colleagues saw this as a win for “team GIS,” an attitude I found odd: Aren’t we all geographers after all?! Like Allan Pred, whose recollections of becoming the token quant in geography at Berkeley (Pred, 1983) I read soon after arriving, the thing I found most compelling about the place was its (benign) indifference. Like Pred, I found that freeing.

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Whatever the truth about any earlier antipathy toward giscience, the tangible result was that there was no GIS program housed in the geography department at Berkeley, but there was a campus-wide GIS minor. That allowed space to think about what it means to teach GIS in a department committed (at the undergraduate level at any rate) to geography writ large, unencumbered by teaching nuts and bolts GIS skills, since such a class was available elsewhere on campus. The freshman geospatial course I developed in geography took full advantage. The technical skills dimension was not desktop GIS, but web-mapping, and the class was structured—like this book—around concepts like scale, space, place, boundaries, and so on.8 I was also able to deepen connections with critical GIS colleagues in North America, and work with graduate students who had evaded or refused geography’s silos. Many had other first degrees and saw no reason why critical geographies and giscience shouldn’t be friendly fellow travelers. Professionally, Berkeley was energizing, and I wish we had felt able to stay, but after the 2016 election we were keen to leave a place that suddenly seemed much more foreign, and return to Aotearoa New Zealand, which, it was by then clear, is home. Back there, in Te Whanganui-aTara Wellington, I have tried to translate the lessons of Berkeley, but here, the silos endure. We offer a GIS program that has little space or time for bridging to bigger ideas in geography, and the students tend to be skills- and job-focused. Whatever the forces are that keep giscience and geography so distinct, they are thriving in Aotearoa New Zealand.

Reflections In sum, since I missed out on wider debates on geographical thought in my giscience education, it has been a series of accidents, traced above, that have led me to try to intervene to the extent I can, by changing my own teaching, and writing this book. The contingent details all feel like they matter: my becoming a geographer alongside a wave of critical human geographers at Penn State; my subsequent choice to write 8

Slides from that class are available at http://southosullivan.com/geog80/.

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a review of critical GIS; and then a position at Berkeley where thinking seriously about the intersections of giscience and geography felt obligatory, and the absence of a GIS program housed in the geography department allowed room for it. I didn’t start out a geographer, except in the sense that we are all geographers, whether naïve (Egenhofer & Mark, 1995), accidental (Unwin, 2005), folk (Bunge, 1971), amateur (Merrifield, 2017), or whatever. In one or other of those senses I have always been a geographer. So, like most, I arrived in academic geography prepared by everyday experience for thinking about space, place, scale, boundaries, movement, space-time, and so on. Yet, coming to geography via giscience I was not required to think too hard about any of those big ideas except in narrowly technical ways. Picking up and using available geospatial tools as they are, taking whatever assumptions about these concepts they embed for granted was (and still is) the norm, outside a narrow slice of the giscience literature. That slice where thinking more deeply about such concepts is best represented is the Conference on Spatial Information Theory (COSIT) series. But that literature remains very academic, unlikely ever to be taken up by widely accessible platforms. Furthermore, the theoretical touchstones for that community tend to be psychology, computer science, mathematics, and philosophy, not geographical thought. Meanwhile, limited debates about space in relation to mainstream geospatial platforms seem to have run out of steam by the time the first GIS textbooks started appearing in the mid-1980s (Burrough, 1986). When I encountered GIS, some of these concerns were coming to the attention of the giscience community through the GIS and Society Research Initiative 19 of the U.S. National Center for Geographic Information and Analysis (Harris & Weiner, 1996). This was a response to an earlier GIS and Society meeting in 1993 (see the special issue of Cartography and Geographic Information Systems, Poiker, 1995). The details of this story need not be repeated here (see Schuurman, 1999). The striking thing, in retrospect, is how little impact these developments had on my giscience education. It wasn’t until a full decade later, when I chose to engage with it (O’Sullivan, 2006), that critical GIS came into focus for me.

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Critical GIS has accomplished many things, not the least of which has been a softening of antagonisms that seemed at one time to equate any use of GIS with reactionary stances, rendering such use beyond the pale for many in human geography. It seems clearly preferable to explore the possibilities for progressive uses of geospatial computing than to eschew exploration entirely. Tensions remain, and there are certainly contradictions inherent in recent work under the rubric of critical GIS (Lucchesi, 2022) where it may be “contradictory to rely upon infrastructure, algorithms, data, and platforms constitutive of dispossession in our own mapping work” (McElroy, 2022, p. 359). This quote hints at where critical GIS has been less successful. Given that GIS is more than a piece of software but rather a complex network of machines, institutions, people, and practices, critical GIS has changed GIS, and changed it for the better. What critical GIS has not done is to change the affordances of the computational tools and associated representations around which doing GIS revolves, so that users are not forced to choose between accepting its default representations of geography, or walking away and adopting other methods more congruent with the needs of their project. Further, it would be nice to imagine that by now critical GIS thinking would have percolated widely, but experience in teaching programs over two decades suggests that critical consideration and remaking of giscience’s default representations remains peripheral, relative to challenging the ethics of GIS practice (Elwood & Wilson, 2017). Meanwhile, the “geographical information science” coinage (Goodchild, 1992) at the time of the GIS and Society initiatives, and the term’s rapid adoption, also seems likely to have had the effect of “constraining the entry points to participate in the field” and “enhancing its position in the scientific community” (Harvey & Chrisman, 2004, p. 77), while doing little to foster parallel attempts to consider “paths taken or not taken in GIS development” (Sheppard, 1995, 14, but see Goodchild, 2018). By the same token, on the other side of the fence, digital geographies (Ash et al., 2019; Thatcher et al., 2020) have tended to direct critical scholars’ attention toward critiques of geospatial platforms and their societal impacts and away from the ways in which diverse geographies

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are represented computationally and how those representations might be changed. With all this in mind, it is unsurprising that a mix of bemusement, trepidation, and/or disinterest is the reaction of most of my giscience colleagues to the fast flowing currents of geographical thought. And if becoming a GISer makes it unnecessary to navigate those waters, then why bother? This is the gap between geography and giscience that I hope this book can begin to bridge. The gap is real and, I am certain, is detrimental to geography and to giscience.9 Geographers of all stripes— accidental, amateur, folk, naïve, professional—may, with varying degrees of intent, deploy concepts such as scale, space, place, relationality, neighborhood, process, and so on, and these concepts also influence how computation is applied to geographical questions—regardless of whether they have been explicitly recognized in the implementation of the geospatial tools in use. There is therefore much to be learned by geographers and GISers from examining these concepts from these dual perspectives. That’s the idea, and it governs how the book is organized.

PLAN OF THE BOOK The details are spelled out below, but at its core this book is a series of chapters each exploring one, two, or a few related big ideas in geographical thought, the implications of those ideas, and how—if at all—they manifest in giscience. Chapter 2 Location and Space As will become clear, the geographical concepts considered are intimately intertwined with one another, so we could start almost anywhere. Nevertheless, location and space are a promising jumping off point. Location in the form of a dimensionless point has been strongly emphasized as 9

I can’t help but note—in full awareness of the irony—that it has been a contributory factor to the disestablishment of postgraduate giscience at Victoria University of Wellington in 2023, and the consequent loss of my job.

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fundamental in giscience (Frank & Goodchild, 1990; Goodchild et al., 2007), apparently oblivious to Whitehead’s disparaging reference to this concept as mere “simple location” ([1925] 1967, p. 50). In this chapter we explore the much richer perspectives on space in geographical thought. Many of these concepts are clearly related to other concepts discussed in later chapters, which in turn rely on richer conceptualizations of space than those provided by simple location. Chapter 3 Scale and Projection If locating where things are is a first priority in giscience, deciding at what resolution, and over what spatial extent things must be put into relation with one another comes a close second. This brings us to the subject of scale and to the closely related technicalities of different projections. While the concerns of giscience with scale and projection are generally considered to be technical matters, geography’s rich literature on the topic suggests that deeper issues are at stake, which can be definitive for how different phenomena are understood and subsequently contested. In this chapter, I suggest that while giscience does not explicitly recognize such epistemological and ontological issues in its handling of scale and map projections, these matters are nevertheless familiar in practice, via questions concerning appropriate scales for analysis, resolution or grain, and map generalization. Chapter 4 Place and Meaning in Space A recurring puzzle in geographical thought is the relationship between place and space. What the similarities and differences are between spacebased and place-based approaches in geography and in giscience is considered. Much of the difference lies in how people attach meaning to space, in the process turning abstract space and location into concrete— if ambiguous—places such as neighborhoods. The discussion here lands variously on human-centered addressing systems that define places, on experiential perspectives on place, and on how place is intimately bound

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up with ideology and power. I also consider how these concepts are realized in computational systems, focusing on toponyms, gazetteers, and geotags as ways, albeit often narrowly instrumental ones, to associate meaning with geospatial data. Chapter 5 Lines and Areas The archetypical map, familiar from schoolrooms everywhere, is a political map of the world, with the territory of each sovereign state colored to distinguish it from that of its neighbors. The dotted lines, hatched shadings and other devices that show up on such maps in disputed regions give the lie to any notion that the world can be so simply divided. Further, the national boundaries highlighted by such maps are only the most visible example of the centrality of cartography to the assertion of territorial rights, ownership, and other claims to power over land, resources, and (very often) peoples. Notions like region can also be thought of as how place manifests at scales below the national and supranational. Their definition often involves delineating crisp polygons, even when the fuzziness of the concepts in the real world is recognized. Beyond the troubled relationship between the complexities of all of these and their imperfect rendition in maps and data, some fundamental challenges of giscience, particularly the modifiable areal unit problem, are manifest when dealing with polygon data, and this is also considered here. Chapter 6 Relations, Networks, Flows In this chapter we move decisively away from simple location and recognize, as geographers have done for decades, that geographic phenomena can only be properly understood as relational. Any particular thing in the world is only defined through the relations it has with other things of similar or different types. Some aspects of these relations may be mappable and better understood as systems of relations or networks. Network connections are generally associated with flows of materials, people, resources, money, information, and so on, but may be more broadly

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about any assortment of relations among places and things. Network science has grown rapidly in recent years, and here we consider its potential for exploring relational understandings of space and place that underpin contemporary geographical thought.

Chapter 7 Time and Dynamics Geography is sometimes characterized as the discipline concerned with space, while history is concerned with time, a dichotomy giscience is often quick to embrace. Equally, its roots in automated cartography have left giscience much less attuned to time, change, movement, and dynamics, a weakness only recently receiving more concerted attention. Torsten Hägerstrand’s time geography (1970) offers a way forward here, with rich connections to various strands in geographical thought, but also introduces some problems, both practical and theoretical. In this chapter we review these ideas and the associated debates.

Chapter 8 Process and Pattern Reflecting on the previous two chapters, the dynamic spatio-temporal nature of things is perhaps best understood through the intimately intertwined notions of process and pattern, and the relation of these ideas in turn to process philosophies. As elsewhere, we will find that giscience approaches have a tendency to attenuate these rich concepts. I consider the potential for computational simulations and other dynamic representations to address these limitations, alongside concepts in geography aligned with complexity thinking, and a variety of strands in contemporary philosophical thought.

Chapter 9 Doing Giscience Doing Geography In the final chapter I reflect briefly on what the foregoing suggests for the future of giscience and geography.

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On the Imperfectibility of Representations As has been suggested, we could easily shuffle or even upend the sequence in which geographical concepts are considered. Why proceed from the most reduced abstraction of simple location toward richer representational approaches that can capture aspects of meaning, process, dynamics, and change over time? This sequence risks emphasizing representations as somehow prior to the things represented; why not start from the nature of the world, and then pare our representations back bit by bit? The logic for working through concepts in this sequence is fourfold. First, it mirrors how concepts in giscience are often presented, starting from simple and building to richer and more complicated models. Second, over 20 or so years teaching giscience, I have found that it is difficult to jump into the deep end of process-relational models from the outset, even if, as proponents of process thinking argue, it is an intuitively satisfying approach. Third, the sequence is somewhat historical, reflecting the increasing richness over time of how concepts from geographical thought have been represented in giscience. Finally, books are linear, and lacking the chutzpah of Gunnar Olsson (1980) I had to start somewhere!10 Another danger of this ordering of chapters is my implying or readers inferring that successively richer representations can eventually yield a perfect mirror of the world; this might even suggest that if only we could represent the world more faithfully we might also be able to perfect the world. This is not a position I subscribe to.11 My major interest as a geographer has been in working with dynamic simulation models of complex dynamic geographical systems (see Chapter 8), a subfield where the necessity for many models at varying levels of detail, scale, complication, and elaboration is clear. There is no perfect representation or

10As

Jarvis Cocker puts it in Common People. Jenny Odell recently put it, “I can’t help but ask the question: What does it mean to construct digital worlds while the actual world is crumbling before our eyes?” (2019, p. xiv).

11 As

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model of the world. As George Box reminds us, “[m]odels, of course, are never true, but fortunately it is only necessary that they be useful” (1979, p. 2). Geographical computation relies on representations, but, like mapping, is processual (Kitchin & Dodge, 2007). This is a much more fruitful place to begin, and a more accurate reflection of where I am coming from in terms of the relationship between the world and our attempts to represent it computationally. Seen from this perspective, giscience can be understood in part as a kind of geographical metaphysics, or in more contemporary jargon as a body of ontological theory, confined to those things that giscience has got around to considering and has expressed in computational representations. Doing GIS as “both technical and critical” (Wilson, 2017, p. 2) should be as much about thinking with and through the representations we are manipulating computationally as it is about the manipulations themselves. All too often, doing GIS involves adopting pre-given representations without thinking too hard about the concepts behind them or the commitments they entail. As Doreen Massey suggests, “[c]onceiving of space as a static slice through time, as representation, as a closed system and so forth are all ways of taming it” (2005, p. 59). I am therefore keen to avoid focusing only on the representational aspects of giscience, even if by the end of the book those representations are explicitly neither static nor closed. Like Massey, I also want to draw attention to how space embeds power relations. By placing giscience in the context of geographical theories that recognize the power-laden nature of our representations, I hope to encourage more reflection on these aspects of doing GIS. Many cartographers have recognized the power of maps (Wood, 1992) yet giscience remains relatively resistant to recognizing its relationship to power, notwithstanding the efforts of the critical GIS community over many years (Pickles, 1995; Schuurman, 1999; Wilson, 2017). It is more useful then to think about computational models as propositions (see Krygier & Wood, 2009; Wood, 2010b), or arguments, or if we stick with representation, as representations of theoretical positions about a complex, unequal, and power-laden world.

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How to Read the Book Returning to the more mundane question of the chapters proceeding from simple location to process-relational dynamics: Yes, we move from the ostensibly simplest giscience models to potentially richer ones. We proceed from where giscience finds itself, or perhaps where geographers more widely consider giscience—rightly or wrongly—to be, through to other places, where it might aspire to be. But we set off in this direction aware that the starting place of simple location really is not obvious, however natural seeming it might appear. That it seems in any way natural is the product of hundreds of years of effort: in six hundred years of surveying, cartography, nation-building and GIS, the idea that there is a (single) geographical space has become naturalized [. . . ] This means that it is very difficult to imagine space as anything other than some kind of neutral container within which places [. . . ] may be located. And this in turn means that any attempt to challenge this picture is very hard work and runs against the grain of common sense (Law & Hetherington, 2000, p. 44).

Turning giscience away from the simplicity of its dominant representations toward something that reflects better the astonishing and contested complexity of the geographies that surround us is one of the aims of this book. But again, the point is not to argue that any one representation or perspective is correct, it is merely to show that many other representations are possible than the dominant ones we default to, often merely because they are so deeply embedded in the tools we research and teach with. Different subfields in geography, such as physical geography, biogeography, and Marxist, feminist, humanistic, and other flavors of human geography, come in and out of focus at different points in different chapters. A book could be written relating any of these (and other) subfields to giscience12 emphasizing the particular approaches to specific geographical concepts prevalent in that subfield. I have aimed for broad 12 Indeed,

some of the most compelling introductions to GIS are through the lens of a particular subfield. See, for example, Cromley & McLafferty’s excellent GIS and Public Health (2012).

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coverage, without any pretense to completeness. I am particularly conscious that Indigenous, Black and queer geographies are short-changed, largely because I feel especially ill-equipped to do these perspectives justice. Suffice it to say that an emphasis on particular subfields in particular chapters is not intended to imply that others are silent on the matter. I also recognize that many of these concepts are not the exclusive domain of geography, but it has been difficult enough to trace them within geography without taking on the additional challenge of reading even more widely in physics, psychology, architecture, archaeology, ecology, and beyond. I can only hope that readers are inspired to seek out perspectives closer to their own subfields where I have neglected them. In any case, the chapters can be read in any order. There are crossreferences throughout, since none of these topics is entirely separable from the others, and the many literatures and approaches are mutually constitutive of one another. It’s difficult to say much about space without also talking about place and scale; or about place without talking about boundaries and movement; and so on. There are perhaps more references back from later chapters to earlier ones where the concepts invoked might be in some sense more basic. The intention is to allow readers to treat the book as a set of semi-independent yet closely related essays reflecting on the relationships between geographical thought and giscience, and how these often perplexingly and frustratingly separate, at times even antagonistic fields, can mutually inform one another to enliven a more thoroughly geographical computing.13

13A

website with supplementary material, including the figures, code to produce versions of selected figures, updated web links where applicable, and additional thoughts and commentary is at www.guilford.com/osullivan-materials.

Chapter

Location and Space he concern about the conceptualization of space seems to be undoubtedly at the root of geography,” suggests Nunes (1991, p. 15) in a survey from within giscience that is unusually broad in its engagement with wider currents in geographical thought. Or again, space is “the basic organizing concept of the geographer” (Whittlesey, 1954, p. 28). Geography as a discipline has not been particularly good at accounting for its existence, but space often features in elevator pitches for what geography brings to the table relative to other fields. This tendency is amplified when giscience and GIS are introduced to the conversation, when space and location become central for enthusiasts and skeptics alike. “GIS are particularly powerful and useful computer-based data-handling, analysis and mapping systems that have the capacity for integrating spatial data of any kind,” according to John Pickles (2004, p. 155), a trenchant critic of GIS. More recently language about the value of a spatial perspective has been superseded by location: “ArcGIS Desktop is the key to realizing the advantage of location awareness”1 is a typical marketing claim. The mantra “location, location, location” could as easily be the GIS professional’s as the realtor’s.

“T

1

https://desktop.arcgis.com/en/ in January 2023.

17

2

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It makes sense then to start by looking more closely at notions of space in geography and giscience. We start with the (not so) simple idea of location as it is embedded in contemporary GIS and other geospatial computing platforms. GIS is explicitly built on a notion of space as primarily defined by location, itself represented by an association between spatio(-temporal) coordinates S = (x, y [, z, t]) and a collection of attributes A = {a1 . . . an }. This tuple ⟨S, A⟩ has been presented (Frank & Goodchild, 1990; Goodchild et al., 2007) as the atomic form of geographic information—the geoatom—a fundamental building block out of which all geographical representations in GIS are built. This representation is so central to giscience that it is almost invisible, and therefore deserves closer scrutiny. What are the possibilities and also the limitations of such representations? What alternative foundational representations might different kinds of GIS be built on? What is the relationship between space-as-location on the one hand, and the rich ontologies of space that geographers more widely deploy in their attempts to understand and explain the world?

THE NATURE OF SPACE The geoatom perspective on space is congruent with what Whitehead disparagingly terms “simple location” ([1925] 1967, p. 50). His disdain for simple location derives from the fact that this approach suggests that [t]he characteristic common both to space and time is that material can be said to be here in space and here in time, or here in space-time, in a perfectly definite sense which does not require for its explanation any reference to other regions of space-time ([1925] 1967, p. 50).

Further, Whitehead continues, as soon as you have settled [. . . ] what you mean by a definite place in space-time, you can adequately state the relation of a particular material body to space-time by saying that it is just there, in that

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place; and, so far as simple location is concerned, there is nothing more to be said on the subject ([1925] 1967, p. 50).2

Whitehead’s disparaging tone about simple location notwithstanding, as a practical matter, we should recognize that simple location is far from simple. We are accustomed to having our phones instantaneously position us as precisely located points on maps. But the underlying machinery of the Global Positioning System (GPS) that makes this happen is astonishing in its intricacy, complexity, and scale. Around 30 satellites spanning over 50,000 km, carrying high precision atomic clocks, precisely synchronized, paired with complex microprocessing capability in billions of receiving units. The accuracy requirements of the system are such that the atomic clocks on board the satellites are set to run slow to offset the relativistic effects of their 4 km/s orbital velocity. Even setting aside the Rube Goldbergian3 intricacies of GPS, which might be considered a third millennium aberration, precisely determining a location on Earth’s surface has never been simple (Sobel, 2007; Rankin, 2016; Evans, 2017; Pike, 2018). That the foundations of GIS are built on the notion of precise coordinates bears directly on discussions in geographical theory considering space as absolute, relative, or relational and which of these is the most productive for geographical thinking. David Harvey provides a wonderfully concise statement of these varieties of space in the introduction to Social Justice and the City: If we regard space as absolute it becomes a thing in itself with an existence independent of matter. It then possesses a structure which we can use to pigeonhole or to individuate phenomena. The view of relative space proposes that it be understood as a relationship between objects which exists only because objects exist and relate to each other. There is another sense in which space can be viewed as relative and I choose to call this relational space—space regarded, in the fashion of Leibniz, as being contained in objects in the sense 2 3

In place of simple location Whitehead ([1927] 1978) offers “region” as a more apt spatial primitive, a topic we return to in Chapter 5, and also in Chapter 8. Heath Robinsonian in British English.

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that an object can be said to exist only insofar as it contains and represents within itself relationships to other objects (1973, p. 13).

The following short sections expand on each of these in turn as they have been further elaborated on in the literature, although it is hard to add greatly to the spare outline above.

Absolute Space The absolute space perspective conceives of space as an empty container in which the stuff of the world—objects, things, phenomena—are located (see Figure 2.1). Given this perspective on space, the primary information required to describe the world is the location and nature of the objects in the space. This quickly leads to the geoatom or something very like it. Locations are indexed by coordinates and objects are described in terms of their properties. Implicit in the framework is the impossibility of more than one entity occupying a particular spatial location at the same time, so that entities are individuated in space-time. As described by Harvey, absolute space is associated with Euclidean geometry, and a fixed immovable frame of reference. This perspective is so deeply embedded in post-Newtonian scientific thought, which in turn is so hegemonic in Western thought, that it is initially difficult to see much wrong with it. But even taken on its own terms questions arise. What is space itself? Is it an empty void? Apparently not, since “[i]t is not true that a Vacuum is nothing; it is the Place of Bodies; it is Space; it hath Properties; it is extended in Length, Breadth and Depth” (de Voltaire, [1738] 1967, p. 180). In the depths of interstellar space these kinds of considerations obviously carry some weight. On Earth, with which geographers are concerned, there is no void, there is stuff everywhere. Nevertheless, an absolute model of terrestrial space is frequently deployed as if we were dealing with empty space, and enumerating or defining objects within it. This approach is undeniably useful, for example, when planning a kitchen, constructing a high-speed rail network, or even defining the boundaries of nation-states. Applied to colonization, enclosure, and the

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Figure 2.1. A representation of an absolute space, showing a coordinate frame as is usually associated with this perspective on space. Points in this space are completely defined by a set of coordinates specifying their simple location.

exercise of state and corporate authority generally, conceptions of absolute space can also be considered responsible at some level for many of the world’s ills. While a political-economic order similar to late capitalist modernity might be built on a different conception of space, many key aspects of that order are intimately bound up with an absolute model of space, particularly property rights in land (the cadastre), the notion of the individual self (the point objects of human dynamics), and the geographically bounded nation-state (Pickles, 2004). An absolute space perspective is also bound up with “the god trick of seeing everything from nowhere” (Haraway, 1988, p. 581) . Space is a neutral container, where everything is simply where we know it to be,

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as shown on page or screen. Maps and GIS routinely deploy this pretense of omniscience presenting themselves as neutral and authoritative, when they are anything but. Maps and GIS data are complex outcomes of many selectively chosen acts of observation, recording, encoding, simplification, and so on. These processes are especially well hidden when even the frame inside which things are presented is taken for granted and singular. Whether relative or relational perspectives entirely avoid this failing is open to question, but they at least acknowledge that different perspectives are possible.

Relative Space Relative spaces exist relative to entities and their relations to one another. Directly opposing the notion that space is a thing in itself, Leibniz argued that “Space without matter is something imaginary” (quoted in Elden, 2013, p. 297). This insight leads to the conclusion that there can be no fixed frame of reference applicable in all cases to all entities and all subjects of concern. At cosmological scales this framework yields Einstein’s relativistic universe where all motion is measured relative to the frame of an observer, and space-time bends to accommodate an absolute limit on the speed of light. At the more mundane scale of terrestrial measurements, we recognize that the times, distances, and rhythms of daily commutes in a particular urban region are governed by different measurement systems than global capital flows, or ecological movements, and that no single frame of reference can make these different relative distances commensurable. From a relative perspective, space and time are intimately bound up with one another, and distance collapses into a concept more like the cost in time, energy, or resources of overcoming the friction of distance. These are spaces that Bill Bunge considered in his meta-cartographic “traverse” of distance (Bunge, 1962, pp. 52–61) and Tobler (1961) was grappling with in broadening the concept of map projections, at the outset of the quantitative revolution. A relative perspective on space greatly complicates—and enriches—our picture of the world, by recognizing that many different distance metrics are needed for many different

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purposes, and further that each metric is encountered or experienced differently by different observers. Thus, for example, we can construct potential travel time maps centered on a particular location, but those maps will vary by mode of transport, by cost, by time of day, and so on (see Figure 6.14 and also Chapter 7). It is worth considering the degree to which absolute and relative perspectives on space really diverge from one another or not. There is after all no single absolute frame of reference with respect to which an attempt has been made to apply a monolithic and singular absolute space. The nearest thing is the geocentric system of latitude and longitude but, in practice, local coordinate systems usually take priority over geocentric coordinates, even when the metric in use is one of simple distances. Thus, absolute space as deployed in practice is generally a complicated overlapping set of different coordinate reference systems (Clarke, 2017; Rankin, 2016), although this does not really detract from the absolute spatial mode of thought at work and it is generally possible to resolve discrepancies between such reference frames by technical means. When other metrics than simple distance are deployed, resolving discrepancies becomes much more challenging or even impossible. By their nature, simple distance measurements can be triangulated and are internally self-consistent. The same is not necessarily true of other measurements of the cost in time, energy, money, or whatever, of traversing the space between two entities. More complex geometries than those that can occur in two- or three-dimensional Euclidean space may appear (Sheppard, 2002). It might take longer to travel from A to B than from B to A. Shortcuts may be available but not from all places or at all times. In general, resolving such complex geometries and presenting them as conventional maps is impossible, and this presents interesting technical problems to giscience, challenging our geographical imaginations (see L’Hostis & Abdou, 2021). Nevertheless, in principle, absolute and relative space are not so different. Any mapping of a collection of things in an absolute space implies a set of relative spaces measurable from the perspective of each of those things (or from any other empty location in the space). Any relative space can be portrayed (if only approximately) as an absolute space. Many of the techniques for tackling such problems were a

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central focus for quantitative geography after initial optimism about simple Euclidean geometry as the language of space dissipated (Forer, 1978; Gatrell, 1983).

Relational Space From a relational perspective, there can be no empty space, devoid of entities, and space only exists contingent on entities. Conversely, entities only exist in relation to other entities, those relations being expressed through the processes that give rise to those entities. From a relational perspective, we no longer think in terms of entities, but instead in terms of processes. As processes unfold they make and remake space, while space in turn acts back on processes, altering and shaping their unfolding. Viewed relationally space is not a container within which processes occur, but is itself a process, actively made and remade over time. Entities do not exist as such, but rather are more or less enduring features of the processes that produce them. This perspective is central to Whitehead’s process philosophy ([1927] 1978, see also Chapter 8) and also appeared much earlier in Leibniz’s monadology (but see Malpas, 2012). From the relational perspective, everything contains to some degree its relations to everything else (Leibniz insisted that everything contains everything else). An object is not simply the object, but also the social, economic, political, and material relations and processes that came together to produce it. The laptop I am writing on was produced somewhere, designed somewhere else, assembled from parts manufactured and designed in other places. My possession of it is a function of my role as a professor in a university at a particular place and time. All of these social and economic relations are embedded in the laptop, along with innumerable complicated histories of the materials out of which all the components of the laptop are made. And so on, and on. It is difficult and even a little unnerving to start seeing the world in this way. Pragmatically, it is much easier just to take things at face value, for what they appear to be. But when we really want to understand what’s going on around us, this kind of relational thinking in space and time becomes essential.

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This tripartite classification of space into absolute, relative, and relational is not unambiguous. In Harvey’s account relational space is only cursorily defined (through objects) as existing “only insofar as [each object] contains and represents within itself relationships to other objects” (1973, p. 13).4 Revisiting these definitions later (Harvey, 2006, pp. 123– 24), the difference between relational and relative space is more clearly conceptualized with respect to how processes define their own spaces, so that it becomes essential to consider not only space, but space-time. A processual, space-time perspective on space is often assumed in any discussion of space, although Cox (2021) argues that human geography in fact remains stuck on a relative perspective, where space is a more or less fixed structure of relative locations at which things are placed. Cox further claims, “[t]here is an inevitability about the relation of space to process in physical geography that seems to be absent in human geography” (2021, p. 11). This means, Cox suggests, that physical geographers work with relational space concepts (without necessarily giving it much explicit thought in such terms), while human geographers discuss abstract notions about space, but, lacking the same concrete embedding of processes in space, remain stuck with relative space, whether they realize it or not. For example, market relations and processes may be conceptualized as outside of space, with no necessary specific relationship to space (see Sayer, 1985). Whatever the merits of this argument, it clarifies a little the intention behind distinguishing relative and relational concepts of space. Relative spaces can be thought of as more or less fixed structures in which things are embedded in relation to one another, and are in this sense not so different from absolute spaces. At the same time relative spaces, to the extent that their measures of relation are contingent on movement, flows, perceptions, and so on associated with processes, approximate to the relational spaces of those processes. Thus, relative spaces can be either absolute, relational, or perhaps even both, depending on your point of view! This might help explain why the term “relative space” has fallen 4

Harvey offhandedly acknowledges with respect to relational space that he “neglected [. . . ] to explicate its meaning,” some 23 years later (1996, p. 250). See also Chapter 8.

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into disuse since early discussions, with many authors favoring a binary of relational space presented as in opposition to absolute space. Harvey (2006, Figure 1) offers a tabulation of contexts where the threefold perspectives on space might apply. Some of these are difficult to make sense of. For example, it is unclear why “circulation and flows of energy, water, air, energy” exist in a relative space, while “electromagnetic energy flows and fields” are relational. Other distinctions are clearer. “Cadastral and administrative maps” clearly inhabit absolute space, while “thematic and topological maps (e.g. London tube system)” are relative space representations. Whatever we make of these abstract ideas about space, it is important before considering space in giscience to emphasize that these three conceptualizations are just that: conceptualizations. As ever with models of any kind, no model is correct, but all we need is for them to be useful (Box, 1979), and each of these models—absolute, relative, relational— however hard it might be to separate them, has its uses. As Harvey further notes, “[t]he problem of the proper conceptualization of space is resolved through human practice with respect to it. In other words, there are no philosophical answers to philosophical questions that arise over the nature of space—the answers lie in human practice” (1973, p. 13).

SPACE IN GISCIENCE Absolute Space in GIS What, then, does the human practice of giscience make of space? Perhaps unsurprisingly, particularly as it manifests in GIS and other mapping platforms, giscience presents us with a would-be absolute space. For many giscientists, the most direct consideration of how space is represented is the raster-vector debate, which revolves around technical questions of which approach to the representation of geographic phenomena is preferable (Peuquet, 1984). But as Helen Couclelis suggests, “the technical question of the most appropriate data structure begs the philosophical question of the most appropriate conceptualization of geographic space” (1992, p. 65). For Couclelis, the philosophical question

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revolves around whether the world consists of a collection of objects or is a continuously measurable field of values, whether of land elevation, air temperature, population density, or other quantifiable phenomena. The object view—equated with vector representations—forces the world to conform with its precisely defined geometric points, lines, and polygons, while the field view remains more agnostic, instead requiring the user to detect patterns in data to identify features (Tomlin, 1994). Many aspects of the human world fit reasonably well into the vector-object perspective, while many aspects of the natural world are more readily accommodated by the raster-field perspective. But seen through the lens of absolute, relative, and relational models of space, the two views are essentially the same, both depending on a fixed coordinate frame within which points or cells can be referenced. Further, even novice GIS users are aware that one of the most important first steps in the planning and execution of any project is determining an appropriate map projection for the task at hand. Put differently, the coordinate system for the absolute space within which analysis will be conducted must be determined. In almost all cases the primary consideration governing the choice of projection is associated with the severity of the geometric distortions to the phenomena at hand due to the chosen projection (see also §Scale and Map Projection, Chapter 3). Next-generation GIS may assume a priori that geodetic (i.e., latitude–longitude) coordinates are the correct frame of reference, given that advances in computation render many advantages of planar projected coordinates moot, but short-circuiting the choice of coordinate system in this way runs the risk of distancing giscience further still from geographic thinking about space. It is important to recognize here that there is nothing in particular preventing coordinate systems that portray relative spaces being used with conventional GIS platforms (Bergmann & O’Sullivan, 2017). Most geospatial toolkits perform geometry operations, such as intersection, the measurement of length and area, and point in polygon tests, in a planar, two-dimensional Euclidean coordinate space, and not in the (approximately) spherical coordinate space of Earth’s surface. This design choice was made early in the development of GIS as automated cartography

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Figure 2.2. Three views of Aotearoa New Zealand SARS-CoV-2 vaccination uptake (at October 6, 2021). In the middle is a conventional map view. The left-hand map is a cartogram scaled to population of statistical areas, while √ the right-hand map is a cartogram scaled to A where A is the area of each census district. The last of these reduces the visual dominance of the large but sparsely populated rural areas while making it easier to discern detail in urban areas. Assembling different spaces like this is not straightforward with contemporary geographical computing tools.

(Goodchild, 2018). Even as more globe-centered approaches based on spherical or ellipsoidal geometry develop,5 it is unlikely that support for Euclidean geometry will be dropped (and see Chrisman, 2017, on the challenges of spherical geometry). 5

For example, in the R-Spatial ecosystem, the package sf (simple features) has an option setting sf_use_s2 which can be easily toggled to switch between calculations based on a spherical approximation to Earth surface, and more traditional Euclidean geometry.

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Figure 2.3. The cartogram deformation grid for the first cartogram in Figure 2.2. This grid contains all the information needed to project other layers into the cartogram map space, if they are sourced in the same projection as the original data layer.

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As an example, tools for easily generating cartograms have become more widely available in recent years,6 so that type of map transformation can now be readily generated. The example in Figure 2.2 shows three different cartogram spaces (the middle one a standard map) in which a conventional choropleth map might be displayed. While it is relatively simple to make such maps, it is difficult to work with the resulting data layers using standard geospatial tools. Tools struggle to recognize whether or not data are projected or have no known projection. This may make it difficult to do things as simple as reading them, or having read them, to display them alongside other views.7 ScapeToad can project other layers into the cartogram map space at the time of cartogram calculation. It also generates a deformation grid output (see Figure 2.3), but later taking the information contained in this grid and using it to project other data layers into the cartogram space is not supported. In sum, if a user wants to define an entirely new map transformation relative to their particular context of inquiry (their “practice”), and then use geospatial platforms to manipulate data in that projection, it can be difficult and frustrating. Cartograms may seem like a special case, but as is clear from the previous section, it has long been accepted in geography more widely that “distance can and must be measured in terms of cost, time, social interaction, and so on, if we are to gain any deep insight into the forces moulding geographic patterns” (Harvey, 1969, 210, referencing Watson, 1955). Another common use case is working with historical base maps. While such maps may not meet the expectations for geodetic accuracy of modern map projections, they often represent contemporary understandings of space more faithfully, and are thus relevant to the questions at hand. Rather than being able to use the contemporary, historical base map, a GIS user is expected to georeference their map, warping it to match modern, anachronistic map projections that conform to an essentially 6 7

See ScapeToad http://scapetoad.choros.place/. A common workaround (at the time of writing) involves converting to the shapefile format and deleting the associated .prj file containing projection information. It is also not unusual to have to repeatedly delete this file during a workflow to prevent tools from assigning a default geocentric coordinate system to the data!

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arbitrary absolute spatial notion of accuracy, relative to questions of interest. This seems the opposite of what would be desirable for supporting the needs of these GIS users, when the contemporary understanding of space, already embedded in the source materials, surely has interpretive value. Ironically, it is exactly the data included in the deformation grid shown in Figure 2.3—a series of mappings of known control points from one coordinate system to the other—that are needed and that are used when basemap imagery is georeferenced that would be required to support this functionality. The only change necessary to geospatial tools that can perform georeferencing (in other words, any GIS) to allow support for arbitrary projections in any desired space would be to remove the expectation that the coordinates in datasets be in some known projected coordinate system (see Bergmann & O’Sullivan, 2017).

Relative Space in Quantitative Geography The narrowness of spatial representation in GIS is unfortunate, because a great deal of work in quantitative geography and spatial analysis effectively adopts a relative model of space, even as GIS tools do not. Much of spatial analysis boils down to incorporating a spatial weights matrix tailored to the particular questions at hand into otherwise fairly standard statistical concepts of correlation, similarity, difference, and so forth (O’Sullivan & Unwin, 2010; Bailey & Gatrell, 1995). A spatial weights matrix is a compact summary of the relations among a collection of entities, determined from their locations in space, generally derived from some function of their Euclidean distances of separation. A simple example is provided by distance-based approaches to point pattern analysis (Ripley, 1981; Stoyan, 2006). Consider the two sets of points, located in a two-dimensional absolute space, shown in Figure 2.4. One pattern appears evenly spaced or dispersed, while the other appears clustered or aggregated. One way to make the difference in the patterns clear is to measure the distance from each point to its nearest neighbor in the pattern, and to examine the distribution of the resulting nearestneighbor distances. This is shown in the histograms alongside each pattern where the contrast is clear.

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Figure 2.4. Two point patterns in absolute space characterized using nearestneighbor distances. The difference between the upper evenly spaced pattern and the lower clustered pattern is apparent when we measure the nearest distances for every point in each pattern, as shown in the distributions plotted on the right.

Such a distance-based measure of point pattern draws on a relative concept of space insofar as what is analyzed is not the absolute location of points relative to a fixed frame of reference, but the position of each point relative to its nearest neighbor. Of course, the approach also depends on the points having coordinates relative to a fixed absolute frame of reference, and also some agreed-upon approach to measuring their separation distances (there is no shortage of possibilities; see Deza & Deza, 2016). Shuttling back and forth between an absolute and a relative perspective on space in this way is commonplace, but almost always a context-specific choice, which may be difficult to replicate given the poor support geospatial tools provide for spaces not in standard projections.

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PROSPECTS FOR RELATIVE/RELATIONAL GISCIENCE Despite the dominance of absolute space in GIS platforms, the prevalence of relative space approaches in spatial analysis holds out some hope. Therefore, it is useful here to review approaches that, similar to the point pattern example, push giscience in the direction of relative, perhaps even relational conceptualizations of space. Many of these are both widely known and widely used by giscientists, but have not necessarily become embedded in platforms in the same way that absolute space has in GIS.

Data Structures That Include Adjacency We should first note that many data structures incorporate adjacency and by implication a (limited) relative space model. These include early formats such as GBF/DIME, TIGER, and POLYVRT (Cooke & Maxfield, 1967; Peucker & Chrisman, 1975; Broome & Meixler, 1990), on which Esri’s Arc/INFO coverages were based, as well as more recent examples such as TopoJSON.8 These formats were developed to address technical and practical issues in the management of polygon data layers. The obvious approach to storing a polygon is as a sequence of point locations, along with an indication that the points are the vertices of a polygon. Any software handling these data can then handle the series of points as the corners of a polygon. A typical format of this simple features kind is GeoJSON,9 an example of which is shown in Figure 2.5.10 Here, a two-part polygon is stored as two lists of coordinate pairs, with points listed in counterclockwise order. The GeoJSON format requires the first vertex to be stored twice to close the polygon. Other formats may leave closure of the polygon implicit. Simple features formats have a number of problems. Because they are effectively just lists of polygons, which might be presented in any 8

See https://github.com/topojson/topojson-specification. See https://tools.ietf.org/html/rfc7946. 10A useful tool for getting a feel for GeoJSON can be found at https://geojson.io.

9

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Figure 2.5. A GeoJSON file including a single multipart polygon.

order, any time we want to deal with the relationships between polygons, inefficiencies are inevitable. Finding other polygons near a given polygon requires searching through the list of all polygons. Spatial indexes can make it easier to restrict a search to only those polygons known to be nearby and are one solution to this search problem (Samet, 1990), that requires no changes to the simple features data model. An even more basic issue arises when polygons are expected to mesh together to completely cover a region, without any gaps, as is required in many situations, such as cadastral databases. Because every polygon edge is stored twice, every coordinate on a boundary between two polygons is also stored twice. If any inconsistencies between the two copies of each point arise, then corresponding overlaps and slivers occur in the polygon layer. An example is shown in Figure 2.6. Inconsistencies might arise

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Figure 2.6. Slivers and gaps in a set of polygons. These can arise in data structures that store each polygon independent of all others.

as a result of polygons being independently edited, or when procedures such as automated generalization (see §Scale-dependencies, Chapter 3) are applied. A solution to this problem is to organize information about polygons so that each vertex is only stored once. There are a number of ways to do this. For example, all vertices can be stored in a table, assigning each vertex an ID number. Each boundary between two polygons can then be stored as a sequence of point IDs with specified start and end points, and also, in most implementations the identity of the polygon that is to the right and left of the edge, when it is traversed from the start to the end node. Finally, polygons are stored as a sequence of edges (Peucker & Chrisman, 1975, is an accessible early description of the approach). If a vertex location is changed, then it changes in all polygons to which it belongs, resolving the overlaps and slivers problem. Details of the exact implementation vary from format to format. The underlying ideas and variants are discussed by Worboys and Duckham (2018, pp. 177–87). While this data format is considerably more complicated

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than simply storing a list of lists of coordinate pairs, it enforces topological consistency, and offers numerous advantages. In addition to enforced boundary consistency, the approach allows rapidly finding the neighbors of any selected polygon, since traversing the polygon edges will return a list of all the neighboring polygons. It is surprising that in the 1990s Esri’s shapefile format—which does not offer either of these advantages—became dominant in the GIS world, presumably because it was assumed that increased processing capability meant that calculation of polygon neighbors and so on could be performed rapidly as required.11 Whatever its limitations, because the 1990s were the decade when GIS really took off, the shapefile became a de facto standard, and simple features, without topology, remain dominant, including more recent examples like the GeoJSON and GeoPackage formats. As a result, it is not uncommon to encounter issues with slivers and overlaps in datasets, even those maintained by official sources. Topological data formats are implicitly relative in their representation of space, since every polygon is stored along with relations to its neighbors. It is important not to overstate the significance, since the only relations recorded are trivial immediate adjacencies. Also, the motivation for such formats is practical not theoretical. These formats appeared in the context of handling datasets representing a quintessentially absolute spatial perspective where all land is unambiguously assigned to specified zones for administrative or commercial reasons. Thus while it is technically convenient, for the reasons discussed, to work with data formats that impose topological consistency, it is important to recognize that they emerge out of an absolute perspective on space.12

11 A

slightly bemused David Theobald suggested it was because shapefiles can be drawn on screen more quickly; see “Understanding topology and shapefiles” at https:// www.esri.com/news/arcuser/0401/topo.html. 12 An interesting challenge to the logic of this perspective is provided by Gordon MattaClark’s artwork Reality Properties. Fake Estates; see Manolescu (2018, pp. 180–85). It is interesting to consider the degree to which the slivers of land this work highlights may have been an unintended side effect of the lack of topology in shapefiles!

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The Voronoi Model of Space An extension of the topological approach to polygon data has been proposed by Christopher Gold (1992) making use of Voronoi polygons (see Okabe et al., 2000). Voronoi polygons—also known variously as Thiessen polygons or proximity polygons—are a partitioning of a region of space, based on a set of entities (most often points) where each polygon is a subregion of the space that is nearer to its generating entity than it is to any other entity in the set. An example is shown in Figure 2.7. The Voronoi tessellation is frequently used in spatial analysis. For example, in facility location problems, large Voronoi polygons in the tessellation derived from existing facility locations are diagnostic of underserved areas. In point pattern analysis the Voronoi polygons associated with a set of points can help in identifying areas of high-intensity clustering or the outer edge of clusters (Estivill-Castro & Lee, 2002).

Figure 2.7. Voronoi polygons associated with a set of point locations.

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When dense control points are available, natural neighbor interpolation (Sibson, 1981), derived from Voronoi polygons, can be very effective. As Gold (1992) points out, the Voronoi model can be extended to any set of generating entities, whether points, lines, or polygons, although the computational geometry becomes a little more complicated. An approximate approach is to convert all spatial objects in a scene to points while retaining the original object IDs, and then perform the Voronoi transformation on the complete set of points (see Fleischmann et al., 2020). The resulting Voronoi polygons can then be dissolved together based on the object IDs. An example is shown in Figure 2.8. Gold (1992) and Edwards

Figure 2.8. Voronoi polygons associated with lines and polygons approximated by conversion to closely spaced points. A road (dark gray) and building footprints (gray) have evenly spaced points (black) assigned along their length. These are used to generate Voronoi polygons (gray outlines), which are dissolved based on entity IDs, to give Voronoi polygons for the line and polygon objects. The resulting black outlines seem to match well with intuitive notions of the neighborhood of those entities.

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(1993) argue that such polygons correspond well with human ideas of where the neighborhoods of such objects are. Although this claim has not been verified in any systematic way, it appears plausible on examination of maps the technique yields.

Object Fields Some authors have suggested a hybrid of the vector-object and rasterfield perspectives in the guise of object-fields (Cova & Goodchild, 2002; Goodchild et al., 2007; Yuan, 2022). In this formulation, every location in a space, at some resolution, can be associated with an arbitrarily complex spatial object. For example, at every location across a space the other locations visible from each location can be approximately determined by a visibility analysis that associates an isovist with each location. These results can be summarized in a field of isovists where isovists are represented as a collection of points, as a (multi-)polygon, or as a set of pixels in a raster. Exploration of an object-field might display the associated isovist polygon when a mouse hovers at the associated location. It is interesting that merging the object and field perspectives in this way leads to an approach that might be considered relational from the perspective of the earlier discussions. For example, an object-field of isovists is exactly equivalent to the visibility graph described by Turner et al. (2001) and O’Sullivan & Turner (2001), where relations between places are explicitly captured by the relational structure of a graph (see also Chapter 6). Although there is no necessity for an object-field to be relational in this way, the idea lends itself directly to the construction of networks of second-order relations among locations. Each location has an associated more or less complicated spatial object, and the associated spatial object may in turn have relations either to other locations or to their associated objects. When adopting an object-field approach, it makes sense to think of locations in terms of how they relate to other locations in some way. Although Cova & Goodchild (2002) present mocked-up examples, the approach has not been implemented as a default in any platform I am aware of.

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Graph Databases Although the database technology that underpins geographical information systems, relational database management systems (RDBMS), is “relational,” this is a misnomer from the perspective of this chapter. The relational in RDBMS refers to the relations that compose the database, but relations in this context are what are more generally considered data tables (Codd, 1970). Ironically, relational databases are poor at dealing with relations in the more usual sense of the word.13 In an RDBMS, geographical entities are necessarily individuated. Each row in a table represents a single geometry—whether point, line, polygon, raster cell, or some more complicated type, like a multipolygon. Data-rich entities will tend to have an associated data table in an RDBMS and the focus of the data model is on those entities and their properties. Relations between entities are expressed by matching attribute values of entities in different tables, where (for example) the ID of a school that a student attends might appear in the students table as a foreign key. To summarize information about the schools attended by students, a temporary join between the students and schools matches students and schools into an extended table, based on the foreign key in the students table. In this light a GIS is a relatively limited extension to an RDBMS that can accommodate attributes that are geometric entities, such as points, lines, or polygons. Further, a GIS can support matching geometric entities according to various geometric operations such as intersection, containment, overlap, and so on. That a GIS is really this simple extension of RDBMS is clear on considering PostGIS, which is “a spatial database extender”14 that augments a conventional database by adding geometric objects. Similarly, the geospatial ecosystems in programming languages such as R and Python are based around packages that take a standard data table format and allow for storage and manipulation of geometries as a special kind of column in the data table. This is the approach taken in both sf (in R) and geopandas (in Python). 13It

is a further irony that RDBMS superseded the network data store model, which centered the relations between data items. See Haigh & Ceruzzi (2021, pp. 274–75). 14See https://www.osgeo.org/projects/postgis/.

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Because relations between entities in RDBMS are based on temporarily matching attributes between data tables, relations as such have only second-order status in the model—they exist only by implication, rather than being explicitly represented. The conceptual frame of the model is that entities exist and are independent of one another. In graph databases, by contrast, relations are first-order concepts that have equal standing with entities. This means that graph databases can take advantage of algorithms based on ideas from network science (see §Network Science, Chapter 6) to enable more efficient exploration of data understood as a complex interconnected collection of entities. Where the designer of an RDBMS focuses on data-rich entities, the designer of a graph database will consider both entities and the relations that may exist between them. Where the basic element in RDBMS is the tuple of attributes describing each entity in a table, in a graph database the basic element is a triple of a subject, an object, and the relation between them. This triple is also central to the Resource Description Framework (RDF) for the exchange of semantic information on the web. Graph databases have become more commonplace since the mid2000s, with a great deal of hype around “leveraging complex and dynamic relationships in highly connected data” (Robinson et al., 2015, p. xi), although they are still much less widely used than RDBMS. They remain underexplored in giscience and GIS, where the data table with a geometry column model remains dominant, to the detriment of richer, situated representations of geographical knowledge (Bergmann, 2016; Gahegan & Pike, 2006). RDF-based approaches to the exchange of geospatial information are an alternative pathway toward a more relational model of space in giscience (Claramunt, 2020). The role of network science with respect to more relational perspectives on geography is explored in more detail in Chapter 6.

Spatial Analysis and Spatial Models We have already seen how spatial analysis deploys spatial weights matrices representing the relations among events in a point pattern, thus invoking a relative model of space.

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Figure 2.9. A range of spatial weights applied to polygon data. In the top row contiguity criteria are applied: Queen’s contiguity, Rook’s, and Rook’s with lag 2. In the second row k nearest neighbors, 3, 6, 12 based on polygon centroids. In the third row distances between centroids up to 1,000, up to 1,500, and between 1,500 and 2,000 m. Finally, in the bottom row are the Delaunay triangulation, the Gabriel graph, and relative neighbor graphs.

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This construct is highly flexible and easily applied to any kind of spatial entity contingent on some rule for measuring the strength of relation between any pair of entities. Examples of purely binary yes/no matrices constructed based on geometric rules are shown in Figure 2.9. It is simple to extend this further to assign relative importance to different strengths of relationship, or even to base relationships not on distance and geometric criteria but on other aspects, such as shared characteristics, commuter flows, and so on. Again, the relationship of these methods to network models is a close one, and is considered further in Chapter 6. Other kinds of spatial models rely on similar structures. For example, cellular automata (see §Cellular Automata, Chapter 8), both regular and irregular, require a neighborhood to be defined for each cell. Cells exist in a lattice of relations between cells. In regular grids, the relationships between cells are usually identical across the whole space. Couclelis (1997) suggests that the underlying spatial model in this case is neither absolute nor relative but proximal (see also Takeyama & Couclelis, 1997; Takeyama, 1997). Proximal space focuses on a difference between sites (locations in absolute space) and situations (locations in proximity or adjacency relations to other locations) and captures aspects of both. O’Sullivan (2001) shows that this concept can be extended to arbitrary spatial entities (not just cells in a grid), resulting in this context in irregular or graph-based cellular automata. We consider these and other dynamic modeling approaches in more detail in Chapter 8 where their processual aspects are also discussed.

FROM SPACE TO EVERYTHING ELSE Because how space is theorized and represented is foundational to every other aspect of geography and giscience, we have paid close attention to it in this chapter. Many of the themes discussed reappear under different guises in later chapters. In Chapter 4 the vexed relationship between space and place is central, while relationality and relative space are critical aspects of the discussions in Chapters 5 and 6. Relational space-time is a

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topic taken up again in considering time and dynamics (see Chapter 7) and processual thinking (Chapter 8). Milton Santos suggested that “[t]echniques are the group of instrumental and social means that people utilize in order to realize their lives, [. . . ] to create space” (Santos, [2002] 2021, p. 13). Just so, giscience proliferates computational spaces at every turn, many of which also become spaces in the material world. This may help explain the incomprehension of many giscientists at the suggestion that their ideas about space are naïve and simplistic. From the foregoing I hope it is clear that giscience as a whole has a firm grip on both absolute and relative space, even if absolute space is central to dominant platforms. Relative space makes things more complicated, but is not in principle any more difficult to handle computationally than absolute space. Data representations almost always start embedded in some absolute frame of reference (usually geodetic coordinates). They may often remain in that space, but equally or more often will be translated into one or several other relative spaces depending on the context and the questions being asked. Often the public face of such work—as maps or other visualizations—remains firmly ensconced in the absolute spaces of familiar map projections, even if the analysis and conclusions inhabit other more abstract spaces of relations. The further step toward fully relational space in giscience might lie not in any single relative space, but in the moving back and forth among many relative representations, in the ongoing doing of giscience, rather than in any particular analysis of a static absolute or relative space (cf. Kitchin & Dodge, 2007, where maps are argued to be processual). Alternatively, the explicit inclusion of movement and change in time geography (see Chapter 7) or of process in simulation models (see Chapter 8) might offer more direct pathways.

Chapter

Scale and Projection cale is fundamental to geography. When observing any geographical process, whether physical, biological, social, economic, political, or whatever, available evidence is always mediated by the scale at which we make our observations. This statement clarifies how wrapped up in the concept of scale are both an implicit scope or extent across which observations are made, along with some level of detail or resolution at which we note meaningful differences between one location and another. This makes clear that the notion of scale is unavoidably bound up with other key concepts such as space and location (see Chapter 2) and process (see Chapter 8). It also draws attention to the fact that scale is always in some sense socially constructed, being bound up with acts of observation at particular times and in particular places (Sheppard & McMaster, 2004). This chapter explores some of these complexities. First from the perspective of geographical theory; in human geography, where recognition of the social construction of scale has held sway for some time; and in physical geography, where the challenges of translating across scales have long been recognized. And second from the perspective of cartography and giscience, where scale is also a key concept but one where a narrower technical definition is central. This purely technical approach, which pertains to the relationship between the physical size of phenomena in the

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world and the size of their cartographic representation is muddied considerably by (among other things) the emergence of seemingly scale-free, infinitely zoomable web maps, the geometry of map projections, and by cartographic generalization. Each of these topics is considered, along with a brief look at the resulting effects of scale on the analysis of spatial data. The picture that emerges is one where, although some nuances of geographical theory concerning scale are inevitably lost in computational approaches, seriously engaging the concept demands that we recognize the force of arguments about scale’s epistemological character and social construction.

SCALE IN GEOGRAPHICAL THEORY Scale as Size or Scope In everyday usage the concept of scale is more or less synonymous with the size of phenomena of interest. Something large-scale is big, and something small-scale is, well . . . small. This leads to an apparently natural way of thinking about scales of interest, from the cosmological to the quantum. It is worth bearing in mind the truly vast range of scales on which the universe is organized and understood in this sense. The universe is estimated to have a diameter of up to 93 billion light years (Bars & Terning, 2010, p. 27), or around 1027 m.1 The smallest subatomic scales observable are on the order of 10−18 m. Thus, the sciences collectively are concerned with phenomena whose scales range across about 45 (base 10) orders of magnitude. This puts into perspective geographers’ frequent presumption to speak authoritatively about scale, when we consider that terrestrial scales extend across a much more parochial range from around 107 to 10−3 m, a mere ten orders of magnitude. The lower end of that range, arbitrarily set at one millimeter, is arguable, when geographers might be plausibly concerned with, for example, microplastic particles or microorganisms. In 1

Estimates diverge widely. 93 billion light years is an upper estimate that accounts for differences between what is observable, which is limited by the speed of light and the age of the universe, and also depends on theoretical models for the expansion of the universe.

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some branches of the geosciences, an argument can be made that scales range down to the molecular level, which extends the range by a half dozen or so more orders of magnitude. Even so, 15 orders of magnitude remains a narrow focus from a cosmological perspective! Of course, even a perhaps conservative 10 orders of magnitude is unimaginably vast, requiring us to somehow hold in mind a grain of sand in relation to the whole of the Earth, an arguably futile effort.2 Consequently, in practice, it is much more typical for researchers to restrict their scalar focus and to study entities and phenomena whose sizes encompass perhaps three or four orders of magnitude, a 1,000or 10,000-fold range.

Scale as Hierarchy The bracketing of phenomena into manageable size ranges leads directly to thinking about the world in terms of a series of qualitative scale ranges. Such bracketing can be justified not only for reasons of practical observation, but because processes tend to operate at particular scales and tend not to have effects at all scales. As de Boer suggests, [i]n principle, the form and functioning of any geomorphic system is the end product of the interaction of processes operating at all scale levels, from the smallest to the largest. Luckily, to understand a geomorphic system one does not have to consider, as a rule, every level of scale since, depending on the scale of the system and the objective of the investigation, certain levels will be dominant whereas others play a secondary role and can be ignored (1992, p. 304).

This argument is made in the specific context of geomorphology but can reasonably be applied to any subdiscipline in geography. This leads more or less directly to notions of a hierarchically nested series of scales (see Figure 3.1). While the figure shows a set of scales that might be deployed in social, political, or economic geography, similar sequences can be considered in other domains. Biogeographers, for 2

In the absence of mind-altering molecules.

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Figure 3.1. An example of how a series of qualitative scales might be considered nested one within another. See also Figure 1.2 in Herod (2011).

example, may work with a nested hierarchy (from largest to smallest) of kingdoms (or realms), regions, dominions, provinces, and districts (Morrone, 2018, p. 285). In this case there is considerable controversy about nomenclature and how such regional and scalar hierarchies can be reliably defined based, among other things, on whether flora or fauna are used to guide the determination of boundaries between areas at different scales. Similar challenges arise in any domain that is not readily encompassed by a single scale of observation and analysis. Such controversies highlight how scalar hierarchies are an outcome of the processes relevant to understanding how the world works, from a particular perspective. As Jonathan Phillips suggests in a paper evaluating the degree to which different scales in geomorphology are related to one another and can therefore be considered linked, “even where phenomena are continuous, hierarchical structures are often imposed to make analyses tractable” (2016, p. 72). This makes clear that scale is not naturally given per se, but an outcome of particular sets of observational practices and analytical methods, applied in particular contexts. Of course, to the extent possible, data collection and analysis methods should be aligned with spatial (and temporal) scales relevant to particular phenomena of interest. Even where this is possible, it is clear that scale is not only dependent on the underlying nature of things, but is very much an outcome of the relationship between the

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phenomena under study and the apparatus and methods available for their investigation. An important further point to make about neatly nested scale hierarchies is that the nesting is often conceptual more than it is scalar in the sense of being size-based. Taking the hierarchy proposed in Figure 3.1 as an example, there are many cases where a particular region, say California or the Midwest of the United States, is much larger than a particular nation such as Ireland or New Zealand. Again, some urban settings (Tokyo, New York, London) are larger in important respects than particular nations or regions. Further, the linkages that might exist among urban areas, regions, nations, and the global are complicated and messy, and extend both between scalar levels and within them (see Chapter 6). Nevertheless, and in spite of the unruliness of reality relative to any conceptually clean scalar hierarchy, there are advantages to thinking in such terms. It is, for example, possible to set aside processes at scales far removed (whether higher or lower in the hierarchy) from the core scale of interest. So, in a study focused on (say) changes in the California public school system statewide, perhaps it is possible to ignore effects in individual school districts or schools on the one hand, and also to ignore effects in neighboring states, or developments in educational governance and policy at the federal or global levels. Our expectation is that larger scales (national, global) define a relatively stable context within which changes at the scalar level of interest, in this case the state or regional level, play out. Meanwhile, smaller scales such as the household level are governed day-to-day by the changes at the state or regional level that are the subject of the study. This general framework for analysis falls under the rubric of hierarchy theory. Simon (1962) is among the earliest and most lucid proponents of the idea that hierarchically structured systems are common in natural and human systems because they enable levels of complexity that would otherwise fail to evolve, self-maintain, or (in the case of artificial systems) be designed and subsequently manageable. Hierarchies are decomposable, meaning that they consist of more or less independent subsystems that are themselves composed of more or less independent subsystems at levels below, and which together compose other subsystems at levels above

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Figure 3.2. A schematic illustration of how a hierarchy of spatial elements might be organized. This hierarchy is also a tree structure.

(see Figure 3.2). Crucial to this picture is the observation that interactions between levels are weaker than those within levels between subsystems. At the same time interactions between subsystems at a particular level are weaker than those within the subsystems themselves.3 The resulting hierarchical structure is what enables (for example) a botanist to study interactions among individual trees more or less independent of cellular-level processes on the one hand or whole ecosystem processes on the other. 3

Intriguingly, elsewhere, Simon (1973, p. 23) summarizes this property thus: “Everything is connected, but some things are more connected than others.” Phil Agre (2003, pp. 418– 19) points to the spatial structure implied (if not required in all cases) by this perspective, which is of course reminiscent of the first law of geography that “everything is related to everything else, but near things are more related than distant things” (Tobler, 1970, p. 236).

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Of course, any bracketing off of levels (and scales) is always an approximation. In truth in most cases, everything matters—even if only a little—at all scales. Thus, while it may be useful to consider a nested hierarchy of scales and associated processes, it is important to recognize that such hierarchies are an external scheme imposed on the world to organize thinking from a particular perspective—economic, social, cultural, political, biological, hydrological, ecological, climatological, and so on—rather than reflective of a real set of structures in the world (see also Harvey & Reed, 1996). The inadequacy of such schemes becomes particularly apparent when, as is often the case in geography, we want to consider the interactions across and between multiple domains or perspectives. Also, contrary to Simon’s general claims, social systems, the subject matter of human geography, are often messier and less neatly decomposable than many natural systems, perhaps because social processes are less tied to specific spatial matrices through which they operate. A related argument is central to Christopher Alexander’s (1965) contention that “a city is not a tree,” where he argues that many of the failings of mid-20th century urban planning can be traced to reorganizing urban space into functionally distinct areas (residential, commercial, industrial) in ways that prevent such designed cities from becoming vibrant (messy!) urban places.

Scale as Socially Constructed Emphasizing the perspective of a particular analyst sheds light on the perhaps less obvious contention prevalent in theoretical human geography that scale is best understood as socially contested and produced. This position is commonly traced back to an article by Neil Smith, the subtitle of which invokes “the production of geographical scale” (1992). As Jones III et al. (2017) argue, the thinking underlying this idea is found in Smith’s earlier work on uneven development (Smith, 1984) and its relationship to gentrification (Smith, 1982). There, Smith discusses distinct scales at which capitalist processes of uneven development unfold, such

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that, “[w]hile gentrification represents the leading edge of spatial restructuring at the urban scale, the process is also occurring at the regional and international scales” (Smith, 1982, p. 151). There is not much suggestion here that scale itself is a product of these processes. Rather the urban, regional, and international scales are pre-given levels at which processes of investment and disinvestment operate. Elsewhere in the same paper, however, Smith hints at the idea that a particular scale is an outcome of a particular set of social processes, when he argues that “[t]he urban scale as a distinct spatial scale is defined in practice in terms of the reproduction of labor power and the journey to work” (1982, p. 146). Although this shift is more implied than directly stated, it is nevertheless significant relative to contemporary treatments of scale that relied more on pre-given nested hierarchies. Exemplary of this is Peter Taylor’s “Geographical scales within the world-economy approach” (1981), which defines global, national, and urban scales as, respectively, scales of reality, of ideology, and of everyday life. While Taylor identifies each scalar level with a particular set of processes, he is also clear about the primacy of the global scale. In the context of then unfolding rapid changes in the industrial structure of developed economies he argues that “the state and its ideology stand between the experience of people we wish to radicalize and the reality of the world-economy which exploits and destroys them” (Taylor, 1981, p. 10), thus making clear that scale, or more accurately the way in which processes at different scales operate, has material effects on outcomes. This framework is systematically set out in a later paper (Taylor, 1982) with a political geographic emphasis. As recounted by Jones III et al. (2017), the idea that scalar levels themselves are an outcome of processes comes into focus more in later work by Smith and Dennis (1987), who suggest that a key aspect of the same industrial transformations that concern Taylor is a redefinition of the scale—a rescaling—of economic regions, from relatively localized ones centered on single metropolitan areas, to more extensive polycentric ones. In a U.S. context, such economic regions may remain subnational, but elsewhere they might cross national boundaries as the communications and logistical networks that underpin economic activity expand their reach. This is not specific to the United States,

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but was common to other deindustrializing regions in the early 1980s (Massey, 1995). The details of the economic geography arguments are unimportant for our purposes. What matters is the idea that the scales of analysis are themselves produced as an outcome of processes under study. A nice formulation of this idea is spelled out in a later paper by Smith, where he suggests that “[i]t is possible to conceive of scale as the geographical resolution of contradictory social processes of competition and cooperation” (1992, p. 64). While Smith is discussing political and economic processes, this formulation could equally be applied to ecological or geomorphological processes, provided that we think broadly about notions of competition and cooperation. The concept is readily applicable to ecology in an obvious way, where competition and mutualism between species will play out in the scale of habitats, home ranges, ecotopes, and so on. In geomorphology, processes of uplift and erosion might be considered analogous. It is notable that Smith, jumping off from a consideration of those evicted in New York’s 1990s battles over gentrification, goes on to consider “a sequence of specific scales: body, home, community, urban, region, nation, global” (1992, p. 66), thus significantly extending the reach of the concept, beyond the narrowly political and economic emphasized in the earlier debates. Nevertheless, given its origins in economic and political geography, it is unsurprising that further theoretical development through the 1990s of theories of scale as socially constructed tended to emphasize economic and political processes under capitalism. Among many contributions to these themes was work by Smith (1992), Herod (1991), Brenner (1997), and Swyngedouw (1997). Taylor (1999) widened the scope in recognizing the significance of the domestic sphere and particularly the idea of “home,” although paradoxically he is concerned with the idea of home at scales from the domestic to the global, and in concluding is strongly focused on the whole-Earth or global scale. A necessary corrective to this tendency was administered by Sallie Marston, who argues for much closer attention to the scale of the household, which is foregrounded by consideration of social reproduction:

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[p]reoccupied with questions of capitalist production, contemporary writing about scale in human geography has failed to comprehend the real complexity behind the social construction of scale and therefore tells only part of a much more complex story (2000, p. 233).

This intervention led to some concern expressed by Brenner that there was a danger in expanding the remit of the concept of scale, that it would be confused with other key concepts such as “space, place, locale, location, territoriality, distanciation, network formation and so forth” (2001, p. 597). He suggests in particular that the idea of scale is in danger of being confused with the notion of place; when researchers discuss, for example, the scale of the home, they are really concerned with the home as a place, rather than with a set of scalar relations among levels in a hierarchy. This is a plea for a return to a more consistently hierarchical (as Brenner puts it, “plural”) perspective on scale. In response, Marston and Smith (2001) forcefully assert the importance of continuing to develop theories of scale, and suggest that Brenner, in his appeals to the work of Lefebvre, is guilty of confusing not place and scale, but space and scale. It is debatable how much light such debates shed on the matter at hand, and whatever the merits of the argument Brenner (2001) is certainly guilty of taking a line that under current social relations minimizes feminist geographies (see Monk & Hanson, 1982). Others commenting on the scale literature suggest that much of the debate is confused because different notions of scale-as-extent, scale-as-level, and scale-as-(social)process are deployed interchangeably, muddying the debate (see, e.g., Sayre, 2005).

The End of Scale? Rather surprisingly, given this robust defense of the concept of scale, only a few years later, Marston et al. (2005) argue for a human geography “without scale.” The paper’s title is slightly misleading, as it is really hierarchical notions of scale, rather than scale per se, that the authors object to:

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we argue that attempts to refine or augment the hierarchical approach cannot escape a set of inherent problems [. . . ] in place of the hierarchical [. . . ] we offer a flat alternative, one that does not rely on the concept of scale (2005, p. 417).

A flat perspective is an ontological position that asserts that everything that exists whether material or immaterial, and whatever its size or duration, exists on an equal footing such that none inherently determines, controls, or contains the others (see also §Related Strands in Geographical Thought, Chapter 8). In this perspective, a hierarchy of nested scales makes no sense. Events at some notional national scale do not predetermine or dictate events regionally. Researchers should not approach their objects of study with preconceived ideas about scale, but should instead be open to seeing things for what they are: a flat ontology must be rich to the extent that it is capable of accounting for socio-spatiality as it occurs throughout the Earth without requiring prior, static conceptual categories (2005, p. 425).

They argue that for all the vigorous, sometimes contentious debates, scale as a concept never really escaped Taylor’s early, hierarchical conceptualization. While much ink had been spilled on the subject, with mixed results, it still seems extreme to seek “to expurgate scale from the geographic vocabulary” (2005, p. 422).4 This position is, I think, best understood as a political argument, not a theoretical one. Hierarchically nested, vertical scale thinking has consequences for how we understand events: Invariably, social practice takes a lower rung on the hierarchy, while ‘broader forces’, such as the juggernaut of globalization, are assigned a greater degree of social and territorial significance. Such globe talk plays into the hands of neoliberal commentators [. . . ] the standard trope [. . . ] is to shift blame ‘up there’ and somewhere else (the ‘global economy’), rather than on to the corporate managers who 4

Perhaps, after well over a decade of it, Marston et al. had had enough of the scale debates and just wanted it all to end; informal conversations with colleagues at the time (and since) suggest that if so, then they were not alone.

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sign pink slips. In this fashion ‘the global’ [. . . ] can underwrite situations in which victims of outsourcing have no one to blame, a situation possibly worse than blaming oneself (2005, p. 427).

Paying greater attention to specific interactions among people and things, regardless of any prior notion of their scale, will enable a clearer sense of why and how things happen as they do. In place of the distraction of scale, where “states of affairs rarely fit neatly into scalar (or local–global) [levels]” (Woodward et al., 2010, p. 274), the site is proposed as an alternative approach to framing research. What this means in practice is clearer only with regard to more specific examples, such as the suggestion in response to Prytherch (2007) that a productive site for shedding light on the operations of Walmart is the shipping container (Woodward et al., 2008, p. 82). The shipping container is a complex driver and outcome across scales of material, economic, regulatory, legal, labor, and other relations (Levinson, 2006). Tracing these effects can help us understand how Walmart works as a complex assemblage (see §Related Strands in Geographical Thought, Chapter 8). Overall, these post-scale objections to scale oppose pre-supposing a fixed hierarchy of globally applicable scales, rather than scale and scalar effects per se. MacKinnon (2011) argues persuasively for a more nuanced position, acknowledging a tendency to reify specific scalar levels (local, urban, national), but also an unsustainable denial of scalar aspects in flat ontologies. Complex assemblages of human and nonhuman objects exert their effects at some scales and not others. There is also a tension such that emphasizing constant flux in flat ontologies denies the persistence of some scales—such as the national or urban levels. At the same time, the persistence of these levels can cause more structuralist perspectives to assume that these levels are permanent and not continuously made and remade through particular practices. In Chapter 8 we will see how process philosophies loosen some of these tensions. For now, MacKinnon’s (2011) argument that scalar levels have meaningful real existence, but that these depend heavily on ongoing practices and narratives to maintain them, is a constructive attempt to resolve the difficulty of continuing to work with scale while recognizing its contingent

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character (see also Manson, 2008). Crucially this position recognizes the scalar thinking implicit in recognizing the messy complexity of phenomena. It is hard to coherently maintain a scale-free perspective on things and argue for a flat ontology, when this puts (for example) individuals, trade unions, corporations, shipping containers, shipping lanes, and national law into relation with one another, yet many of those phenomena have intricate (often hierarchically scaled) internal structure.5 While these details may not matter in some contexts, so that immediate interactions are not scalar, but are concrete grounded events, this surely does not mean that such structure is irrelevant. Taking sites seriously surely involves pursuing the intricately scaled nature of the world.

SCALE IN GISCIENCE The political nuances and ramifications of scale find no direct analog in giscience and cartographic representations, in spite of the inherently political nature of GIS and mapping, which are so often central to the social construction of actually existing scales (see Chapters 4 and 5). Even so, as discussed in relation to physical geographic perspectives on scale, it is widely understood that scale mediates how all geographical phenomena are perceived, represented, and experienced. This is directly recognized in a framework for formally thinking about scale presented by Dan Montello at the first meeting of a series that became the Conference on Spatial Information Theory (COSIT). Montello begins by reiterating the central importance of scale: As a problem for geography [. . . ] scale has always been a concern of cartographic coding and decoding. But once the scale of the cartographic representation is fixed, all the decisions made with the map become largely scale-independent. A clustered pattern is a clustered pattern. It is this scale-independence of maps, of course, that gives them their great power and utility (1993, p. 312).

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Broadly this argument is made by Prytherch (2008) in a brief rejoinder to Woodward et al. (2008).

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The disconnect between this statement and then-contemporary discussions of scale in human geography is striking. As will become apparent, Montello’s assertion of the scale-independence of maps is also arguable (see §The Arbitrariness of Boundaries, Chapter 5) from a giscience perspective and indeed, he goes on to argue that from the perspective of human perception, space is anything but scale-independent. Further, since it is potentially desirable to embed human understandings of space in computational models in giscience, it is important to consider how human perception of space changes with scale. Montello briefly considers earlier frameworks (e.g., Ittelson, 1973; Gärling & Golledge, 1989), noting in these the importance attached to multiple perspectives for human understanding, and the resulting distinction between large-scale (i.e., extensive) spaces that require movement through them for proper understanding, by contrast with small-scale spaces which can be made sense of from a single perspective without such movement. Montello then proposes a more detailed qualitative classification of scales into a hierarchy from figural, to vista, through environmental, to geographical (see Figure 3.3). Figural space is the realm where an object or image of an object can be comprehended in a single view because it is “projectively smaller than the body” (Montello, 1993, p. 315). The perceptual emphasis of Montello’s framework is clear when we consider that this scale encompasses both the Moon and a coffee cup! Vista space is as large or larger than the body but can be comprehended from a single viewpoint (hence the name). The qualitative and fuzzy nature of the scheme is again clear when Montello cites as examples of such spaces “single rooms, town squares, small valleys, and horizons” (1993, p. 315). Environmental spaces are larger than the body and can only be comprehended by moving through them, often over long periods of time. The most familiar instance of such space is the experience we have of getting to know a city, slowly stitching together a mental map of how its neighborhoods, streets, and landmarks are spatially related to one another. Geographical spaces are larger still, indeed so large that they cannot be meaningfully understood by moving through them, but instead must be reduced down to a figural space in the form of maps or other representations. This points to

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Figure 3.3. Montello’s (1993) qualitative classification of spatial scales.

a deep connection between maps and geographical spaces, which can only be apprehended cartographically. It is interesting that this framework echoes work in human geography centered on the scale of the body, albeit out of a rather different motivation. A similar framework drawing on an unpublished presentation by David Zubin (for a summary of this work, see Mark et al., 1989, pp. 13–17) is presented by Helen Couclelis (1992), but she emphasizes the size of objects not their projective size. Such relatively rich, qualitative frameworks for thinking about scale are rare in giscience, but have attracted more interest in environmental psychology than in geography. In giscience, scale is more often considered from a technical perspective as the relationship between the world and its representation in data or maps—or in Montello’s terms the relationship between the figural space of the map and the geographical space of the world.

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On traditional paper maps, this relationship is expressed as a representative fraction that explicitly tells us the ratio of a distance on the printed map to the distance in the world between the corresponding locations. Typical topographic map scales expressed in this way are 1:50,000 and 1:63,360, respectively equivalent to 1 cm representing 500 m, and 1 inch representing 1 mile. These would generally be considered medium scales, while more detailed large-scale maps have smaller ratios of (say) 1:2,500 or 1:10,000. Small-scale maps, on the other hand, are used to show whole countries at scales such as 1:1,000,000 (1 cm to 10 km) up to perhaps 1:100,000,000 (1 cm to 1,000 km).6

Scale and the Web Map For experienced map users, particular numerical representative fractions become second nature. For many others, a scale bar which directly shows what distance in map space is equivalent to some stated distance in the real world is more useful. On contemporary web maps, scale bars are essential. The reason is mundane but nevertheless an important pointer to how different contemporary digital mapping is from paper-based precursors. Considering this in a little more detail also leads directly to a consideration of map projections. Cartographers no longer have much control over the final physical form in which maps are presented to users. Screen size and resolution (i.e., the size of individual pixels in a display) are dependent on individual map users’ devices and can vary widely. The same tile-based web map delivered on a 30-in, 1920×1080 monitor might appear almost seven times larger than on a smartphone with a 5·8-in, 1440×2560 screen. In the former case a 256×256 pixel tile image would measure almost 89×89 mm but only 13×13 mm in the latter. A scale bar representation will change size with the screen display and is self-correcting, but the representative fraction for each of these would be wildly different and is not 6

It is often observed that small numerical ratios correspond to highly detailed large-scale mapping while large ratios correspond to less detailed small-scale maps, leading to terminological confusions, when large-scale studies may be using the word scale to refer to scope or extent, in a manner more aligned with our earlier discussion of scale as size.

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reliably knowable to the map provider at the moment when the map is served to a requesting web client (the computer or phone in this case). Although platforms are constantly changing, what we might call the classic web map is based on a nested hierarchy of scales, or zoom levels of detail. Level 0 is a single square map tile (tile 0/0/0) that encompasses the whole Earth—or at any rate, most of it—see Figure 3.4. This tile is repeatedly subdivided into quarters, with each subdivision increasing the scale or zoom level, resulting in tiles that provide more detail but across a smaller region of Earth’s surface. This nested hierarchy is how the ability to smoothly zoom in and out from planetary scale to the high level of detail associated with local street directions is supported. At any particular zoom level, a web map image is composed of a set of tiles at the appropriate level laid out to produce the appearance of a continuous map. This enables websites and applications to progressively load the map information in small pieces (the tiles) rather than having to load a very large map image of the whole Earth at any particular scale.

Figure 3.4. Tiles from levels 0, 1, and 2 of the web map hierarchy. Each level is obtained from the level above by progressive subdivision into quarters. Map tiles in the terrain design by Stamen Design, under CC BY 3.0. Data by OpenStreetMap, under ODbL.

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When this approach was first introduced, map tiles were preprocessed image files (as are those in Figure 3.4). More recently, the implementation details have changed such that the nested tile hierarchy provides a reference framework, similar to a quadtree (see Samet, 1990), within which the map elements (roads, buildings, and so on) needed to produce a useable map at a desired zoom level and extent can be retrieved and rendered in the desired style. This approach is referred to as a vector tiling although the tiles are now a hierarchical reference frame that controls the rendering of geometries from a database rather than permanently stored already rendered images. This is desirable for reasons of storage efficiency and flexibility. Typical current whole Earth tile stores extend from zoom level 0 to level 21. At zoom level 21 there are 242 or around 4 trillion tiles. Even allowing that around 70% of tiles are water—and could be stored as a single uniform blue tile in many cases—the storage requirements for a tiled image map at this level of detail are formidable: somewhere on the order of 100 petabytes. It is easier to store geospatial data than pre-rendered images when faced with numbers like these. Apart from the obvious way in which this scheme relates to theoretical conceptualizations of scale (compare Figures 3.1 and 3.4) what is the scale of these map tiles? Because of the lack of control over the final size at which tiles are presented to a user, we cannot express scale as a representative fraction, but need to think instead in terms of the distance per image pixel. For a level 20 tile (say) a square tile has edge length 40,075/ 220 km or around 38.2 m. Tiles are usually rendered as 256×256 images, so each pixel at this level is around 15 cm across at the equator. At a different latitude the scale is different, however. For example in Wellington, New Zealand, at latitude 41°17′ 20′′ south the parallels are not 40,075 km around as at the equator but only 30,112 km, meaning that a single pixel at level 20 at this latitude represents only 11·2 cm.

Scale and Map Projection The scale disparities among web map tiles at the same level in the hierarchy, but at different locations on Earth’s surface, draw attention to a central technical challenge of mapping that significantly complicates the

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otherwise fairly trivial concept of map scale. Zoomed in close, the scale disparities just noted do not matter much: A level 20 tile at the equator and one at 40° latitude will never appear in the same map view, given that they are separated by several hundred thousand intervening tiles. But in tiles at or near the top of the hierarchy, the problem is severe, as demonstrated in Figure 3.5. This apparently square map represents substantially different distances from east to west than from north to south, and also has very different scales in the east–west direction at the center of the tile, than at the extreme north or south edge. The problem, of course, is that while a map (or computer screen) is usually a flat two-dimensional surface, the Earth’s surface is curved in the third dimension, forming a globe. Traditional maps—and most, if not all digital, on-screen maps—must resolve this fundamental mismatch between the flat surface of the map and the curved surface of the Earth. A map projection specifies the relationship between a location on the curved surface of the Earth and the spatial representation of that location on a map. This involves defining the relationship between Earthcentered latitude–longitude (𝜙, 𝜆 ) coordinates and map-centered (x, y)

Figure 3.5. Some key approximate distances on tile 0/0/0, illustrating the impossibility of assigning a single scale to this particular projection. Map tile in the terrain design by Stamen Design, under CC BY 3.0. Data by OpenStreetMap, under ODbL

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Figure 3.6. The definition of latitude and longitude relative to the Earth’s surface.

coordinates. Latitude and longitude are defined relative to the Earth understood as an approximate sphere rotating around an axis through its poles (see Figure 3.6). Lines of latitude (or parallels) are circles parallel to the equator defined by their angular offset north or south of the equator measured at the center of the Earth. Lines of longitude (or meridians) are great circles passing through the poles. A prime meridian is defined to pass through Greenwich, London, and meridians are measured by their angular offset at the center of the Earth from this datum. Any point on the Earth’s surface can be located using the geocentric coordinate system. Corresponding points on a map will have a pair of (x, y) coordinates in the map space, and the map’s projection is defined by the two relationships x = f1 (𝜙, 𝜆 ) y = f2 (𝜙, 𝜆 ) which specify how to project any particular location on the Earth’s surface onto the map space. Most projections in common use can only

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Figure 3.7. Two simple world projections. (a) Platte-Carrée, and (b) Lambert’s Cylindrical Equal Area.

be described using complicated mathematical formulae, which are not particularly illuminating to the present discussion.7 A simple projection is the null projection where x = k𝜆 and y = k𝜙, sometimes known as Platte Carrée, which treats longitude and latitude, respectively, as the x and y plotting coordinates, scaled so that the nominal map scale is correct at the equator (see Figure 3.7a). Variations on this projection where the scale is correct at the ±𝜙0 parallels are obtained when we set x = k𝜆 cos 𝜙0 . Another simple example is Lambert’s Equal Area Cylindrical projection where x = k𝜆 and y = k sin 𝜙 (see Figure 3.7b). The rescaling of the north–south dimension in this case has the effect of making this an equal-area projection such that regions of equal area on the Earth’s surface are mapped onto equal-area regions 7

See, for example, Snyder’s Map Projections for details (1987).

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in the map. These are examples of cylindrical projections often characterized by the meridians being portrayed as parallel north–south lines, and the poles by the north and south edges of a rectangular map. The latter is an obvious distortion in such projections, since on Earth’s surface the meridians converge to a point at the poles. The cylindrical projection of tile 0/0/0 shown in Figure 3.5 is a variation on one of the oldest known map projections, that of Gerardus Mercator. This projection was designed to have the useful property that straight lines on the map are lines of constant bearing, which makes navigation by compass much simpler (see Figure 3.8). A side effect of this property is that the projection is conformal, meaning that the shapes of areas on the Earth’s surface are preserved. However, a further side effect of preserving the shapes of regions is that relative areas of regions are grossly exaggerated the farther they are from the equator. A little thought makes it clear why this occurs. Meridians continuously converge from the equator where they are at maximum spacing toward the poles where they meet. A degree of longitude at the equator

Figure 3.8. A loxodrome on the sphere and in the Mercator projection. This line of constant bearing spirals toward the pole without ever reaching it, but resolves as a straight line in the Mercator projection, greatly simplifying navigation. Note how exaggerated the Mercator projected view is at high latitudes.

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is approximately 111 km but this decreases with increasing latitude, by a factor cos 𝜙. Since the Mercator projection is cylindrical with meridians remaining equally spaced regardless of distance from the equator, there is an exaggeration of scale in the east–west direction by a factor 1/cos 𝜙 at latitude 𝜙. To preserve the shape of regions, the north–south scale must be exaggerated by the same factor. This means that, for example at ±60°, where the scale in both directions is exaggerated by a factor of 2 relative to the equator, areas are exaggerated by a factor of 4. In fact, the exaggeration of scale in the Mercator projection is so severe that the poles cannot be mapped, because they are infinitely far from the equator in the projected coordinate space. Earlier, it was noted that tile 0/0/0 of the web map reference system does not include the whole Earth, and this is why. To give a square tile the maximum latitudes included in tile 0/0/0 are at around ±85°3′ 4.06′′ . There is no particular reason for choosing this projection as the basis for interactive zoomable web maps, although repeated division into quarters of square tiles is computationally convenient. Indeed, long before tiled web maps (or for that matter the web!) a system along these lines was proposed by Tobler and Chen (1986) using a cylindrical equal area projection with standard parallels ±55.654° (see Figure 3.9). The dominance in recent years of Web Mercator has reopened arguments about the political impact of map projections in reinforcing dominant political and cultural ideas concerning the relationship between the global north and south. Fortunately, more recent developments seem likely to result in an interactive 2.5D globe being presented to users at whole Earth scales in many cases, which may slowly correct misconceptions embedded over time by the prevalence of the Mercator projection (see Crampton, 1994). While the political impacts of various map projections (intended or not) are important, the key issue here is not so much that any given map projection distorts, as that it is well suited for some purposes but not for others. The Mercator projection is really useful for navigation, but terrible (in almost all cases) for small-scale thematic mapping. The deeper point, as already implied by different perspectives on space discussed in Chapter 2 (see §Absolute Space in GIS, Chapter 2), is that there

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Figure 3.9. Tobler and Chen’s equal area cylindrical projection in a square, which was proposed as a potential basis for a recursively subdivided “scheme for the storage of geographic information on a global basis” (1986, p. 370).

is no particular reason to prioritize narrow geometric concerns such as distance, area, and direction in computational representations. The cartograms in Figure 2.2 can be considered examples where the scale is one relating population to area according to some representative fraction in exactly the same way that a more conventional map scale does. Map projection is a wide-ranging topic central to any serious consideration of cartographic representation. The issue for the present discussion is how a chosen projection can subvert any particular choice of scale in complex ways. Even taken on its own terms, there are no maps—not

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even topographic maps—that preserve the same representative fraction map scale across their full extent.8 This can also be understood as reflecting the observer-dependent nature of scale discussed in the theoretical geography literature. Another aspect of the topic to which we return is how different ways of seeing the world imply different map projections (see §Graph Drawings as (Possible) Projections, Chapter 6). Once we understand projections in this way, the potential to expand the concept beyond a narrow focus on geometric fidelity is clear and opens up a wider range of representations in geography to being understood as map projection.

Scale-Dependencies: Resolution and Generalization At the outset of my discussion of scale I considered the range of spatial extents across which the work of geographers might range, settling on something like 10 orders of magnitude, from (say) grains of sand to (say) continents. Attending to the extremes of this range and meaningfully relating them to one another is close to impossible, necessitating in most cases a narrower focus, so that researchers concerned with particle grain sizes are more likely to do their work at catchment scales or smaller, for example. This points to an important alternative emphasis in thinking about scale—that of grain in relation to extent. This approach emphasizes the relationship between the finest details or smallest phenomena of interest relative to the overall extent of the areas across which we are studying them. The wider this range, the more difficult (or even impossible) scaling up from processes at one scale to processes at other scales will generally be. Logistical concerns often limit our ability to zoom in arbitrarily closely (i.e., to reduce the grain size) given a particular study extent. These considerations are nicely summarized by Wiens:

8

This claim is technically correct, but in practical terms an exaggeration. For example, assuming that the nominal map scale is correct at the center of a 1:50,000 scale, generously proportioned one meter square map sheet, then at the corners the nominal scale would be off by on the order of only 0.005%, assuming a widely used transverse Mercator projection. The world really is not flat, but locally, flat is a pretty good approximation!

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[e]xtent and grain define the upper and lower limits of resolution of a study; they are analogous to the overall size of a sieve and its mesh size, respectively. Any inferences about scale-dependency in a system are constrained by the extent and grain of investigation— we cannot generalize beyond the extent without [assuming scaleindependence], and we cannot detect any elements of patterns below the grain. For logistical reasons, expanding the extent of a study usually also entails enlarging the grain (1989, p. 387).

This statement is made specifically with reference to field-based data collection in ecology, but is equally relevant to the more general challenges of any spatially explicit study. From computational and geospatial data perspectives, these arguments correspond to concerns with resolution and generalization. Resolution is usually understood in relation to the smallest elements that can be resolved in imagery data. Generalization refers to the various operations applied to geospatial data to make them suitable for display at different map scales, and often has similar effects to resolution in making details available to viewers or not. Both concepts inhabit similar conceptual terrain, as expressions of the tension between the grain and extent of geospatial data of all kinds. The resolution of sensor platforms and the data derived from them strongly affect their potential applications. Features smaller than the resolution are undetectable. Features up to twice the resolution may not be reliably detected, and only larger multipixel features can be easily distinguished one from another. Raster data can be conveniently resampled by aggregation to lower resolutions, coarsening it, by averaging pixel values in the original high-resolution layer to pixel values in the new lower-resolution layer. However, the reverse process of disaggregation by interpolation or smoothing cannot recover the original data (see Figure 3.10). Working with multiple data layers, the lowest-resolution layer may constrain the reliability of results to at or around that resolution, although this is not always so. Some phenomena, for example, mean annual temperatures may inherently only make sense at coarse grains. This example shows how spatial resolution interacts with temporal and measurement resolution (Lam & Quattrochi, 1992; Lam, 2019).

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Figure 3.10. An original raster dataset aggregated by a factor of 10, then disaggregated back by interpolation, showing the data loss that results.

The same interaction between spatial, temporal, and measurement scales is true of data attributed to points or polygons. Census polygons at the “block” level (typically meaning around 100 people) will record relatively coarse information about the associated population, such as counts of persons in broad (say) 15-year age ranges. While this might (depending on the jurisdiction) be stipulated by privacy constraints, a thought experiment suffices to show that something more fundamental is going on. Given a group of 100 people, if age group counts by year were reported, there would be high variability among broadly similar census blocks. Some blocks would have zero populations reported at some ages, based solely on the census date and on the birth dates of respondents. National censuses of population happen at long time intervals of 5 or 10 years, and so, even though data will have been collected giving exact ages, reporting it to this precision is only likely to make sense at coarser

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spatial resolutions, for areas with populations of (say) 5,000 or more. The challenges of dealing with uncertainties in noncensus data collected on populations such as the American Community Survey further emphasize this point (Spielman et al., 2014). In this case the vagaries of sampling mean that small area (high spatial resolution) data are highly unreliable unless they are aggregated over several years of the survey. Cartographic generalization, long practiced in the production of paper maps, also sits uncomfortably at the point where grain and extent meet. The too often quoted conceit of the one-to-one scale map9 is intentionally absurd but nevertheless has been and remains a geospatial technological dream, most recently in the form of digital twins (Batty, 2018), but going back at least to “mirror worlds” (Gelernter, 1991) if not further. Such a map is impossible and absurd. The point of maps is not to mirror the world, but to represent it in specific ways for particular purposes. Including everything in small-scale maps is impossible; even including everything in a notional 1:1 scale map is impossible (that’s the point of the much quoted parables). In small-scale maps, the first line of defense is selecting what to include or exclude, although that only partly addresses the challenge of simplifying the map sufficiently for it to be useful. In addition, the cartographic twins of things in the world are generalized so that they remain legible at a small scale, or elements are removed completely to avoid clutter and confusion. Generalization is usually considered to consist of combining a variety of operations (Raposo, 2017, provides an excellent summary), among them simplification, aggregation, selection, and exaggeration (see Figure 3.11). Routine application of any one of these operations might be relatively straightforward (although often it is not), but combining several operations across multiple datasets to produce an overall effect in a map is extremely complex. A significant source of difficulties is anticipating the interactions among different data layers. For example, it is not a 9

Variously attributable to Lewis Carroll in Sylvie and Bruno Concluded, Luis Borges in On Exactitude in Science, Umberto Eco in On the Impossibility of Drawing a Map of the Empire on a Scale of 1 to 1, and approvingly discussed by Jean Baudrillard (1994) in Simulacra and Simulation.

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Figure 3.11. Map generalization showing a simplified layer after processes of selection, simplification, and aggregation—look closely!

simple matter to generalize a road layer for a particular scale of presentation on page or screen. But it becomes significantly more complicated when generalization of roads has implications for how building or parcel, or any of the other layers that interact with the road layer, should be represented. Thus, in the same way that the resolution of geospatial data is a complex interaction of the effects of spatial, temporal, and measurement scales (especially of classification), generalization reveals the subtleties of the impact of scale on giscience in practice. And indeed, early success (Douglas & Peucker, 1973) quickly gave way to recognition that automated generalization is far from trivial (Brassel & Weibel, 1988) and the emergence of multiscale maps (i.e., web maps) has intensified the design challenge (Roth et al., 2011). Even on narrowly technical grounds then, it seems likely that ongoing maintenance by different actors, for different purposes, of somewhat related, nonidentical(!) digital cousins will prevail, rather than that monolithic singular digital twins will emerge other than in specific limited domains.10 A further scale-dependent effect, much discussed in giscience is the modifiable areal unit problem (MAUP), which we consider in detail in §The Arbitrariness of Boundaries, Chapter 5. 10Although

there can be little doubt that sweeping claims will continue to be made for the political, economic, and social efficacy of digital twins and mirror worlds!

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THE SALIENCE OF SCALE Scale is considered central by geographers of all stripes, even human geographers who hanker after a geography without scale. The salience of scale is also recognized in giscience. This differs from the case of space, where having settled on absolute space in most platforms, what is lost in that approach disappears from view. Chosen approaches to space are embedded in data formats, making their further diffusion and uptake even more likely. In this way, decisions about how to represent space are pre-encoded, and unless geographers have the capacity to develop their own formats, the limited spatial imaginary of these formats becomes a taken-for-granted default. By contrast, scale enters the picture at every stage of working with geospatial data. Some of these stages are hidden. The selections, simplifications, and omissions in a particular dataset, arising from its scales of collection and collation, may pass unnoticed. But, how things come in or out of focus at different scales, as data are manipulated, displayed, aggregated, or combined with other data, is often highly visible. Further, these effects are explicitly considered as concerns of giscience (see, e.g., Lloyd, 2014). The impacts of scale on data collection, and subsequent processing, storage, and visualization, are too significant to escape attention as merely technical challenges demanding solutions. How these technical challenges play out surely deserves closer attention in geographical thought more generally. Considering what is recorded and mapped (or not) at different scales might even shed light on how scales are socially constructed, and on some of the ways that scale operates (or not) politically. Interactive web maps are a recent development in this context, and it can be instructive to spend time slowly zooming in to such maps to see what features appear (or disappear) at successive levels of detail. As we will see in the next two chapters, what is included or not, and in what guise—generalized to a point, or rendered in more detail—is politically charged, and understanding these choices as purely technical dimensions of scale hides those politics. The scale dependencies of geospatial data are after all more than technical matters.

Chapter

Place and Meaning in Space eography has more than its fair share of interrelated conceptual terms that defy easy definition: space, region, area, locale, network, boundary, neighborhood, and so on. Even in such elusive company, place may be the slipperiest character, almost impossible to pin down. It can be taken as a synonym, antonym, or close relation to almost any of the above, a spectral other when discussing any of them. Since we consider all these concepts elsewhere, it is convenient for now to emphasize the idea of place as a localized concrete expression of abstract space and to see place and space as somehow opposed. Opposing space and place in this way is useful and instructive, but also taken for granted enough that we should question the move. We return to this question at the end of the discussion. Place and space are clearly closely related concepts, so much so that they are sometimes used interchangeably.1 A comprehensive survey of philosophical takes on both is Edward Casey’s The Fate of Place (1997b). He identifies Western notions of universalism as central to the persistent priority given in philosophical thought to space rather than place:

G

1

Lefebvre (1991) and Massey (2005) are influential authors whose usage of space is arguably better aligned to thinking about place.

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This universalism is most starkly evident in the search for ideas, usually labeled, ‘essences,’ that obtain everywhere and for which a particular somewhere, a given place, is presumably irrelevant. Is it accidental that the obsession with space as something infinite and ubiquitous coincided with the spread of Christianity, a religion with universalist aspirations? (1997a, p. xii)

This hint at a religious origin for universalist ideas notwithstanding, there has been a persistent linking (in Western thought) of space with rational or scientific perspectives and of place with naïve or primitive perspectives. Given how “[p]lace presents itself to us as a condition of human experience” (Entrikin, 1991, p. 1), while abstract space has required significant intellectual labor to be conceptualized into existence, this prioritization is surprising but perhaps inevitable in light of Western thought’s fixation on Cartesian dualism and the elevation of mind over matter. This tension is central to many narratives of progress and colonial projects of displacement and conquest (see Massey, 2005, pp. 1–4). Consequently, geographical theory repeatedly returns to the space–place binary, as will be clear even from the overview of these ideas in this chapter. Taking up the opposition between space and place, it is unusual for a person to think of their location in terms of geocentric (i.e., latitude– longitude) coordinates, or a map grid easting-northing reference, except in very particular circumstances. Instead, we think of ourselves as being in a particular place or places at any given moment. Some of these places are named locations, of lesser or greater specificity, such as Berkeley, California, or Wellington, New Zealand, or Northland in Wellington, New Zealand. Some places are personally meaningful, such as home or turangawaewae or work or my local pub, and require more information to be reliably geolocated to a particular point on a map. Again, some other places, even named places, may be ambiguous or vague, such as a particular neighborhood or suburb. For example, Tokyo’s Shibuya or San Francisco’s Mission District cannot be delineated on maps with certainty. The concept of place has been and remains a challenging one for giscience, the spatial bias of which often ends up reducing place to the

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⟨x, y, A⟩ geoatom of location in absolute space plus attributes tuple, but this approach drains places of their particular and unique character. As a result, attempts in giscience to be more platial necessarily challenge dominant computational representations (Mocnik, 2022). Place has become particularly salient in the realm of information retrieval (or search) and location-based services. Such services are location-based in the sense that the machines involved in their delivery operate using coordinate-based spatial referencing systems, built on the geoatomic logic of Chapter 2, but when people interact with these services, it is human conceptions of place that determine where a location actually is. “Where is the best pizza near 41°16′ 41′′ S 174°45′ 24′′ E?” is a question rarely asked.2 “Where’s the best pizza in Wellington?” or “in Northland?” or “near my home?” are humancentered questions that require a computational engagement with place and its many meanings. Such mundane questions and the translations between the different ways they can be posed lead to interesting questions at the heart of geography and giscience.

FROM SPACE TO PLACE The examples already noted point to the dichotomy between space, particularly absolute space (see §The Nature of Space, Chapter 2), on the one hand, and place on the other. Loosely speaking, space, conceived absolutely, belongs in the realm of calculation, coordinate systems, and geodesy; while place belongs in the realm of everyday life and practice, emotion, and meaning. People generally attach little meaning to particular coordinate locations.3 The North and South poles, the Greenwich Meridian,4 the International Dateline, and Null Island5 are exceptions. 2 3 4

5

Google attempts an answer, but got it wrong at the time of writing. Confluence hunting is a not-very-notable, if enjoyable (for some), exception. See the degree confluence project at https://confluence.org. At the 2010 GISRUK Conference dinner on a Thames riverboat, I was bewildered by the joyous reaction of other attendees on crossing the meridian. As a resident of Greenwich for several years in the 1990s, who crossed the meridian almost daily, I had clearly become jaded. See https://en.wikipedia.org/wiki/Null_Island.

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It is interesting that in a virtual world of pure space specific coordinates can become meaningful places. Thus Second Life’s precursor AlphaWorld, as mapped in Dodge and Kitchin’s Atlas of Cyberspace, exhibits high-density (virtual) development along lines in the cardinal and ordinal directions from the origin at (0, 0) (see Dodge & Kitchin, 2001, pp. 195–208). In this abstract space, coordinate locations such as (666, 666) in the northeast cardinal direction acquire meaning through their memorability. Nevertheless, even in this setting, what is built at particular locations and the life that then unfolds there eventually supersedes such accidents of labeling.

Making Space Legible: Addressing the World Returning to the real, physical world, the closest humans come to using referencing systems in everyday life is in street addressing systems. Like many other everyday things, street addresses seem natural and obvious. However, differences in how street addressing works in different countries make clear that this is certainly not the case. Notable exceptions to Eurocentric ideas of the seemingly obvious way for street addressing to work are provided by the hierarchically nested addressing used in Korea and Japan, where districts (ku) are divided into neighborhoods (chome) that group together several dozen houses and thus form a block. Houses are numbered according to the block to which they belong and not as a function of the street (Farvacque-Vitkovic et al., 2005, p. 9).

This mode of addressing requires a completely different approach to geocoding (Lee & Kim, 2006). The importance of the development of the street address based TIGER and GBF/DIME formats for the development of GIS in North America (see U.S. Bureau of the Census, 1968, 1970; Holtzheimer, 1983) is further evidence of how much we take such systems for granted. In fact, address systems emerged over long periods of time to render spaces governable, navigable, and legible to commerce (Rose-Redwood, 2006, 2012). Standardized address systems are strongly associated with the emergence of the state and extensive

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networks of nonlocal trading under capitalism. They occupy a position somewhere between the cold rationality of coordinate systems and more loosely defined notions of place in everyday life. The tensions between human-centered and machine-centered indexing of location are clear. Fully geocoded machine-readable addressing systems are still emerging. Geocentric latitude–longitude coordinates are a pre-existing example, but for a variety of technical reasons geohashing schemes are favored. For example the geocentric coordinates 55°12′ N 7°51′ W correspond with the geohash code gcf6j2g in a system introduced by Gustavo Niemeyer.6 Geohashes convert two geocentric coordinates to a single alphanumeric address which is more convenient for indexing in databases, and which has the property that locations near one another in two-dimensional space are likely to be close to one another in the index. Some schemes also have the feature that as the code is shortened the precision of the associated geolocation is reduced. This property makes them hierarchically organized orderings of two-dimensional space into a single linear dimension and is typically accomplished by means of fractal space-filling curves or hierarchically nested polygonal schemes as shown in Figure 4.1.

Figure 4.1. Geohash ordering schemes. From left to right are the Morton curve, Hilbert curve, and iteratively scaled and rotated hexagonal grid schemes.

6

See https://blog.labix.org/2008/02/26/geohashorg-is-public.

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Niemeyer’s geohashing scheme relies on the z-order curve (the lefthand panel in the figure) first proposed by Morton (1966), which is convenient to program as the codes can be calculated by interleaving bits from the binary representations of the spatial coordinates. Google’s S2 index uses a mapping of the Hilbert curve (middle panel in the figure) on to Earth’s surface.7 The hierarchically nested hexagonal scheme in the right-hand panel of Figure 4.1 is based on repeatedly downscaling by an (area) factor of one-seventh while rotating the hexagons to match vertices with those at the next level up. The particular hierarchy illustrated is used in the H3 indexing scheme developed by Uber,8 and is similar to many discrete global grid (DGG) systems (Sahr et al., 2003). These schemes all have the property that shortening the index reduces the resolution of the associated geolocation. Equivalently, the first part of an index provides information about the approximate location, in a way that is natural for users accustomed to the progressive accuracy provided by a street address: New Zealand (country), Wellington (city), Brooklyn (suburb), and so on. An example lacking this feature is what3words, which is nevertheless argued to be human friendly (Jones, 2015). This claim rests on the idea that sequences of three words, even meaningless ones, are more memorable to people than coordinate pairs or text indices as ways to index locations on Earth’s surface. This logic is deployed to assign a unique and arbitrary three-word index to every location on Earth’s surface at a resolution of 3 m. Thus, mouse.dinner.book is (at the time of writing) in a field near Esher in southwest London. To minimize the chance of errors, crucially “[t]he system is also non-topological; the three words used to reference any square on the Earth’s surface are not dependent on the three words to reference any of the adjacent squares” (Jones, 2015, p. 12). Thus, the easily confused address mouse.dinner.books is near Herkimer in upstate New York on the other side of the Atlantic Ocean. This approach makes for unambiguous spatial references to highly specific locations, although it is questionable how human-friendly it really 7 8

See https://s2geometry.io/. See https://h3geo.org/.

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is. The lack of hierarchical logic to the index words means that there is no way, other than by using the what3words website or API, to determine the location of a particular word combination, even given the index word combinations of nearby locations. So, while what3words provides potentially more memorable mnemonics for particular places, the disconnection of the mnemonic from any spatial logic makes it less legible, and impossible to reason with. By contrast, street addressing schemes that use building numbers, street names, neighborhood names, and even postcodes embed a logic of place that is legible to most humans, as do the hierarchical addresses used in Japan and Korea. Any of these reflect more closely the rich meanings that people and cultures attach to places, when compared with the emphasis on point location of machine-oriented indices. A more typical attempt to rationalize the addressing of places is provided by the still relatively recent (c. 2008) development of postcodes in New Zealand’s national postal addressing system (the U.S. ZIP code and U.K. postcode systems were introduced much earlier). It is instructive to note that in this case, “postcode boundaries do not necessarily reflect suburb boundaries” (New Zealand Post, 2018, p. 3), a situation also typical of postcode schemes in other jurisdictions. The four-digit codes are formally and unambiguously defined—every address is in one and only one postcode area—but suburbs are less clear, and maintained largely through usage and shared understanding of where they are. For this reason, the suburb name is not part of the correct postal address, although it is commonly included as if it were, and is auto-completed in online forms. We can illustrate the ambiguity of suburb boundaries using information collected from the public about their understanding of where their neighborhoods are, as shown in Figure 4.2. This apparently chaotic situation is not unusual for sub-city level places in urban areas. Surprisingly, meaning-making can attach to seemingly lifeless numbering schemes, so that over time, culture turns codes into recognizable places, like Los Angeles’ 90210 or London’s NW3. A similar place-based cultural cachet can even attach to only loosely geographical markers such as telephone area codes, like Manhattan’s 212 or San Francisco’s 415. When London’s telephone area code switched in

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Figure 4.2. Neighborhood areas as delineated by respondents to a web map survey in Wellington, New Zealand. Alignment of some boundaries (often along roads) is evident, but so also are divergences in personal definitions of neighborhoods, which are not consistently aligned with any official postal or administrative boundaries. Neighborhood data from Rickard (2020). See also the Bostonography project at https://bostonography.com/ 2012/crowdsourced-neighborhood-boundaries-part-one-consensus/.

1990 from 01 for the whole metropolis to 071 for inner suburbs and 081 for outer suburbs, many users, particularly businesses, were disappointed to be assigned the 081 code.9 Subsequent changes saw London area codes merged back into a single code 020, with an additional digit added to the local numbers, but the extent to which the inner/outer geographical split had become culturally embedded led to a persistence in preference

9

It was probably only numerological oddballs like me who were excited to (briefly) have the phone number 0171 701 7107 in the midst of all these renumberings!

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for 0207 numbers, even though this no longer has any geographical meaning.10 Such apparently arbitrary labels, whether the names of neighborhoods or suburbs, postcodes, or telephone area codes, can have considerable impact in the realm of real estate. The late 1960s saw the beginnings of the transformation of the declining industrial area of Manhattan south of Houston Street into the hip neighborhood of SoHo (see Zukin, 1982). While the renaming of the South Houston Industrial Area as SoHo did not cause this transformation, the reimagining of the area underpinning the renaming was an important part of the process. The remaking of the place economically and culturally was directly mirrored in its renaming and redefinition. Similar stories have played out in other urban neighborhoods such as the nearby Tribeca (Triangle below Canal), in a process where urban neighborhoods—at least in the United States in the modern era—are routinely produced by the real estate industry and city governments (Molotch, 1979). More recent accounts acknowledge a greater role for local communities, local activists, and others, suggesting that neighborhoods (whether old or new) are “spatial projects” that are both sites and outcomes of contest and struggle (Madden, 2014).

Place: The Intersection of Space With Experience A recurrent theme of the various schemes for rationally organizing and ordering space touched on above is how they almost invariably become imbued with meaning: Spaces become places. The meanings are not attached to the labels or numbers per se, but to the geographical places those labels signify. Considering such matters brings us closer to an understanding of place as location imbued with meaning through experience, or more completely as both a context for and a product of physical, social, economic, and cultural processes. Places carry meaning not only because of human understanding, culture, and experience, 10 The

ascendancy of mobile phone numbers untethered from geographical referents will presumably lead to less status anxiety around phone numbers, although history suggests this might take some time.

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but also because they are sites where the processes that make places are shaped and remade by the particular character of the places themselves. An influential extended discussion of these general ideas is Yi-Fu Tuan’s Space and Place: The Perspective of Experience (1977).11 As the subtitle suggests, Tuan sees experience as central to any understanding of the nature of place. This perspective draws in part on ideas that were dominant in behavioral geography in the 1970s (see Golledge & Stimson, 1997, for good coverage of this literature). Touchstones of this tradition were work by cognitive psychologists on the development of a child’s view of the world (Piaget & Inhelder, 1967), and Kevin Lynch’s use of nonmetric sketch maps in The Image of the City to portray residents’ collective and shared overall sense of the organization of their cities. Closer to geography, and taking Piaget and Inhelder, and Lynch as key points of reference is work on the importance of mental maps in understanding human behavior (Gould & White, 1974; Downs & Stea, 1973). This work can be seen in two somewhat opposed ways. On the one hand, it may be an attempt to rescue spatial determinism by establishing that it is not the objective (measured) spatial geometry of the world that drives events, but subjective (perceived) platial, experiential “maps in mind.” On the other, behavioral geography is also related to a recognition that relative space cannot be easily measured and a turn toward phenomenology (Buttimer, 1976). Tuan’s insistence on experience as vital to a sense of place is a theme that he repeatedly returns to in Space and Place. He discusses, for example, how the body imposes a schema of up-down, front-back, left-right, on space (1977, pp. 12ff, and pp. 34ff). At other scales, such egocentric perspectives give rise to notions such as here and there, this and that, us and them (1977, p. 25). Traditional systems of measurement carry this further when parts of the body form a basis for units of length. Some echoes of this idea are found in the notion of naïve geography (Egenhofer & Mark, 1995), which calls for direct computational representation in giscience of more intuitive or qualitative ideas about spatial relations, 11 Of course, consideration of the notion of place long predates Space and Place. See Glacken,

1967; Casey, 1997a, for extended discussions.

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such as “near” and “far” or “up ahead” moving beyond the geometric emphasis that dominates the field (Ligozat, 2013). The lack of a strong connection between Tuan’s (1977) framework and dominant currents in the critical geographic mainstream is surprising in light of his insightful writing on, among other things, “architectural space,” “attachment to homeland,” and “the creation of place.” Perhaps a tendency to focus on the individual rather than on how individual experience relates to larger scale processes of capital accumulation and state formation—dominant themes of contemporary Marxist geographies— explains the disconnect. One point of contact is the suggestion that “place is whatever stable object catches our attention” (Tuan, 1977, p. 161), meaning that landmarks are important, and that place making is about creating such objects of attention, whether widely visible or more local, or ideological and shared (e.g., schoolbook maps). This idea aligns with those in Henri Lefebvre’s The Production of Space, which was originally published in 1974 but did not much influence English language geography until a translation appeared almost two decades later (Lefebvre, 1991).12 The emphasis on landmarks also calls to mind The Image of the City (Lynch, 1960), which has influenced work on cognitive mapping in behavioral geography (Couclelis et al., 1987), and occasionally informed giscience (see Banai, 1999). Experience is a tricky idea to pin down. Another potential avenue, perhaps more amenable to computational representation, opens up when we consider that experience can only build through time, a recurrent theme for Tuan. Space becomes place over time, so that when we know a region of space well, it becomes place; consequently, “[s]ense of time affects sense of place” (Tuan, 1977, p. 186). Perhaps the most evocative statement of this idea occurs early in Space and Place when place is equated with pauses, or stability and the home, while space is matched with possibility and movement:

12 Lefebvre

also emphasizes experience in his Critique of Everyday Life (2005) —work also published decades earlier in French.

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The ideas ‘space’ and ‘place’ require each other for definition. From the security and stability of place we are aware of the openness, freedom, and threat of space, and vice versa. Furthermore, if we think of space as that which allows movement, then place is pause; each pause in movement makes it possible for location to be transformed into place (Tuan, 1977, p. 6).

These dichotomies are recurrent in geographic thought, with space often associated with change, movement, and the restless onward march of globalized capitalism, while place is associated with resistance to change and preservation of the familiar (see Massey, 2005, pp. 4–6, and also discussions in §Relational Space, Chapter 2 and §Place in Relational Space, this chapter).

Everything in Its Place The humanistic approach to place presented by Tuan runs the risk of making place a purely subjective thing. As Malpas argues “[t]he crucial point about the connection between place and experience is not, however, that place is properly something only encountered ‘in’ experience, but rather that place is integral to the very structure and possibility of experience” (1999, 31–32, emphasis in original). This understanding comes to the fore more in cultural geographic treatments of place, where emphasis falls on the question of what is in place or out of place in particular settings. In In Place/Out of Place Tim Cresswell (1996) considers a number of examples of activities and behaviors whose in/out of place status sheds light on how society is organized and controlled. The most accessible of the case studies is urban graffiti.13 Cresswell describes how New York graffiti in the 1970s moved from illegal street art to SoHo’s commercial art galleries, and suggests that

13The

other two case studies, of alternative hippy rave convoys, and the Greenham Common Women’s Peace Camp at a cruise missile base, both in 1990s Britain, require more specific geographical and historical context than I have space for.

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a kind of geomagic is performed by the simple act of taking graffiti off the streets and (dis)placing it in the gallery—out of the unofficial spaces and into the sanctioned and revered domains of established and commercial art. Crime, with a flick of the wrist, becomes art; the valueless is turned into price-tagged and packaged art ready for your living-room wall (1996, p. 58).

Graffiti is a practice whose meaning is bound up with where and when it is or is not considered appropriate (in place or out of place), so that how it is experienced, whether as artist or as audience is intimately bound up with place. Graffiti is only graffiti if it is out of place for someone; even then it is only graffiti to those people for whom it is out of place. Spray-painted words and pictures in places where they are not considered out of place are not graffiti, they are street art, or simply spray-painted words and pictures. Graffiti may seem a specific example, but the broader argument is that all our behavior is governed by such place-based rules and judgments, and that culture and place are mutually constituted by these relationships. Cresswell goes on to argue that understanding place is essential to understanding how ideology is created and maintained. Ideological beliefs have effects when they shape and control how people behave in and experience the world. Shared—even if contested—understandings of what actions are allowable or not in particular places mean that place, and how different places are defined, are central to the maintenance of ideology, and therefore of power. This points to an underlying conservatism in the humanistic perspective of experience, concerned as it is with how places are defined by the experiences that unfold in them. This is particularly clear when places such as home and related ideas of belonging are discussed. Equally, returning to the in/out of place perspective, the salience of place to ideology and its maintenance and enforcement also points to the salience of place in relation to resistance. As Don Mitchell puts it, “[s]pace, place, and location are not just the stage upon which rights are contested, but are actively produced by—and in turn serve to structure—struggles over rights” (2003, p. 81). Struggles around what

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activities and practices belong, or which people belong in a place and what they may or may not do there, are thus central to social change. This overall framework helps to shed light on topics as diverse as protest and free speech, homelessness, and migration. Accounts differ in the degree to which the places are clearly defined, particularly those associated with the assertion of property rights (Staeheli & Mitchell, 2008) or jurisdictional boundaries, themes central to Chapter 5. Places are as likely to be ill-defined as not. A recent widely experienced example is provided by mask-wearing during the COVID-19 pandemic under various lockdown provisions where norms around masking and when and where it was expected or not were often unclear and shifting from day to day, often without much direct relation to current quarantine orders. If all the examples noted seem tied to social geography, it is important also to consider topics like pollution and invasive species ecology, where substances and beings that are considered in or out of place are focal. While regulation and management of pollution or invasive species often entails the drawing up of boundaries, the underlying questions of what belongs in a particular place (or not) remain much more ambiguous (see, e.g., Pereyra, 2016).

Place in Relational Space Clearly, space and place are related: At a minimum, a place is some region in space. Conversely, places create a space within which people can engage in particular practices (this loose definition of place is congruent with what Lefebvre, 1991 means by The Production of Space). Since Newton and the rise of strong concepts of absolute space, place has tended to be seen as subsidiary to space, either solely to be thought of as an area of space, or even as merely a point location in space (Casey, 1997a; Entrikin, 1991). As we have seen in Chapter 2, pending developments discussed in more detail below, this position has been the default for most giscience. Assuming that the richer conceptions of place discussed above are of interest, the question arises of what would be a more nuanced understanding of the relationship between these key concepts than “a place is a region of space” or “space subsumes place.” Perhaps the most compelling

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account is Doreen Massey’s (1991a) idea of “a global sense of place,” set out with reference to a rich description of an imagined walk along Kilburn High Road, in northwest London. She notices signs of the large local Irish, Indian, and Pakistani communities. She registers planes overhead on their descent into Heathrow and wonders about where they’ve come from and what life is like in those other places, apart from, but connected to this one. It is the time of the “first” Gulf War, and she chats with a Muslim newspaper seller unhappy about it. In sum: People’s routes through the place, their favorite haunts within it, the connections they make (physically, or by phone or post, or in memory and imagination) between here and the rest of the world vary enormously (1991a, p. 28).

From this, Massey goes on to argue that places are not singular or unitary, nor are they synonymous with narrow or closed notions of community, which is often a reason for place-based perspectives to be considered inherently conservative. She also suggests that places are processes, not things (see also Pred, 1984, and Chapters 7 and 8), that they are constantly unfolding and being made and remade, which means that they are often messy and contradictory, reinforcing their non-unitary nature. Furthermore, places in this sense do not have clear boundaries. They are not defined by boundaries so much as by webs of connection—to other places (see Chapters 5 and 6). Finally, “none of this denies place nor the importance of the uniqueness of place” (1991a, p. 29). Whatever uniqueness places have is not derived solely from a set of local attributes or an internal history, but rather from the geographically specific sets of relations to other places and to wider systems that each place has, interacting with the particular history of that place. Based on this perspective, she closes the paper arguing that this sense of place, [is] an understanding of ‘its character’, which can only be constructed by linking that place to places beyond. A progressive sense of place would recognize that, without being threatened by it. What we need, it seems to me, is a global sense of the local, a global sense of place (1991a, p. 29).

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In later work Massey reiterates this general account (2005, pp. 130–42) tying it more closely to her thinking on the relational nature of space (see §Relational Space, Chapter 2). More so even than usual, this paper has to be understood in the context of the academic debates from which it emerged. There are two distinct but related threads. First is the locality debate in (particularly British) economic and regional geography in the 1980s, sparked by Duncan and Savage (1989) and nicely covered by a special issue of Environment and Planning A (Duncan & Savage, 1991). This debate was concerned with rethinking the nature of economic regions in the context of 1980s globalization, which was implicated in the rapid deindustrialization of regions of the United Kingdom. The extent to which regions could no longer—if they ever could—be usefully understood as relatively bounded, somewhat independent economic spaces was central to the debate, and arguments revolved around how to think about regions differently. The locality emerged as a more nebulous concept that didn’t carry the same baggage of boundedness as the region, or of being taken as given via some arbitrary administrative division of space. There were few clear attempts to define locality, however. Perhaps the most concise is those social relations which provide the material base for ‘everyday life’ in a particular place; local relations through which repeated social interaction occurs and that thus allow people to become attached to and identify with a particular place (Chouinard, 1989, p. 52).

Massey was very much involved in these debates (1991c, 1995) although nowhere does she really define the term either, and she often used it in formulations like “region/place/locality.” In any case, the global sense of place seems clearly to draw on the appeal made by notions of locality to a more porous and relational conception of the region, albeit without place having the same, relatively fixed urban scale implied for localities. Second, and a more proximate prompt to Massey’s thinking on a global sense of place, is her response to David Harvey’s The Condition of Postmodernity (1989). There, Harvey argued that the postmodern or poststructural turn in contemporary social science and political economy

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was a consequence of the unsettling ways in which globalizing capitalism was reshaping geographical space. Poststructuralism denies that any one grand theory or metanarrative can explain the world, but Harvey suggested this was a consequence of an accelerating global capitalism compressing space-time in ever more urgent pursuit of profit. Furthermore, Harvey argued that not to recognize this underlying driver and to retreat into the comforting certainties of identity, which he ties to localisms such as place, was (and is) inherently reactionary and conservative. There is much to argue with in Harvey’s book, not least its dubious positions on feminism (Deutsche, 1991; Massey, 1991b). The global sense of place argument is clearly aimed at Harvey also, given the prominence accorded space-time compression and fragmentation of place in the opening paragraphs of the paper (see also Massey, 1991c). From the perspective of thinking on place, it is important to resist a temptation to retreat into a simple dichotomy between a relational space of connections and flows “out there” (or even “up there”), contrasted with more localized concrete concerns grounded (or even stuck) in place. This can easily lead to glibly contrasting abstract and globalized space with concrete and local place, and it is this tendency which Massey is arguing against. She reiterates the danger in later work: One cannot seriously posit space as the outside of place as lived, or simply equate ‘the everyday’ with the local. If we really think space relationally, then it is the sum of all our connections, and in that sense utterly grounded, and those connections may go round the world (2005, p. 185).

Evading this danger is central to Massey’s paean to Kilburn High Road. Harvey (1989) frequently counterposes global, dynamic, restless space with local, static notions of place, and the latter is portrayed as tied to reactionary politics clinging to tradition and exclusion, what Sheppard succinctly refers to as “the conservative parochialism of place-based imaginations” (2006, p. 127). Driving home her point, Massey (1991c) directly counters that there is nothing inevitably reactionary about placebased politics. Ultimately her argument, reiterated much later, “is not that place is not concrete, grounded, real, lived etc. etc. It is that space is

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too” (Massey, 2005, p. 185). Thirty or more years ago these arguments were urgent. In the 2020s amid a global pandemic and accelerating climate change, with national debates in much of the world dominated by reactionary, nativist politics, they feel urgent still. Massey’s (1991a) recourse to a rich, subjective narrative as the best way to talk about place is itself interesting, and aligns well with arguments made by Entrikin14 that narrative is necessary to understanding place, because it can “incorporate elements of both objective and subjective reality without collapsing [. . . ] the two views” (1991, pp. 25–26). Entrikin’s point is that places exist both in virtue of their being subjectively experienced and objectively present in the world as distinctive settings different from other places. This betweenness demands that we take seriously both the subjective and objective character of places if we really want to understand them. Narrative approaches allow geographers “to draw together agents and structures, intentions and circumstances, the general and the particular, and at the same time seek to explain causally” (1991, p. 25), something that it can be difficult to do in other ways.15

PLACE IN GISCIENCE This emphasis on narrative in relation to place is superficially troubling for geography, because it might suggest that history trumps geography, although this would be an overly hasty conclusion because it radically underestimates how bound up with one another are time and space (see Chapter 7). More pragmatically, emphasizing plot over setting might be seen as challenging the primacy of the map as geography’s story-telling device of choice. It also presents an even more serious challenge for giscience which is heavily committed to maps. A GIS-centric counter to the importance of narrative accounts of place might argue that the layering together of different aspects of a study area is a process of synthesis 14But

see also Sayer (1989).

15 If you doubt the power of narrative explanation, I recommend The Wire TV show (Simon,

2002–2008) as a primer on postindustrial urban geography in general and Baltimore around the turn of the millennium in particular.

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that can give an overall picture of a place. But Entrikin hints at the problem with this argument when he suggests that “[a]s one proceeds toward a decentered, theoretical view, place dissolves into its component parts” (1991, p. 24), a casualty of Haraway’s god trick (1988). The GIS problem is actually in some ways the opposite! The layers sit on top of or alongside one another; they are unrelated to one another except incidentally through shared location. They do not combine to form a complex, interlocking, and holistic representation of a place. If one layer is removed, it is simply gone, and the remaining layers are unaffected. Current platforms organized around a logic of thematic layers unavoidably dissolve places into component parts.16 Whatever the merits of narrative synthesis relative to GIS or maps or atlases, the dual subjective–objective character of place helps explain why giscientists have struggled with the concept. Most often the struggle manifests as a frustration with the elusiveness of a definition: The concept of place has a long history in geography and related disciplines, but has been plagued by a fundamental vagueness of definition: what, exactly, does the term mean? (Goodchild, 2011, p. 21)

Space by contrast offers a clear (if disputed, limited, and partial!) definition at least in its absolute guise (see Chapter 2). Absolute space may not be conceptually adequate to geography, but it is certainly implementable, and sometimes even useful. Even given a widely agreed, unambiguous definition of place, the nature of the concept—its betweenness—would make it difficult to formalize, so that it could be computed with as readily as can locational coordinates. Rather than tackle head-on the challenge of formalizing the subtleties of place, giscientists have tended to sidestep the issue and focus instead on limited interpretations of the meaning of place that are amenable to formalization, and therefore computation. Goodchild (2011) effectively

16This

is a setting where graph databases (see §Graph Databases, Chapter 2) as an alternative foundation for geospatial platforms might open up richer possibilities.

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focuses on just two: place-as-location and place-as-context.17 We consider these below, along with other more platial approaches in giscience. The more ambitious agenda of such approaches is well covered in recent, more fruitful discussion of the prospects for taking place seriously in giscience (Purves & Derungs, 2015; Hamzei et al., 2020; Mocnik, 2022), although the stumbling blocks highlighted by Goodchild remain the prevalent response.

Place as Vague Location: Gazetteers As Mocnik notes, “Geographical Information Science scholars [. . . ] tend to use the term ‘place’ even when, in fact, they presume a paradigm similar to the one assumed for Geometrical Space” (2022, p. 798). Inevitably given this propensity, the troublesome thing about place in much of giscience is that a place is not a simple location: Whatever we choose to include in the definition, one of the strongest challenges of this place concept for data modellers [. . . ] is the lack of precise locations, crisp boundaries and single universal names for many places that people talk about in everyday life (Davies et al., 2009, p. 175).

Street addressing (discussed earlier in this chapter) is about providing humans with more legible ways to talk about location, often using place names. The challenge of place that giscientists have directed most attention to is the inverse one of translating human ways of talking about location—place names or toponyms—into geographical coordinates, because capturing the human cognitive notion of place is considered crucial for smooth communication between human users and computer-based geographic assistance systems (Winter & Freksa, 2012, p. 31).

17There

are five subsections in the article, but the first three, “Ambiguities,” “Digital Gazetteers,” and “Volunteered Geographic Information,” all concern place as vague location, while the fifth, “Place as Spatial Concept,” is not fleshed out.

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This is in danger of completely missing the point that London is not at all the same thing as its Wikipedia coordinates 51°30′ 26′′ N 0°7′ 39′′ W. Often, solutions to this problem are not so naïve as to assume that a location refers to a point location, but may return a polygon area representing an administrative boundary or approximate area of interest. In any case, the gazetteer problem of translating from toponyms to locations (somehow defined) is technically challenging and of some interest, even if it does not adequately address the concept of place. Toponyms can be vague in a variety of ways. First, many toponyms occur numerous times across different settings. For example, there are 35 proper places called Springfield in the United States—Virginia alone has two.18 There are a great many more not-really-proper places going by the name Springfield that a geocoder could possibly return (and will return if you really insist on it—see Figure 4.3). Many of these are shops, cafés, or even private residences that have a name in addition to, or instead of a street number. In any particular context it will probably be obvious to a human which Springfield they are interested in, but much less so from a computing perspective, and this is one challenge in the realm of place-as-location. For some toponyms the most likely place being queried might be a shrewd guess almost every time—for example, there are many Londons, but it is likely that London, the capital of the United Kingdom, is the topic of interest most of the time. The priority among other repeated toponyms is less obvious: None of the Springfields in the United States is particularly large, so even narrowing the search to those may not help much. At the time of writing, if I search for Springfield on Google Maps, I get the one in Aotearoa New Zealand, an example of my current geographical context being used to narrow the search. A second source of vagueness in toponyms relates more closely to the nebulous nature of places, discussed in the previous section. Most obviously, place names often refer to geographical features that cannot be sensibly narrowed down to a singular point in absolute space. The 18This

is apparently why Springfield was chosen as the everytown name in The Simpsons. If it had been further located in a fictional Washington County (of which there are 32), that would have nicely added to the confusion, albeit at the risk of being a bit too specific, since there is a Springfield in Washington County, Kentucky.

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Figure 4.3. The 514 Springfields returned by the nominatim geocoder at https://nominatim.openstreetmap.org at the time of writing (August 2022). In addition to the many settlements called Springfield in the United States, there are many streets, street addresses (i.e., residences), neighborhoods and even some cafés called Springfield. The large number of Springfields in Europe are branches of a Spanish clothing store.

Rockies, The Urals, the Desert Road (in Aotearoa New Zealand), and the Midlands are all places, but it is not easy to pin their locations down to a point. Even so, most of the time, a search engine will put a pin on a map in response to a place name query—see Figure 4.4. In one case a polygon area is associated with a road, although the Desert Road shares with Route 66 the sense of it being a place more than a mere road, so this is not entirely unreasonable. In general, this is a difficult problem—one with which a human would also struggle! The map pin in Figure 4.4a has presumably been somehow derived from an area designated as the Rockies, but how exactly that area is defined is not obvious. This mirrors the challenge of something as seemingly straightforward as deciding if a mountain exists (Smith & Mark, 2003) and if so where is its summit (or summits). A slightly frivolous example of the latter problem is the classification of “Munros” in Scotland, mountains above 3,000 feet in height, where some peaks above that height are considered insufficiently

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Figure 4.4. Google maps of four vague places mentioned in the text: (a) the Rockies, (b) the Urals, (c) the Desert Road, and (d) the Midlands. Only the last of these does not get a map pin or other delineation.

far from another peak, and are classified not as Munros but as Munro Tops. Uncertainty about the extent of things is equally applicable to more mundane places like urban neighborhoods (see Figure 4.2). We revisit the question of delineating boundaries in Chapter 5. Yet another source of toponymic confusion is arriving at consensus on the correct name for places. The names of many places are disputed, reflecting contested histories. Even when names appear uncontroversial, there are often long histories of naming and renaming. Paying attention to these often sheds light on the multiple meanings of a place. To take a locally relevant example, that there are many places around the world called Wellington is a consequence of the rapid colonial expansion of the British Empire in the decades after the 1st Duke of Wellington’s victory over Napoleon at Waterloo. I grew up in a street called

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Waterloo Park in Belfast, a city whose name is a colonial Anglicization of the Gaelic Béal Feirste meaning “mouth of the Farset,” the river on which the original settlement was established. Back in Aotearoa, across the Cook Strait (Te Moana-o-Raukawa) and Marlborough Sounds from Wellington, is the Marlborough region, and the town of Nelson—all three named for British imperialists of varying significance. Further south in Te Waipounamu or Te Waka a-M¯aui—much more satisfying M¯aori names than the geographically banal South Island—Cook also has Aotearoa’s tallest peak named for him, although the M¯aori name Aoraki is increasingly used, and the mountain’s official name is Aoraki/Mt Cook. More toponymic gymnastics are to be found farther ¯ south where Dunedin (Otepoti) is an Anglicization of the Scottish Gaelic Dùn Èideann (Edinburgh). Back in Wellington, in addition to its older English name Port Nicholson (yet another imperial luminary), there are at least three possible M¯aori names: Te Whanganui-a-Tara (a name for the harbor), P¯oneke (a transliteration of the early English name), and Te Upoko o te Ikaa-M¯aui. The last of these means “the head of the fish of M¯aui” which relates to the M¯aori name for the—yawn—North Island, Te Ika-a-M¯aui, “the fish of M¯aui.” Meanwhile, I am writing in a neighborhood, Brooklyn, which has a Central Park, and several streets named for American presidents (Lincoln, Washington, Cleveland, Garfield, McKinley, Taft, Jefferson). To add to the polyglot toponymic riches, Wellington’s hippest street is Cuba Street, named for one of the first colonial settler ships, which by word association has spawned a coffee roaster and restaurant called Havana, and a bar called Fidel’s (there is also a music venue on Cuba called San Fran). In short, toponyms are complicated and often surprising. They also matter a great deal and are much more than mere labels (see Figure 4.5). As much or even more so than drawing lines on maps (see §Drawing Lines, Chapter 5), naming a place asserts at a minimum connection, but often ownership or authority—power—over that place (Berg & Kearns, 1996; Eades, 2017; Madden, 2018; Giraut & Houssay-Holzschuch, 2022). The names that are used for places therefore matter a great deal, and are more than accidental. Thus, while a concern for accurately

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Figure 4.5. Toponyms in Aotearoa that include at least one word probably in ¯ language. The greater density of Maori ¯ names on Te Ika-a-Maui ¯ (on the Maori the left) reflects both greater settlement of that island before European colo¯ nization and continuous Maori presence. Based on a map in We Are Here (McDowall & Denee, 2019), resources available here: https://github.com/ fogonwater/we-are-here/ including place names from Toitu¯ Te Whenua – Land ¯ Information New Zealand and Te Hiku Media’s’ Nga-kupu tools to identify ¯ Maori words in text, from https://github.com/TeHikuMedia/nga-kupu.

geolocating a named place is not unexpected from a technical perspective in giscience, and also not unimportant from a practical perspective, it misses the possibilities in names—especially toponyms—as geographical data that might be informative of the complex cultural geographies of place. Some of the potential of toponyms for helping us grasp the meanings of places and draw out their connections is explored in tools like Frankenplace (Adams et al., 2015).

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Place as Geographical Context One perspective in giscience that might be considered platial is the uncertain geographical context problem (UGCoP, see Kwan, 2012). The UGCoP refers to the difficulty of knowing with certainty the relevant geographical context affecting outcomes in a given study. Geographical context is a catch-all term for the total set of impacts from the surroundings which might affect (usually) social outcomes for different people. The idea emerges most obviously when researchers seek to understand environmental effects on health outcomes, but might equally apply to any work on neighborhood effects (Sampson et al., 2002). Taking geographical context seriously immediately reveals the inadequacy of simplistic notions of coincidence in space as a way of understanding what it means for things to interact in place. For example, in studies that attempt to link urban design to physical exercise and as a result to health outcomes, it is necessary to somehow define for each subject in the study population what is the environment understood as affecting their behavior. Often this has been done by considering the statistical area (such as a census tract) where each subject lives, and somehow associating with that area relevant factors, like the amount of green space, access to public transport, road density, and so on. This effectively assumes that the activity space of individuals resident in each census tract is confined to the census tract itself, which will only rarely be the case, and furthermore that the census tract is somehow sealed off from everywhere else in the wider region. In reality, depending on personal circumstances (age, employment, and so on), a resident of a particular census tract may stay close to home most of the time when the tract might be a reasonable proxy for their activity space, or they might be there only when they are asleep, and range widely across the city or region they live in for work, education, leisure, and other activities. This means that there is great uncertainty around any study of environmental effects on people’s behavior, and it is unclear that any fixed definition of the neighborhood of an individual is valid (Black & Macinko, 2008), or what the effects of choosing different definitions might be on findings (see, e.g., Mavoa et al., 2019). Other approaches using GPS tracking may yield more useful data

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as proxies of the activity spaces of individuals, although these methods have their own challenges (see Mavoa et al., 2018). There is no simple way to resolve the UGCoP short of careful attention to study design, the collection of much more detailed information about individual behavior and life histories (which may raise their own concerns about privacy), and more careful interpretation of research findings. For now, it is notable that geographical context depends on individual movement over time (possibly extending to lifetimes), which again points to the importance of human experience and properly representing time for a comprehensive understanding of place.

Place and Meaning Much of giscientists’ engagement with the notion of place at a level beyond geolocating toponyms revolves around how meaning can be associated with geographical data. The ambiguity and relational fluidity that attaches to place per se is not attached to the cartographic representation of place, which generally remains wedded to the simple locations of points and polygons (Payne, 2017). There has been only limited cartographic work exploring how to map ill-defined areas associated with toponyms (but see Brindley et al., 2018). Most energy has been devoted to working with new attributes—or new kinds of attributes—in the object-attribute tuple, while the geographical objects themselves remain the familiar points or areas in standard spatial relational databases. This often involves adding data such as photographs, sounds, user comments, hyperlinks, and so on to more or less conventional spatial data. An excellent overview of the thinking behind these approaches is provided by Purves and Derungs (2015) who echoing Goodchild (2011) bemoan the elusive nature of place, but pragmatically settle on three concepts emphasized by Agnew (2011) : location, locale, and sense of place. These refer, respectively, to specific locations in (absolute) space; to kinds of place (such as home, work, forest, and so on) which might not be fixed in space; and to feelings of attachment or belonging (or not) relative to meaningful places. The last of these is closely related to the ideas of Tuan (1977) and Massey (1991a), while this threefold notion of place also

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closely mirrors theoretical ideas about where queries in information theory (Shatford, 1986). Purves and Derungs therefore adopt this threefold definition as “a basic framework to move beyond the much criticized, and still predominant, reduction of place to a name and a set of coordinates” (2015, p. 77). Taking this approach, Purves and Derungs then explore how a query like “Mountains in the Alps” “contains both location(s) and locale(s) [. . . ] and its meaning is modified according to the individual who posed it, thus incorporating notions of sense of place” (2015, p. 78). This involves first noting the vagueness of “mountain” (see Smith & Mark, 2003) and the ambiguity of “Alps”—Europe or New Zealand? A specific mountain range or high-altitude pastureland?—before going on to five case studies that variously explore: the use of digital data to delineate vernacular regions; drawing maps from historical records; mapping vague locales (like mountains); georeferencing texts; and linking locations and locales. In setting out this agenda, of central importance is the introduction of novel sources of digital data about geography, particularly volunteered geographic information (or VGI; see Elwood, 2008; Goodchild, 2007) and sources being developed in the digital humanities, particularly digitized historical records. That these approaches have “the potential to facilitate the transformation of GIScience from a space to a place based science” (Purves & Derungs, 2015, p. 79) is the optimistic claim. Work along the lines represented by the five case studies can be found in contexts other than “Mountains in the Alps.” Delineating vernacular regions involves searching sources for references to places and associated supposed locations, and then somehow combining those locations to map where the regions are. This is closely related to work on mapping neighborhoods (Brindley et al., 2018), but might also include mapping ill-defined regions like the Midlands, the Highlands, or the Cotswolds (Jones et al., 2008), and areas like the “downtown” of a city (Hollenstein & Purves, 2010). This work, at least in its general intention, updates much earlier examples (see e.g., Hale, 1971; Zelinsky, 1980). On a technical level, the work typically involves assembling collections of point or polygon data tagged with various toponyms or descriptors, then using a

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method such as kernel density estimation to produce probabilistic maps of how those toponyms relate to location in a conventional map view. Broadly similar approaches are applicable to mapping places in historical texts and other sources (Cooper & Gregory, 2011), to mapping the locations associated with locale place words like hill, bar, downtown, and so on (McKenzie & Adams, 2017), and to delineating urban areas with particular word associations (Curtis et al., 2016). Important in many of these examples is the notion of a geotag. Geotags are most often social media data that have been tagged with a location, either if tracking is enabled in the relevant app or with hashtags that include platial information such as a place name. More broadly speaking, any text-based descriptive terms that have been, or can be, geolocated in some way, can be considered geotags, so that the concept can be extended to include data extracted from text. Contemporary digital media yield vast amounts of geographically located data of diverse types. In addition to more well understood data types, images, video, and audio are collected on a large scale, often via social media platforms. Large amounts of text of various kinds are also collected by the same platforms. Often, audio, video, and so on also have associated descriptive tags, whether added by humans or automatically generated. For researchers interested in the texture of places these data present interesting possibilities that go beyond more conventional sources like government censuses of the population. They also often emphasize the activities that can occur at particular places, relating in this way both to Cresswell’s arguments about place and to Purves and Derungs’s (2015) emphasis on locale as particular kinds of place. This idea is central to arguments for the importance of affordances—the activities a place can potentially accommodate—to prospects for moving beyond place as a gazetteer problem (Scheider & Janowicz, 2014), and instead thinking of platial reference systems as capable of identifying locations where specific activities might be possible. In a recurring theme, such affordances usually vary through time, often in more or less regular ways, pointing again to the importance of thinking about place in space-time, not merely as ill-defined location.

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Place in Mind: Cognitive Maps An earlier tradition in quantitative geography that is closely related to recent developments in the mapping of geotags is cognitive mapping (Downs & Stea, 1973; Gould & White, 1974). An important aspect of work in this tradition is finding ways to present the metric inconsistencies of individuals’ and groups’ mental representations of geography in map-like displays. The kinds of metric inconsistency that arise in perceptions of space are that it is farther from location P to location Q than the return trip from Q to P, that a sequence of places P, Q, and R are linearly aligned even when they are not, or that streets in the urban fabric of a city meet at right angles and are arranged in a grid when they are not (see Figure 4.6). Taken together, such mismatches between a metrically accurate map of an area and the maps in mind that people may hold of that area make it natural to ask if maps can be made that reflect those mismatches, and thus provide a truer picture of the area. An important inspiration for this approach is Kevin Lynch’s The Image of the City (1960), which included sketch maps of a number of cities based on interviews with residents.

Figure 4.6. Three distortions of metric space that often occur in cognitive maps. (a) Distance from P to Q is not the same as from Q to P, (b) unaligned features are aligned, and (c) a kink in a grid is ignored, often leading to confusion. The last example is based on my own experience of a particular part of Wellington’s streets refusing to resolve itself in my head over several years!

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The sketch maps included elements that are held to contribute to the imageability or legibility of a city, that quality [. . . ] which gives it a high probability of evoking a strong image in any given observer. It is that shape, color, or arrangement which facilitates the making of vividly identified, powerfully structured, highly useful mental images of the environment (1960, p. 9).

Lynch identified several categories of elements of a city image—paths, edges, districts, nodes, and landmarks—which together structure the overall understanding of a city formed by people living, working, visiting, and moving within it. He argues that carefully managing these elements and how they relate to one another can enable urban planners to design cities that are more livable. Interestingly he relates the problems of designing cities to their scale: “the city is a construction in space, but one of vast scale, a thing perceived only in the course of long spans of time” (1960, p. 1). Cities then, are environmental in their scale (see Figure 3.3), and as places are experienced through time. The importance of landmarks in Lynch’s scheme was taken up in cognitive mapping by using multidimensional scaling (MDS) methods to place known anchor points in urban spaces based on their perceived separation distances, and developing bespoke distorted maps from the MDS results (Couclelis et al., 1987). More recent work describes ways to apply Lynch’s approach (Banai, 1999), and to improve automated directions using aspects of his analysis (Winter et al., 2008). The prospects for automating urban image analysis computationally (Filomena et al., 2019) appear promising, offering the prospect of more qualitative approaches to mapping urban places. Tellingly, the resulting representation of an urban place requires several GIS layers: of points (nodes and landmarks), lines (paths and edges), and surfaces (districts with uncertain boundaries), and it is only the combination of all of them that can be considered an adequate (if approximate) representation of the place. Given the underlying perceptual basis of such analysis, it seems likely that the same open-ended and multiple representation would be required for any place, urban or otherwise.

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TOWARD COMPUTABLE PLACE? Place, then, is complicated! Unlike some approaches to space, the concept resists any neat mathematical formalization given its entanglements with power, culture, meaning, experience, and time. There is little doubt that giscientists will continue to improve the capability of information systems to interpret natural language queries about named places and locales. It is much less clear what such developments are likely to add to geographers’ tool-kits. The platial questions Mocnik (2022, Table 1, p. 16) suggests might distinguish strong platial information systems from weak ones are those pertaining to the internal properties of places, rather than to their interrelations (whether spatial, quantitative, or qualitative). This seems a rather circular argument, since it immediately prompts questions about what the intrinsic internal properties of a particular place might be, and how we might know what they are. A strong platial information system under this definition sounds like it might be close to a more generalized information system capable of responding to open-ended queries about the nature of anything, spatial, platial, or otherwise! It is good to be ambitious, but more modest attempts to handle place computationally might also lead in interesting directions. The first step is to consciously incorporate narrative elements into our representations, something that even static maps, given careful design, can already do (Caquard & Cartwright, 2014; Mocnik & Fairbairn, 2018). It is interesting to contrast the synthesis performed by layering in a GIS, with the related but very different experiences offered readers of thematic maps and atlases. In the map “They Would Not Take Me There,” “the authors reimagine historical cartography for the representation of place rather than space by taking a narrative approach to cartographic language” (Pearce & Hermann, 2010, 32, emphasis added). They accomplish both within the main map by carefully directing the readers’ attention to follow particular sequences and by layering on additional sidebars, information panels, and so on. This is certainly more than a single map, but it is telling that taking a narrative approach demands more than merely adding more geospatial layers. Labeling in general and detailed annotation in

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particular, both central to Pearce and Hermann’s cartography, could be much better supported in geospatial platforms and might make such narrative cartography (a little) easier. Thematic atlases like London: The Information Capital (Cheshire & Uberti, 2014) or We Are Here (McDowall & Denee, 2019) also depart from the GIS template. Map spreads are at different scales, on different themes, and with few exceptions each may include several layers carefully combined to tell some aspect of the overall story of their subject place. While many of the maps share layers in common, it is the particular combinations of layers across multiple maps that combine to present stories of these places. Perhaps most instructive of all is Denis Wood’s Everything Sings (2010a) which portrays his home suburb of Boylan Heights in Raleigh, North Carolina. Here all the maps share a base map, yet the base map is never shown, only the single theme of interest on each map. The effect of leafing through these maps is a cumulative account of the place, where mere location—which the base map would emphasize—becomes irrelevant. By forcing the reader to attend to each theme, rather than visually combining them, paradoxically a more complete picture of the place emerges. Recent developments in story mapping,19 where a narrative implying a preferred reading order takes precedence over recognizable map elements, make rich annotation much easier. Platforms supporting story maps have developed rapidly from little more than putting time-lines on a (usually) interactive base map (see Caquard & Cartwright, 2014) to the inclusion and linking of various media such as images, audio, and video. Story maps remain wedded to conventional absolute models of space, even though, as Caquard and Dimitrovas argue, [g]enerally, space (and even time) is neither Cartesian, nor continuous in narratives. It varies due to the fluid structure of events,

19Not

to be confused with mapping or diagramming the concepts in a narrative, more often referred to as semantic mapping. See, for example, Reutzel (1985), or, for visualizing literature and literary history, Moretti (2007).

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descriptions, memories, and the imaginary. Maps and stories simply do not have the same geography (2017, para. 2).

Given that taking place seriously points to considering space as relational, this may be a significant limitation of story mapping approaches, or indeed of more conventional maps and atlases. More experimental approaches to narrative cartographies of place explicitly recognize this problem (Knowles et al., 2015; Caquard et al., 2022) and even advocate abandoning geospatial platforms or remaking them to escape or “loosen” the Newtonian grid (Westerveld & Knowles, 2021). A second approach, as in the examples of work on Lynch’s image analysis, would be to attempt direct implementations of particular perspectives on place. Pointers toward some facets of place that might be implementable are provided in a structured literature review by Hamzei et al. (2020). An example of a detailed framework relating space and place to nature, social relations, and culture is set out in Homo Geographicus (Sack, 1997). This framework is undoubtedly wrong (of course it is!) with its particular quirks and omissions, but Euclidean/Newtonian absolute space is also wrong, and computational representations of that framework have proved fruitful, if limiting. Sack’s framework also includes an iconographic symbol system that might help make an implementation navigable. Or again, Massey’s relationally embedded global sense of place appears a promising candidate for formalization, but has attracted only limited attention in the giscience literature. Capineri’s “Kilburn High Road revisited” (2016) is an exception that (seemingly inevitably) showcases a reliance on geolocated social media data. The framework adopted to inform this work is again Agnew’s (2011) tripartite location-localesense of place model. What seems absent relative to Massey’s account is the global sense with which the original paper is so deeply imbued. This may reflect the limitations of social media data, which are the everyday thoughts of people passing through the place, not the reflections of a professor of geography.20 Taking Massey’s perspective more fully to 20Ironically,

the data used in the study are collected by a corporation in California, far removed from north-west London, and in that sense global!

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heart would require that the perspective be able to shift from the everyday and local to a more distanced global perspective linking Kilburn High Road to other places elsewhere. This brings us back to whether place and space should be thought of as somehow opposed: place as the local, concrete, and particular; space as the global, abstract, and general. The binary is attractive, but [t]he couplets local/global and place/space do not map on to that of concrete/abstract. The global is just as concrete as is the local place. If space is really to be thought relationally then it is no more than the sum of our relations and interconnections, and the lack of them; it too is utterly ‘concrete’ (Massey, 2005, p. 184).

Or, as we saw, a little further on, the “argument is not that place is not concrete, grounded, real, lived etc. etc. It is that space is too” (2005, p. 185). The local and immediate feels more concrete, because it is often visible, right there in front of us. But more remote events are no less real, even if they seem that way. Vast global events like pandemics and climate change can seem surreal—and are often described as such—but have tangible, concrete effects that play out in many places all at once. So the space–place binary can be a helpful tool for thinking with, but it is probably more helpful in the long run to recognize that they reflect different experiential aspects of complex and dynamic realities.

Chapter

Lines and Areas utting lines on a map is an exercise of power with consequences for the areas they delineate. We have already seen the complicated relationship between the delineation of areas on a map and concepts of where different places are (see Chapter 4). Conceptually places do not depend for their existence on being well-defined: It is not a problem if they are ambiguous. By contrast, the intention behind drawing lines on maps is to claim that some spatial entity—whether a country, administrative subdivision, parcel of land, or whatever—is unambiguously defined as existing within the bounds marked. Often such claims are contested and problematic. This is obviously so in the political realm, but may also be true when lines are drawn that supposedly indicate changes in land cover, vegetation, geology, or habitat, and so on. In these cases the contestation may be over knowledge claims rather than political per se. Either way, drawing lines on maps, delineating areas, is inherently an exercise of authority, political, scientific or of some other kind. The line is a claim about the world, resting on the authority of whoever drew it, and that authority is then passed on through maps or in data. In this chapter we examine some implications of taking seriously this perspective on lines on maps and in data. As elsewhere, we consider relevant debates in geographical theory and also aspects of work in

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giscience where lines—more precisely, the polygons they delineate—are more complicated than they appear. While the patently fictional abstraction of the infinitesimal, simple point location passes almost without comment in giscience, problems with polygons are more widely appreciated, even if the implications of the difference between bona fide and fiat boundaries are rarely followed through. Many of these problems are understood to be merely technical in nature, as in the case of the modifiable areal unit problem, and regionalization, both of which we consider. As we shall see, all these giscience concepts relate directly to the deeper philosophical and political questions raised by critical cartography and political geography.

DRAWING LINES: THE ORIGINARY POWER OF MAPS The Map and the State Denis Wood argues in Rethinking the Power of Maps1 that maps did not exist in their recognizable modern form until the advent of the modern state: “People create maps only when their social relations call for them, and the social relations that most insistently call for maps are those of the modern state” (2010b, p. 19). He firmly rejects the idea that maps are representations of the world, because of how this naturalizes map making and map use. Maps in the modern sense have always been about power and the exercise of authority. They set out who has authority over what, and in which places that authority attains. At the same time, they call some places into existence, by naming them and locating them, and also erase other places and their names by omitting them completely. Maps are thus quintessentially platial, both insofar as they define places out of thin air, and also designate what is permitted or not in the places so created (see Chapter 4).

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Rethinking the Power of Maps is a substantially rewritten edition of The Power of Maps (Wood, 1992), “as in hindsight I would wish to have written it” (Wood, 2010b, p. 10).

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In place of the idea of maps as representations, Wood offers this definition: maps are more or less permanent, more or less graphic artifacts that support the descriptive function in human discourse that links territory to other things, advancing in this way the interests of those making (or controlling the making) of the maps (2010b, p. 20).

While this avoids using “representation,” the term “descriptive function in human discourse” enters in its place and does much of the same work.2 The suggestion is that maps are graphical tabulations of those other things that pertain to particular pieces of territory. There is a foreshadowing here of the geoatom, or at any rate of the geometric entity in a geospatial data table, although this is hardly surprising given the close ties of GIS to cartography. I am comfortable with the idea that representation (for some actors in some contexts) remains a function of maps and I don’t think there is an urgent need to make the argument against the idea that maps are representations so absolute. Wood’s vehemence is because maps become powerful when we unquestioningly accept that they simply represent reality. Power relations like land ownership—which often did not exist before they were mapped—are legitimized by the authority of maps, making them even harder to challenge. The conclusion surely is that maps are not simple or natural representations of an uncomplicated, unmediated real world out there, so much as they are representations of power relations. They are representations all the same, even if what they represent is not what we might naïvely assume. Wood’s definition does use the word territory, a far from simple concept, which we look at more closely below. For now, following Delaney, it is enough to recognize that “[t]erritorial configurations are not simply cultural artifacts. They are political achievements” (2005, p. 12), and that maps are crucial to their achievement. Indeed, a claim that maps are central in regulating power relations is unremarkable if we are concerned with the boundaries of national or subnational territories, or with 2

Andrews (1996) finds in an analysis of over 300 definitions of the word map that representation looms large, so successfully avoiding using it in a definition is no mean feat!

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cadastral maps showing land parcels and their ownership. But even maps that are not explicitly about power, suggests Wood (2010b), project power in a variety of ways. Along with many others, he argues that the map is not only an instrument for the operation of state control, it was essential to the construction of the modern state as we understand it in the first place (Buisseret, 1992; Edney, 1997; Pickles, 2004; Carroll, 2006; Branch, 2014). States are abstract things compared to the everyday places in which people go about their everyday lives. Maps and map making have made and continue to make the abstract notion of a nation-state real. They assert the existence of a thing that is otherwise hard to grasp still less submit to or feel allegiance to. “It’s almost as though it were the map that in a graphic performance of statehood conjured the state as such into existence” (Wood, 2010b, p. 32), or, as Branch puts it, “forms of authority not depicted in maps were undermined and eventually eliminated, while map-based authority claims became hegemonic” (2014, p. 6) in the process of modern state formation. In fulfilling this function, the most important feature of the map is how the territory of a state is defined by boundaries. This is why drawing lines on maps is so central to the idea of the state and of cartography. Drawing on Winichakul (1994), Wood suggests that “[s]tate borders are brought into being through mapping, both by the imperative to be mapped and through the medium of mapping” (2010b, p. 32). Maps were and are active agents in processes of state formation. In the present, maps—and by extension GIS—remain central to the maintenance of state power and property rights, while also having a more mundane part to play in the management of state and corporate functions from rubbish collection to the delivery of healthcare and education.

New Lines and Countermapping Maps and GIS are definitively instruments of the state and other powerful interests, but they can potentially also advance opposing interests, albeit often at the cost of accepting underlying assumptions about land, ownership, and power embodied by maps. In a groundbreaking paper, Nancy Peluso suggests that “maps can be used to pose alternatives to the

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languages and images of power and become a medium of empowerment or protest” (1995, p. 387), labeling such efforts countermapping. However, she also argues that [t]he practical effect is far-reaching: the use of maps and a highly ‘territorialized’ strategy redefines and reinvents customary claims to standing forest resources and harvestable products as claims to the land itself (1995, p. 384).

and that mapping almost forces the reinterpretation of customary rights to resources territorially, thereby changing both the claim and the representation of it from rights in trees, wildlife, or forest products to rights in land (1995, p. 388).

When state or corporate usurpation of customary rights is countered through mapping, it is difficult for those making countermaps not to assert similar rights to those claimed by the usurpers, even when the previous relation to land was not one of ownership, but one of stewardship or a pattern of recurrent use over time. Crucially, a cartographic language for depicting such contingent relations between people, land, and places remains elusive. More nuanced depictions of the complexity of customary rights might also struggle in any case for political or legal recognition in a world of maps depicting crisp lines and the polygons they enclose. Branch’s (2014) argument about the hegemony of mapbased claims applies with equal force to counterclaims, so that the path of least resistance is often to accept the terms on which maps operate, and enter into the territorial relation to the world depicted in maps. Although Peluso’s reservations are rarely far from view (see, e.g., Hodgson & Schroeder, 2002), countermapping and its cousins participatory GIS and community mapping are vibrant fields (Mukherjee, 2015). In many cases, Peluso’s concerns have been well-founded. Referring to several countermapping projects in the Americas, Bryan and Wood claim that [i]n every case, [counter]mapping provided a means of nominally recognizing indigenous peoples’ rights, while at the same time

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assimilating them into a territorial order whose lines were codified by the law (2015, p. 97).

That the projects they are considering were funded through the U.S. Agency for International Development (USAID) and related organizations helps to account for such depressing outcomes. Not everyone is so pessimistic about the possibilities, and more genuinely bottom-up community-led projects are less likely to be co-opted by state and corporate interests. Reflecting on lessons from countermapping, Dalton and Stallmann point to “the importance of a critical approach [and] the conceptual and practical importance of participation not only in data collection, but also in analysis” (2018, p. 100). Similar conclusions have been drawn in more community engagement-oriented contexts, where capitalist property rights are already fully embedded, a description that often characterizes projects under the participatory GIS umbrella (Elwood, 2006). The important lesson from all these domains is the emphasis placed on the importance not of maps as end-products (although these clearly do also matter), but on the processes of community involvement (who maps), data collection (what is mapped), and analysis (what kinds of maps are made). From the perspective of this book’s overarching argument that giscience should engage geographical thought, the latter of these challenges, what is mapped and how, pushes us to think more deeply about the different kinds of representations we could make by moving beyond standard geospatial architectures.

TERRITORY AND TERRITORIALITY The notion of territory embedded in the previous discussion is so bound up with the emergence of the modern state that it is difficult to think of a state separate from some defined area of Earth’s surface over which it has exclusive sovereignty. Stuart Elden suggests that territory has been paid insufficient attention in political geography because

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territory is often assumed to be self-evident in meaning,3 allowing the study of its particular manifestations—territorial disputes, the territory of specific countries, etc.—without theoretical reflection on ‘territory’ itself. Where it is defined, territory is either assumed to be a relation that can be understood as an outcome of territoriality, or simply as a bounded space (Elden, 2010, p. 800).

Territoriality, in turn, is a concept that demands careful thought. One approach understands it as almost biological in character, an extension into the human sphere of animal territoriality (see Storey, 2012, 14–18, for a useful review). A second approach is more nuanced, recognizing that human territoriality is social, but tends to treat it as ahistoric (Sack, 1986). But in both cases, Elden argues, territory remains underexplored and assumed to be self-evident. He goes on to sketch, drawing on ideas in a short book by Soja (1971), what a more complete understanding of territory would look like, suggesting that it demands consideration of land, terrain, and territory. These, respectively, revolve around questions of resources and property relations; power, competition and (military) control; and cooperation and social organization. An understanding of territory therefore requires an understanding of land and terrain, and also that territory “is both of these, and more than these” (Elden, 2010, p. 804). Building on these foundations, in The Birth of Territory, Elden (2013) develops a history of the emergence of territory as a concept in Western political thought. This requires tracing developments in philosophy, law, and politics, but also, significantly, scientific thinking about space, including debates around the absolute or relative nature of space (see “The Geometry of the Political” in Elden, 2013, pp. 290–98). Absolute space triumphed over relative space in the scientific and political realms, even if in the latter context this manifests relationally: Sovereignty, then, is exercised over territory: territory is that over which sovereignty is exercised (2013, p. 329).

3

Wood’s (2010b) definition of maps, quoted previously, is guilty in this regard.

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Elden concludes that “[t]he idea of a territory as a bounded space under the control of a group of people, usually a state, is therefore historically produced” (2013, p. 322). Territory is a “bundle of political technologies” that “comprises techniques for measuring land and controlling terrain” (2013, pp. 322–23). Those techniques are not restricted to maps and mapping, but clearly include them.4 A number of historical geographical accounts show how the concept of territory was rolled out in different settings, and confirm the significant role of mapping and surveying in each case (see, e.g., Edney, 1997; Hannah, 2000; Carroll, 2006). A key reference point for many such accounts is James Scott’s Seeing Like a State, which posits “legibility as a central problem in statecraft” (1998, p. 2). The state is centrally concerned with ordering and recording all that it governs—people, land, resources, and so on—a process that demands the kinds of simplification exemplified by a cadastral map, which “does not merely describe a system of land tenure; it creates such a system through its ability to give its categories the force of law” (1998, p. 3). The organization of land surveys was of central importance to the development of the Irish colonial state (Carroll, 2006), and of the United States (Hannah, 2000). Edney’s more explicitly cartographic history of the construction of British India (1997) also highlights the importance of mapping. These are colonial settings, but, Scott also contends, modern statecraft is largely a project of internal colonization [. . . ] [t]he builders of the modern nation-state do not merely describe, observe, and map; they strive to shape a people and landscape that will fit their techniques of observation (1998, p. 82).

We considered aspects of these processes of making the governed (land and people) legible in relation to how address systems and toponyms make ambiguous places legible for various purposes (see §Making Space 4

It is interesting that while territory is bounded land, the world-ocean is sometimes thought to be ungovernable, beyond territorial control (Steinberg, 2009), in part because the ocean can’t be marked out in the same way, and is so obviously in constant flux (but see Havice, 2018).

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Legible: Addressing the World, Chapter 4). In delineating areas, mapping goes beyond merely labeling ambiguous places to defining the places themselves, as specific bounded territories subject to various legal, political, and social arrangements. If space becomes place through experience, then places become territory through mapping.

Escaping the Territorial Trap These historical accounts of territory open up ways to escape from what John Agnew (1994) called “the territorial trap.” The trap he has in mind is the overly simplistic mode of thinking where states are understood as exercising sovereignty over an unambiguously delineated region of space. Furthermore, the boundary of the state’s territory neatly distinguishes its domestic and foreign affairs. Finally, this model posits territories as discrete containers for their societies. Agnew’s critique is aimed principally at international relations rather than at geography, although Alison Mountz (2013) suggests that he was writing at a time when political geography was in abeyance, in part because of these moribund spatial concepts. Mountz’s survey suggests that the simplifications of the territorial trap have been superseded by more recent work in political geography. She argues that such innovation is no accident but “reflects recent geographical shifts in the operation of sovereign power” (2013, p. 830), particularly with respect to “spaces of war and terror associated with the United States and its allies’ ‘war on terror’ ” (2013, p. 830). In this context, the complex sovereign status of sites like Guantánamo Bay highlights just how distant from geopolitical reality is the territorial trap. She claims that geographical thinking on scale (see Chapter 3) has been an important corrective to focusing on the nationstate, and that “most political geographers do not examine the nation state directly, but the spatial dimensions (such as locational intensity, transnational reach, and territorial limits) of sovereignty” (2013, p. 831). Mountz goes on to discuss “prison, island, sea, body, and border” (2013, p. 830) as examples of sites where sovereignty is much more complicated than can be represented by lines on maps. For example, prisons are spaces where citizenship rights of the territory are suspended. Prisons

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are usually hidden away from population centers (Simes, 2021), even as their impacts are most often sharply felt in urban communities (Gilmore, 2007). Their usual invisibility renders prisons disturbing when they are not hidden (see Davis, 1990, particularly chapter 4). The incongruity arises because prisons confront us directly as places where the usual rules are suspended.5 The rights of prisoners are curtailed, so that prisons are inherently gray areas in the territory of the state. Islands sometimes serve as prisons (Mountz, 2015),6 but more generally are also places where states experiment with different regulatory regimes, such as the tax havens of Britain’s Channel Islands, or its various Overseas Territories (most notably the Cayman Islands). Some islands, both independent states and not—for example, Singapore, Hong Kong, Malta, Cyprus, and Ireland—deploy their offshore status to apply different, often more business-friendly commercial regimes than those in force in neighboring mainland markets. The offshore model has often moved onshore in the shape of enterprise zones, themselves a kind of island within the territory of the state, where the standard commercial and employment regimes of the host state do not apply. Borders are the most obvious sites where sovereignty gets “weird” and territory becomes fuzzy. Real borders are far from simple lines crossed in a single step, even if the floor markings in airport immigration halls suggest otherwise. Airport duty-free shopping rests on legal fictions about the relationship between the space where the shops are located and the national territory.7 In many Canadian airports (also in Dublin, Ireland), it is possible to clear United States immigration and customs before boarding, meaning that travelers are already “in the United States” while still in Canada. Similarly, on disembarking in another country, you are not really in that country until after clearing immigration. Many countries require airlines to check travelers’ documentation before allowing them to board flights, and travelers whose documentation is deemed insufficient for 5 6 7

Aotearoa New Zealand’s quarantine hotels, in operation from 2020 to 2022 during the COVID pandemic, engendered similar feelings. The title of Solzhenitsyn’s The Gulag Archipelago is no accident. Duty-free retail and free trade and special economic zones are related experiments in territory; see Neveling (2020).

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entry may be deported and returned to the port of departure at the airline’s expense. Airline check-in is then the de facto first (extraterritorial) stage of the destination country’s border. Since refugees can only seek asylum in the country at the border, this extension of national boundaries offshore has serious implications. Clearly, the question of where is the border of a state’s territory is not a simple one, when immigration enforcement can potentially happen anywhere within the territory (see Stuesse & Coleman, 2014), or even beyond it. These examples highlight “the power of states to alter the relationship between geography and the law” (Mountz, 2010, p. xv), and to manipulate that relationship to the detriment of marginalized people. Border “fast lanes,” facilitated by extensive pre-screening of qualified individuals highlight how the border can even become the body (Coutin, 2010; Mountz, 2018), and provide another example of how scale is socially constructed and politically effective (Varsanyi, 2008, see also Chapter 3). They also dramatically illustrate how inadequately conventional maps embody “the descriptive function in human discourse that links territory to other things” (2010b, p. 20) in Wood’s representation-free definition.

Fiat and Bona Fide Boundaries and Objects Turning to the giscience literature, in a series of papers8 Barry Smith (1994, 1995, 2001; see also Smith & Varzi, 1997, 2000) directly addresses a question raised by the foregoing discussion, “[w]hat sorts of entities are these, which can be brought into being simply by drawing lines on a map?” (2001, p. 131) Consideration of this question yields a conceptually useful distinction between fiat and bona fide objects.9 Bona fide objects are those whose boundaries exist at some physical discontinuity or where some qualitative heterogeneity occurs, and which therefore are usually directly perceivable as things in the world. Fiat objects, on the other hand, depend for their existence on the definition of boundaries that

8 9

One of them is even called “On drawing lines on a map” (Smith, 1995). These Latin terms, respectively, mean “let it be done” and “in good faith.”

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result from “acts of human decision or fiat, to laws or political decrees, or to related human cognitive phenomena” (2001, p. 133). Administrative boundaries, national boundaries, and so on are clear examples of fiat boundaries defining fiat objects. In fact, it is unclear if any examples of genuine bona fide10 objects exist at geographical scales. Many examples that come to mind such as shorelines, forest edges, and so on, on closer consideration, are not at all clear-cut, their precise definition dependent on scientific definitions and agreement about more or less arbitrary datums. We know when we are definitely on the land, and when we are definitely at sea, but the shoreline is a zone of transition whose precise location is not obvious. It nevertheless is likely to appear as a crisp line in many geographical datasets (see, among many others, Smith & Mark, 2003; Bittner, 2011; Feng & Bittner, 2010; Bennett, 2001). Smith’s interest is primarily ontological in a metaphysical vein, and only secondarily computational, and so he is more concerned with the limits that geometry and logic place on fiat objects and their boundaries, than with the social and cultural processes that underpin the power of drawing lines on maps. Even so, some interesting points emerge from his philosophico-mathematical considerations. The boundary of a fiat object, as a Jordan curve, “must be free of gaps and must nowhere intersect itself” (Smith, 2001, p. 142). Following from this, the boundaries between fiat objects are shared, with no intervening gaps and no overlaps. In the next section we consider a few of the situations where the world fails to match this mathematical idealization, and the incongruities that can arise as a result. Also arising out of the discussion is an argument that [t]here are no (or no obvious) candidate ‘atoms’ or ‘elements’ in the geographical world from out of which geospatial fiat objects could be seen as being constructed in analogy with the way in which sets are constructed out of their members (Smith, 2001, p. 142).11 10 “Genuine

bona fide” is almost (but not quite) a tautology.

11 Smith made the same point in an earlier formulation (1995, p. 476). Again, the geoatom-

as-point-location (Goodchild et al., 2007) is called into question. Arguably the concept survives this critique, albeit reformulated, such that the most granular elements in a fiat subdivision of the landscape are (arbitrarily small) geoatomic areas.

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This is a deep, if subtle, critique of the dominant approach in giscience, where a polygon is a topological point set (Egenhofer & Franzosa, 1991). The possible relationships between two polygons understood as point sets can be enumerated in terms of the possible relations between their interiors and boundaries (see Figure 5.1). The interior and boundary require careful set-theoretic definition that need not concern us here (Egenhofer & Franzosa, 1991, pp. 164–65). The fiat/bona fide boundary distinction potentially simplifies this framework in the case of fiat objects, because a collection of fiat objects have boundaries that, by definition, cannot intersect, meaning that many of the relationships shown in Figure 5.1 cannot occur. This does not have any practical implications

Figure 5.1. The 9-intersection model of topological relations between two polygons (Egenhofer & Franzosa, 1991). The different possible relations depend on the relations of both the interior A° and boundary 𝛿 A of the polygons. Smith (2001) argues that possible relations among fiat objects are limited to being disjoint or touching.

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for GIS implementation unless applications are restricted to nonoverlapping collections of polygon layers (which might be the case for a dedicated cadastral system, for example). It points again to the importance of thinking carefully about data structures for collections of spatial objects and whether they explicitly encode spatial relationships or not (see §Prospects for Relative/Relational Giscience, Chapter 2). However, even in settings where only fiat objects exist, it is commonplace to assemble polygons in nested hierarchies (e.g., census blocks, block groups, tracts, and so on), so that at least a few more of the spatial relations between boundaries shown in Figure 5.1 might be encountered, even if it is unnecessary to test for them geometrically, given that the hierarchical nesting relations are known in advance and can be encoded in polygon IDs or lookup tables.12 These technical arguments miss larger points about the process by which boundaries and the resulting polygons were defined historically. The deeper truth which Smith is pointing to, and which fully coheres with thinking about the power of maps, is that the elements are essentially arbitrarily defined by fiat—not arbitrarily in a historical sense, but in relation to physical phenomena on the ground. Fiat objects are those whose existence is an outcome of human cognition and action, and recognition of the concept in giscience aligns well with insights from critical cartography, countermapping, and theoretical geography. State boundaries, electoral districts, school zones, ownership and other rights in land, along with other less impactful things besides (like mail delivery routes) do not exist on Earth’s surface. Where they do exist is on maps and in geospatial databases maintained and operated by corporations and government agencies. While these insights have been prominently discussed, their overall impact on implemented geographical computing platforms has been limited. GIS remains an instrument of states and corporations deploying abstractions in the form of unambiguously defined polygons and polygon coverages, which produce a “map as territory” mindset. This

12 The

computational efficiencies of this idea are an important driver of recent interest in hierarchically nested spatial indexing schemes such as Google’s S2 and Uber’s H3; see Figure 4.1.

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connection is so powerful that many countermapping efforts seem gravitationally drawn into the same modes of thought (see §New Lines and Countermapping, this chapter).

WHEN THE MAP IS AND IS NOT THE TERRITORY The ontological commitments of surveyors, cartographers, giscientists, and others notwithstanding, territory has a habit of resisting being easily mapped. The world itself—even the social and legal world—defies the simplifications of fiat boundaries. We examine some of the frictions that arise in this section. In this context the term territory stands in for all the areally extended fiat objects that giscience calls into existence when they are represented in geospatial data and manipulated computationally.

Exclaves: Territory Interruptus There are many examples of how international boundaries defy expectations that they should define national territories that are whole and undivided. One class of examples is that of enclaves and exclaves. Without getting into the details of the nomenclature, in this context, an enclave is a state entirely surrounded by the territory of one other state, while an exclave is an area of a state that constitutes an enclave inside another state, such that it is disconnected (disjoint) from its parent state. The term exclave is inherently ambiguous, since a Belgian exclave might be a part of Belgium that is an enclave in some other state, or it might be an exclave of some other state enclosed within Belgium. For now, I will use the terms enclave and exclave loosely and assume that the sense is clear from the context. Robinson defined a number of subcategories of exclave, but suggested that “[e]xclaves are not important phenomena in political geography. They are rare and mostly small” (1959, p. 283). Both Robinson and Catudal (1974) provided surveys of then extant exclaves, although more recent work suggests these were far from comprehensive (Whyte, 2002). Catudal (1974) concluded that exclaves are temporary phenomena and

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indeed, since the time of writing many exclaves in his account have been rationalized out of existence by international treaties swapping the territory in question. Undeterred, Vinokurov (2007) sets out a theory of enclaves, in part prompted by the appearance, after the dissolution of the Soviet Union, of many new enclaves (see also Berger, 2010, and the accompanying special issue articles). Vinokurov argues that life in enclaves is difficult if the states involved do not have good relations, so that political geographers ought to take these issues seriously, and not treat enclaves as mere curiosities. Life can be more than merely difficult in enclaves: According to Vinokurov (2007), numerous deaths resulted from the lawlessness and ambiguities associated with the Cooch Behar enclave complex that persisted on the India–Bangladesh border from 1947 until agreed territorial exchanges in 2015 simplified the border, leaving only one large exclave of Bangladesh connected to its mainland by the 78 m wide Tin Bigha corridor. The complexity of the geography of that area is apparent in the map in Figure 5.2, and also when we consider that before the 2015 settlement, there was one counter-counter-enclave, that is, a part of India, within Bangladesh, within India, within Bangladesh(!), along with many other doubly nested enclaves. For present purposes, what is interesting about enclaves is that while mapping them poses no particular challenges—given sufficient attention to detail—this is a case where the map both is and is not the territory. The map defines the territory in some legal sense. But experiences of such territories may be profoundly affected by how the state is maintained or (very often) not maintained in everyday practice (Shewly, 2013). The map is only the territory to the extent that it represents an ongoing process of state action, and in these liminal spaces, many functions of the state do not operate. It is worth noting also that the literature above focuses on more or less unusual enclaves, while ignoring more mundane examples like embassies and other diplomatic missions (Mamadouh et al., 2015), military bases (Davis, 2011), or the spaces in ports and airports, where which state’s territory is operative can be ambiguous to the nonexpert (Mountz, 2013).

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Figure 5.2. The enclave complex of the Cooch Behar region on the India– Bangladesh border. This sketch map is part of a map by Cyberpunk7282 CC BY-SA 3.0 available at https://commons.wikimedia.org/w/index.php?curid= 15903195. A detailed large-scale map is available in Whyte (2002).

Territory, Borders, and Movement Borders, however messy they might be, are made both to contain and to be crossed. States use borders to regulate movement of people and material (Cresswell, 2006; Mountz, 2010). As Ruth Wilson Gilmore succinctly puts it, “edges are also interfaces” (2007, p. 11). This idea finds direct expression in the geometric notion of duality where any configuration of relations can be transformed into its dual configuration. In this case the transformation is that every edge shared by two areas becomes a link connecting them (see Figure 5.3). Gilmore continues, “even while borders highlight the distinction between places, they also connect places into relationships with each other and with noncontiguous places” (2007, p. 11), but this is where the geometric duality

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Figure 5.3. The geometric dual relation between borders and crossings. Dashed white lines are borders and solid black lines are the links between neighboring areas.

analogy falls down. Areas that don’t share a boundary are not connected in planar geometry, but the same is not true of national boundaries, where it is possible to move between noncontiguous states, again calling attention to the complexity of borders and the imperfection of lines on maps as a representation of territory. Reflecting on a potentially nonobvious evolution from writing about place (Cresswell, 1996) to writing about mobility, Cresswell notes that “transgression involves displacement, the moving between in place and out of place” (2006, p. ix), again referencing this dualism. We examine movement/mobility more closely in Chapter 7.

Territory and Property: Cadastral Data Often, enclaves are a result of property rights that pre-existed the delineation of national boundaries. Cadastral maps and databases concerning land ownership have been a significant driver of GIS development (Moudon & Hubner, 2000), particularly in relation to tracking changes in ownership and the amalgamation or subdivision of land parcels over

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time (see §Cartography and Giscience’s Problem With Time, Chapter 7). The creation of cadastral maps and databases is closely bound up with processes of state formation, particularly in settler colonial contexts where appropriation and alienation of land from Indigenous peoples is central. The legacy of such mapping is particularly clear when any attempt is made to determine the present-day land entitlements of descendants of the originally dispossessed, who were often subject to arbitrary judicial determinations, documented in distant courts, based on incommensurable notions about the relation between people and land (see §New Lines and Countermapping, this chapter). Specific examples in Aotearoa New Zealand are provided by recent work unpicking such a mess (Kukutai et al., 2022). The work of Shep et al. (2021) shows how methods similar to some of those used in grappling with ambiguities of place (see §Place as Vague Location: Gazetteers, Chapter 4) can potentially be used to assist in tracing land rights granted and promised many years ago, but never fulfilled. Prominent in this work is the importance of understanding land as a complicated set of relations between parcels of land that change through time, on the one hand, and people, kinship groups, and other collectives, also changing through time, on the other.

Territory and Governance: Statistical Aggregations If maps “blossom,” as Wood (2010b, p. 15) puts it, as a consequence of the rise of the modern state, then it is also to the emergence of the state that we owe the existence of censuses and other statistical13 instruments describing populations. In much the same way that maps can be thought of as making the state, censuses make populations. Census outcomes are used as a basis for the redrawing of other maps, such as electoral maps, and for the allocation of state resources for all kinds of purposes, and as an imposition of the state, they have sometimes been opposed (Anderson & Shuttleworth, 1994; Hannah, 2009). National censuses are also frequently used as a kind of base layer for all kinds of social geographic 13The

word statistics derives from the word state.

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research. To take just one example, studies of spatial segregation of populations by race or ethnicity typically rely on census data, both for the spatial frame that is used and for the definitions of ethnicity deployed (see, e.g., Lloyd et al., 2015). The arbitrary nature of census geographies with respect to the social and demographic characteristics they record is an important technical concern much discussed in giscience, as we explore more fully in the next section. In closing this section on how the map is (or is not) the territory, census boundaries or other administrative or statistical geographies might be the geoatoms that make up the territory from the perspective of the state (or for that matter social scientists), but they are almost invisible in everyday life. They are a kind of infrastructure of governance, largely unnoticed, unless something goes wrong. As an example, in the aftermath of the Flint water crisis of 2014 to 2017, the misalignment of ZIP codes with the municipal boundaries was identified as a major reason why the emerging crisis was not identified earlier (Sadler, 2019; see also Figure 5.4). Health data were compiled in relation to ZIP code boundaries and aggregation of health statistics to these areas masked serious problems with water quality, since many of the ZIP code areas included large populations outside the municipal boundary relevant to the water infrastructure. ZIP code boundaries are designed for mail sorting and delivery with those logistical needs in mind, and are affected by things like the presence of large office buildings, or other centers of employment, and also the infrastructure of the postal system (where it has large sorting facilities and so on). They are not designed other than coincidentally, in relation to population characteristics, or in relation to any other infrastructure. Municipal boundaries, on the other hand, result from complex local, regional, and national histories of urban and industrial development, and state formation, and often embed much earlier configurations of population and land use. There is no particular reason other than convenience to collate health data using ZIP code tabulation areas.14 Even when convenience is an important consideration, and it is 14Strictly

speaking, ZIP codes are not associated with areas at all, but with address points and mail delivery routes; but area representations are widely used to make it easier to

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Figure 5.4. The misalignment of the municipal boundary of the city of Flint, Michigan (grey polygon), with the ZIP code boundaries used for collation of health data (black boundaries and numeric labels).

difficult to obtain or use more precise geospatial information, it seems that information as badly flawed as it was in this case (see also Grubesic & Matisziw, 2006) was no better than no information at all might have been.

THE ARBITRARINESS OF BOUNDARIES As with scale (see Chapter 3), the social contestation and production of boundaries and territories is not explicitly represented in any concrete way in geographical computation, but defined boundaries and the resulting spatial units can have profound effects on analytical outcomes. visualize data and perform spatial data analysis on data with associated ZIP codes (see Krieger et al., 2002).

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Choosing which areas to use in a particular context, or even designing boundaries appropriate to a particular project, is a frequently encountered challenge in giscience. Ideally, the bounded areas used in any analysis would be real—bona fide boundaries to use Smith’s term—but as we have seen, there are often really no such boundaries available, unless we are exploring specific technical questions about particular bureaucracies. So, it might make sense to work with ZIP codes if the questions at hand are about the speed of mail delivery, or with school enrollment zones if the questions are about outcomes in schools. More general questions about social, political, economic, and cultural geographies may not have any associated geographies that are fit for analytical purpose. Furthermore, there is no single list of desirable characteristics of a set of geographies that can guarantee their usefulness for a wide range of uses, although we can identify characteristics that are generally not desirable! All else equal, it is better if areas have roughly similar populations, or more generally, populations that are broadly comparable to one another. In this context, the widespread use of counties and states for mapping geographical patterns in the United States provides a good example of very bad spatial units—at least from a technical perspective. The maps in Figure 5.5, based on counties in California, give some sense of the extent of the problem. Counties are just not a comparable set of things—their wildly divergent populations are almost their defining feature. An associated problem this causes is that counties with smaller populations tend to dominate the extreme positions when we measure the rate of occurrence of anything—such as disease incidence, voter turnout, unemployment, and so on. This is because large populations will tend toward the mean rate of occurrence. These problems are particularly marked in dealing with rare events in spatial epidemiology (see chapter 5 in Cromley & McLafferty, 2012). Disentangling such artifacts of the spatial units from real effects associated with differences between rural and urban places can be challenging. Another difficulty with highly variable spatial units is that large-area, sparsely populated polygons dominate conventional maps, while densely populated areas disappear from view (see the middle panel of Figure 5.5). Cartograms offer one possible way to

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Figure 5.5. The challenge of maps when areas have very different base populations. The left-hand map shows the problem: Populations of the counties of California range from around 8,000 to almost 10,000,000. Mapping population density does not help much (middle map). Changing to a logarithmic scale (right-hand map) yields a more useful map, but also emphasizes just how different the counties are from one another.

mitigate this problem (see Figure 2.2) at the expense of less immediately accessible maps and visualizations.

The Modifiable Areal Unit Problem These challenges point to the need for careful consideration of the system of geographies to be used in particular studies, which leads directly to consideration of the modifiable areal unit problem (MAUP). It is obvious that any system of geographies (usually polygons) applied to a region and used to aggregate statistical or count data translates a set of underlying observations into a table of numbers.15 Less obvious (perhaps) is that the particular set of polygons used can alter the resulting distributions and patterns. A simple example (see Figure 5.6) suffices to demonstrate 15 Another instance of the linking of “territory to other things” of Wood (2010b)

in practice.

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Figure 5.6. Simple illustration of the modifiable areal unit problem. Two attributes (the column and row numbers of the squares) are averaged across columns and rows respectively. In each aggregation the pattern of only one of the two attributes is preserved.

the effect. This is an extreme case to demonstrate the problem, but the effect is real, and in practice much more subtle than this. Perhaps surprisingly, the effect impacts not only simple summary values of attributes, but also secondary measures like the correlations between variables. This was dramatically illustrated by Openshaw and Taylor (1979) who showed how different aggregations of smaller polygons into larger ones could lead to the apparent correlation between two variables ranging anywhere between -1 and +1. How this can happen is illustrated in Figure 5.7. Depending on whether observations that are similar or dissimilar are combined, an initial correlation can be strengthened or even changed in direction, and it is also possible for data that are not correlated at all to appear correlated after aggregation. The example in the figure is for non-spatial data. In a geographical setting, the impact of aggregating data from neighboring zones into larger agglomerations depends on the scales at which similarities and differences manifest in the data, that is on the

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Figure 5.7. How aggregating data can increase or decrease correlation. Original data are shown in the background as crosses with the associated best-fit line dotted. In the left-hand panel the original correlation for these data is 0.47. Aggregating groups of eight similar observations yields the data shown as triangles, which have a correlation of 0.92 (the dashed line), while aggregating sets of eight dissimilar observations gives the data shown as circles with a negative correlation -0.21 (the solid line). In the right-hand panel initially uncorrelated data aggregate to correlations of 0.77 and -0.55, respectively!

scale, extent, and sign of any spatial autocorrelation. This aggregation behavior in data is an instance of an ecological correlation (Robinson, 1950) and the effect was familiar long before Openshaw and Taylor’s experiments (Gehlke & Biehl, 1934). However, often finer-grained data are unavailable, and it may thus be impossible to know the degree to which observed correlations relate to effects the correlation statistics are intended to estimate. The MAUP is driven by two different effects. First is an aggregation effect, which is the ecological correlation already considered, and a clear example of a scale effect (see §Scale-dependencies, Chapter 3). Second is a zoning effect, which reflects differences that can arise aggregating data at a single level, but in different ways, by drawing different lines to delineate different sets of polygons. It is the zoning effect that was explored by Openshaw and Taylor (1979) and that is illustrated in Figure 5.6. The

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Figure 5.8. The zoning effect as a gerrymandering effect. In the left-hand panel the light gray group is in a narrow majority in four of five districts, while in the right-hand panel the result is reversed, after only a few sub-areas (hatched white) are swapped between districts.

zoning effect could equally be called the “gerrymandering effect” as it centers on how aggregate outcomes change as boundaries between zones shift (see Figure 5.8). Gerrymandering is the political process by which electoral district boundaries are manipulated to make election outcomes less uncertain for the parties involved in the design of the districts. Given accurate information about the voting preferences of populations, an effectively gerrymandered map of electoral districts is one that makes the most efficient use of the votes available to the party designing the map. This involves some combination of “packing” an opponent’s votes into large safe majorities where many of their votes are wasted, because they are not required to guarantee a win, or by “cracking” concentrations of the opponent’s voter base by splitting them across several electoral districts (see Monmonier, 2001, especially pp. 8–12). Gerrymandering can be significantly refined using GIS software. Concerns about gerrymandering, especially in the United States, have led to numerous ideas for assessing how fair a given map is. Some approaches center on assessing the efficiency of votes for different parties,

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that is, how many votes each party had to accrue per elected representative. If one party has to stack up more votes than the other to win seats, then perhaps it points to deliberately biased design of districts. Other approaches focus on the shape of districts, suggesting that extremely convoluted district boundaries are an indicator of deliberate, and by implication, bad intention in the design of districts, and that fair districts would have less convoluted, substantially convex shapes. Many of these approaches seem naïve at best. If the desired outcome is that the numbers of elected representatives be proportional to the votes cast for each party, then proportional voting systems are guaranteed to achieve that outcome. What the MAUP tells us is that outcomes in first-past-thepost representative systems inevitably depend on where, by whom, and how the electoral lines are drawn. Meanwhile, it is unclear what would constitute fair design of electoral districts, a question unavoidably entangled with the question of what constitutes a community of interest, which is the legal notion (in the United States) that has become relevant to these questions (Morrill, 1987; Forest, 2004). Given the strong negative connotations of the term gerrymander, it is worth noting that the design of zoning systems can also aim to achieve equitable outcomes. An example, current in the 2010s, is the middle school zones of Berkeley, California, shown in Figure 5.9. This is related to a suggestion made by Openshaw that the MAUP is not so much an insoluble problem but rather a powerful analytical tool ideally suited for probing the structure of areal data sets. The growing speed of computers opens up the tremendous potential offered by heuristic solution procedures, such as the AZP [automating zoning procedure], to identify the most appropriate zoning systems for any particular purpose (1983, p. 38).

In other words, instead of treating the MAUP as an inconvenience, consider it an opportunity to get a better understanding of the geography of a study area by partitioning it in ways appropriate to the topic at hand. Openshaw (1983) also described an outline AZP drawing on earlier work (Openshaw, 1977), and some of these ideas were taken up in designing flexible output geographies for census data (Openshaw & Rao, 1995;

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Figure 5.9. The (approximate) middle school enrollment zones in Berkeley, California, c. 2015. Each zone spans neighborhoods across levels of the socio-economic hierarchy in the city. They are an attempt to mix school populations on that basis.

Martin, 1998). More recently, perhaps following the development of efficient algorithms for partitioning networks (see §Connection, Disconnection, and Communities, Chapter 6), these ideas have resurfaced (see, e.g., Poorthuis, 2018).

Regionalizing Space The inversion of the MAUP into a problem of zone design leads directly to the question of how we can partition a region into meaningful

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subregions for some purpose. Given the primacy of the region as a central concept in geography at various times (see Chapter 7), how to regionalize space has been a consistently prominent question. In this context, regions have generally been considered to be areas with shared characteristics across a range of aspects—economic, cultural, biophysical, ecological, and so on—with the emphasis on different aspects varying depending on the interests and inclinations of particular researchers. For example, Zelinsky (1980) presents vernacular regions of the United States based on the appearance of various toponyms in the names of enterprises (for profit and nonprofit)—work that has much in common with recent efforts at mapping vernacular or otherwise ill-defined places. In addition to the density mapping discussed in relation to that work (see §Place and Meaning, Chapter 4), statistical clustering (or classification) methods are a possible approach to regionalization. These methods partition a set of observations into groups called clusters. A cluster is a set whose members are similar to one another and different from observations in other clusters. The difference between two observations is measured by combining the differences between the values of each attribute for the two observations. For example, if observation x has attribute values x1 , x2 , . . . xn and observation y has attribute values y1 , y2 , . . . yn , then a Euclidean difference measure would be v t n ∑︁ |xi − yi | 2 d(x, y) = i=1

Alternatively, the difference could be based on the sum of the absolute differences between attributes (the Manhattan distance) d(x, y) =

n ∑︁

|xi − yi |

i=1

These two options are both Minkowski distance metrics ! 1/m n ∑︁ m |xi − yi | d(x, y) = i=1

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with m set to 2 and 1, respectively. Any of a wide range of alternative distance metrics can also be used (Deza & Deza, 2016). Differences between every pair of observations are somehow determined, and then observations can be combined into clusters by a variety of procedures. The simplest approach, k-means, selects k initial seeds as cluster centers, and assigns observations to the cluster whose center is closest (i.e., most similar), then recalculates the cluster center, and iterates until cluster assignments stop changing. Agglomerative methods start by pairing the nearest pair of observations, then recalculating the difference between the newly formed cluster of two members and all other observations. Clusters continue to agglomerate in this way until all observations are in single cluster with hierarchical structure, based on the order in which observations were merged. Many other algorithms for clustering data are available (see Hennig et al., 2016). Applied to spatial data, clustering analysis can produce candidate regionalizations, which will vary depending on stochasticity and parameter choices in the algorithm used, and—hopefully, more importantly—on the choice of attributes included in the process. A simple demographic example is shown in Figure 5.10. The important point here is the subjective nature of any regionalization arrived at by such methods. The definition of a cluster ends up being a set of observations identified as a cluster by a clustering technique in a particular context (Hennig, 2015) ! Similarly, there is no generally applicable definition of similarity and difference. Instead, what is meant by similar and different is determined in the context of particular data and a particular clustering method. These circular definitions are fine given the exploratory nature of clustering as a method, but are worth keeping in mind before taking the results of a particular analysis too seriously as truth. A less often noted weakness is that these approaches treat the spatial units in the analysis as independent of one another, which is open to question given relational understandings of space and place (see Chapter 2). Closely related community detection methods from network science may partially address this concern (see §Connection, Disconnection, and Communities, Chapter 6). Regardless of these criticisms, the continued influence of Chicago School urban analysis is testament

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Figure 5.10. A possible regionalization of the San Francisco Bay Area based on demographic variables, such as age, household size, ethnic composition, income, education, and so on. Data available at https://github.com/ lucguillemot/bayareageodemo although this clustering is a simple k -means result with k set to 5, rather than the more complex hierarchical approach presented in that work. Areas with no data are hatched.

to the usefulness of these approaches (Sampson, 2012), when applied with care. An area where these cautions could be taken more seriously is geodemographic analysis (Singleton & Spielman, 2013). Geodemographic analysis is nothing more than the clustering approaches described above, albeit at much larger scale, and using more extensive datasets than those employed to make the example in Figure 5.10. Commercial products in this area often emphasize the large number of attributes used in the analysis, although beyond (say) a couple of dozen variables, it is questionable how much discriminatory value extra variables add. They also develop fine-grained classifications of dozens, even hundreds, of

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market segments.16 Beyond such technical concerns, and reflecting on the discussion of drawing lines on maps earlier in this chapter, the question arises of the extent to which the use of such classification schemes produce and reproduce the different kinds of neighborhood they purport to represent. If commercial, political, and increasingly state action (Longley, 2005) are influenced by such classifications, then to what extent do the resulting actions produce or reinforce the classifications over time? Such concerns are not only relevant to commercial, closed implementations, but also to ostensibly preferable open versions (Vickers & Rees, 2007; Singleton & Longley, 2009). It is also important to recognize that such questions can equally be asked of classifications of biophysical landscapes. The Land Environments of New Zealand (LENZ) classification (Leathwick et al., 2002) was originally developed to support biodiversity conservation by means of a detailed classification of all land in Aotearoa New Zealand based on 15 biophysical variables, pertaining to climate, landform, soil, and so on. A questionable aspect of LENZ, or any classification like it, is that as already noted it treats each location (in this case each 25 m pixel) as independent of every other, with no concept of their relational structure. Given the importance of flows of energy, water, nutrients, and so on through landscape, this limitation should be kept in mind. Returning to the issue central to this chapter, it is notable that among the potential applications of LENZ listed on its website17 is “optimising the management of productive land uses, including locating optimal sites for particular crops or cultivars,” which could easily run counter to LENZ’s original purpose, and is certainly likely to reshape land over time, in another instance of the map potentially making the territory (see, for example Watt et al., 2010).

16These

are often amusingly—or disturbingly—given catchy names like “American Royalty,” “Birkenstocks and Beemers,” or “Urban Survivors.” These labels are from Experian’s Mosaic USA classification (Experian, 2015). 17See https://www.landcareresearch.co.nz/tools-and-resources/mapping/lenz/.

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MOVING ON FROM GEOMETRY Lines and the polygons that they delineate are a much less convenient giscience abstraction than simple point locations. However, unlike point locations, polygons in a GIS or on a map directly represent things in the world. In fact, they often do much more than represent a thing in the world, they actually are that thing, legally and politically. A line in a geospatial database often has precedence over any physical manifestation of the corresponding boundary on the ground. If a property owner builds a fence that lays claim to more land than is associated with that parcel in a cadastral database, the line on the map is likely to take precedence over the fence in any legal dispute. This inversion of the map-territory relationship—the map is the territory, it makes the territory—is to a large extent accepted in both geographical theory and in giscience. Geographers recognize that maps make places, and it is recognized in giscience that many (if not all) lines on maps are fiat objects, that is, “acts of human decision” (Smith, 2001, p. 133). An alternative approach to the fundamentals of geospatial computing follows from the view that fiat objects are the proper geoatoms on which geospatial data structures should be built. This approach is grounded in mereology, the philosophical study of part-whole relations, the topology of part-whole relations mereotopology, and mathematical treatments of these (Simons, 1987). In giscience discussion of how naïve geography concepts (Egenhofer & Mark, 1995), such as near, far, in front of, around, and so on, might be represented and reasoned with computationally is where these ideas have seen most uptake and interest. An alternative to standard GIS’s foundational 9-intersection model for spatial relations between topological point sets (see Figure 5.1) is provided by qualitative spatial reasoning (Cohn & Renz, 2008). For example, Worboys and Duckham (2021) show how qualitative reasoning about the relations among the Voronoi regions associated with spatial entities (see §The Voronoi Model of Space, Chapter 2) might enable automated descriptions of complex spatial arrangements more meaningful than those offered by the 9-intersection model. Stell discusses these ideas in relation to how space as it is experienced might be

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represented computationally, arguing that “qualitative relations can be used computationally as abstractions from quantitative data instead of being seen as an alternative and separate representation” (2017, para. 7). We touch on these ideas again in discussing time and process (see Chapters 7 and 8). Stell (2017) sets out the relevance of these discussions to the present context in discussing how boundaries cannot be coherently handled by point set topologies. Where two spatial entities touch, if our geoatom is an infinitesimal point, then it is impossible to say to which of the two entities a point arbitrarily close to the boundary belongs. This might sound like (literal) philosophical hairsplitting, but it also arises in practical geospatial work in dealing with spatial relations between geometries (very) near one another as a result of imprecision in floating point calculations. Often, the only workaround is to enforce arbitrary precision on calculations, which in effect makes the geoatom not a point, but a tiny pixel and introduces myriad other inconsistencies. In the present context of dealing with lines, boundaries, polygons, and their relations, such problems reflect the dual nature of boundaries, which contain and connect areas (see Figure 5.3). This highlights (again) the importance to any coherent understanding of geographical space of relations, which are the focus of the next chapter.

Chapter

Relations, Networks, Flows n spite of their evident limitations in the face of a much messier reality, fixed dimensionless points in absolute space (see Chapter 2), or bounded regions and areas defined by crisp lines on a map (see Chapter 5), remain the dominant spatial representations in giscience. Those limitations make clear the need to consider other perspectives. Earlier chapters have touched on some of these, particularly when we recognize the relational, contingent, and uncertain nature of the objects and processes under consideration by geographers. More far-reaching even than this insistence on the importance of the relations between and among places, things, and processes, is a broader notion of relationality, which argues that concepts, spatial or not, can only be defined in relation to one another. In spatial terms there can be no “inside” without an “outside,” no “here” without a “there,” no “core” without a “periphery,” and so on. A relational understanding of the world expands this concept beyond the spatial to any definition of anything. Things are defined not only by what they are, but by what they are not. The relations between a thing and all the things it is not are as definitive of the thing as any enumerated list of characteristic attributes of the thing in itself. In their most extreme forms, relational ontologies argue that everything is relational: There are no objects or things as such, only

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bundles of relations to other things—which are also bundles of relations, and so on. . . (see Ladyman & Ross, 2007). However, this position seems hard to sustain in practical terms: If there are only relations, what are they relations between? We are in danger here of reducing the world to an undifferentiated mush of relations, with no “there” there onto which our attention can be easily directed (Briceño & Mumford, 2016). Like it or not, real or not, we seem to need concrete thing-like abstractions (we return to this argument in Chapter 8). A more viable position seems to be that depending on our purpose, the world can be understood in terms of objects and their relations, at a variety of scales, with the relations being at least as important to any understanding of the world as the objects. Which objects we recognize and how we consider them to be related to one another will depend on the particular interests we have in the context under investigation. In a paper reflecting on a long career in academic (quantitative) geography, Peter Gould advocates this kind of pragmatic approach: So we start with the idea that this strange no-thing [space] is structured by other things, which we relate in various ways to each other, and which we measure as various distances to each other as the fancy takes us according to our purpose of utility, curiosity or ambition (1997, p. 128).1

Thus, objects exist, but the relations between them are equally or perhaps even more important, and each of these sets of relations may constitute a kind of space that can be explored, visualized, and analyzed, in its own terms. There is an interesting contrast to be drawn here between this perspective and the perhaps more familiar first law of geography which posits that “everything is related to everything else, but near things are more related than distant things” (Tobler, 1970, p. 236). Everything may well be related to everything else, but depending on what we are interested in, there is no catch-all geographical filter of nearness that determines what is relevant: Rather, what matters is our “purpose 1

This passage is one I was tempted to quote in several places while writing this book, particularly back in Chapter 2.

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of utility, curiosity or ambition.” That our understanding of what exists in the world—our ontology—depends intimately on what we are doing, and how we are trying to understand the world—our epistemology—is a perspective that giscience struggles to accommodate, and is a theme that recurs throughout this book, especially in these later chapters where we consider concepts that grapple with the interconnected and dynamic nature of the world. In this chapter, we examine some approaches consonant with Gould’s position, namely network science. This is a setting where geographers made early contributions (Kansky, 1963; Haggett & Chorley, 1969), although these have long since been overshadowed by the work of mathematicians, physicists, and others (Newman, 2018) as network-flavored ways of seeing the world have become ubiquitous (Watts, 2003; Barabási, 2014; Christakis & Fowler, 2011). To what extent these approaches adequately represent relational spaces and places is open to question, a topic we consider at the end of this chapter.2 It is important to keep this in mind while considering the limitations and potential of network science in relation to geographical theory. Also, for this reason, in this chapter, we spend more time on giscience adjacent approaches, with less emphasis on conceptual work in geography, as much of that ground has been covered in earlier chapters.

RELATIONS, SPACE, AND PLACE In Chapter 2 (see especially §Relational Space) we saw how geographers have generally come to understand space not as a neutral empty container within which objects are located, but as a system of relations among things. Similarly, in the discussion of place in Chapter 4 we noted the 2

Even in its own terms, network science is only one possible approach to analyzing systems of relations among collections of things, and it is important to note that others have been prominent (albeit briefly) at various times in quantitative geography. For example, Qanalysis (Atkin, 1974, 1981; Beaumont & Gatrell, 1982) was flavor of the month for a time in the 1970s only to quickly fall out of favor when its close relation to well-established clustering methods was pointed out by Sally MacGill (1984).

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importance of understanding both internal relations in places and relationships among places. Taking these together, we can only make sense of places through their relations to other places. In this perspective, space itself is more a system of relations among places than it is a thing in itself. This relatively static notion of the relationality of more or less fixed objects in a structural web of interconnection has, for many, been superseded by process-relational perspectives where objects are somewhat fixed permanences that arise out of interactions among processes (see Chapter 8). Nevertheless, regardless of one’s position on the nature of space and place, an approach that treats the relations among things as on a par with the things themselves holds promise for geographical inquiry. The essential step here is to elevate relations among things to equal ontological status with the things themselves. The standard model in giscience—whether raster or vector based—considers a set of spatial elements (pixels, points, lines, polygons) with attributes and only coincidental relations to one another. In Chapter 2 we noted a range of ways in which this model has been, or is being, extended to include various kinds of relations (see §Space in Giscience). Network approaches require that in addition to a collection of independent elements, we consider the relations among them. It is convenient here to use mathematical notation to appreciate the difference this makes. A conventional data table in giscience can be considered as a simple set S of n distinct spatial elements si , or, expressed in mathematical notation: S = {s1 , s2 , . . . sn } = {si } Associated with each element in S there may be a long list of attributes that, taken together, describe the element in its own terms. To take a common example, if S is the set of buildings in an urban area, then each may have an associated list of attributes such as the area of their footprint, the number of floors, details of ownership, and so on. What a conventional GIS data table is not easily able to include is information about the relations (spatial or otherwise) among the buildings.

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A network perspective recognizes two sets of entities: the things themselves (here denoted S) and the relationships between them, say R, where each relation ri j is some pairwise relationship between two elements in S. So the full picture includes two sets, one of entities S, and one of the relations between them R, so that the world, W, becomes W = ⟨S, R⟩ 

= {si }, {si s j : si , s j ∈ S} Stated in words, the world W is composed of a set S of entities si , and a set R of relations si s j between pairs of entities in S. This doesn’t seem like that big of a deal, but extending what we recognize as existing to include pairwise relations among things is a farreaching change. In the case of buildings in an urban area, depending on what we are interested in, the relevant relations might be relatively trivial spatial ones such as “are neighbors,” or more complex ones such as “is owned by the same corporation.” Either of these relations could be derived from the original single-set representation, but remains hidden from direct view when the primary representation is a table of individuated buildings. Having added relations to the picture, instead of a building being a thing in itself, it is also now a place with relations to other buildings, places, and things. Further, when explicitly represented as a set of relations among elements in the form of a network or graph, a wide range of methods for visualization and analysis are available to examine the structure of the relations in detail.

Mathematical Graphs The pair of sets S and R introduced above are more usually denoted V and E in graph theory, the branch of mathematics concerned with what are called networks in more everyday speech. A mathematical graph (or network) G is a pair of sets V and E (see Wilson, 1996). V is the set of vertices {vi } (or nodes) and E is the set of edges {ei j } (or links). Each edge ei j in E is a pair of vertices {vi , v j } considered related in some way, so that the edges define relations among the vertices, and constitute the graph or network structure.

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This definition is of a simple graph, and leaves a few things ambiguous. For example, some definitions may allow loops where a vertex is related to itself, while other definitions do not. Similarly, some definitions allow the existence of more than one edge between any given pair of vertices, while others do not. From our perspective, more interesting variations on the theme are directed graphs where the vertices in each edge are ordered, which means that relations between vertices are directed or asymmetric,3 and weighted graphs, where edges have associated numerical weights that relate in some way to the strength of the relation between the vertices. Weighted graphs have a great deal in common with spatial weights matrices (see §Prospects for Relative/Relational Giscience, Chapter 2). Once we allow direction and weight to be associated with the edges in a graph, we are able to represent a wide range of real-world networks in some detail. For example, transport and infrastructure networks can be represented in this framework, although numerous wrinkles remain. First, while additional vertex and edge attributes are of limited mathematical interest, they may be relevant in applied settings, and can be accommodated by associating with each vertex or edge a list of attributes or properties. Second, from a topological perspective concerned only with network connectivity and structure, it may be irrelevant what precise paths the physical links of cable, fiber, pipes, railway tracks, road surface, or whatever follow. But from many practical perspectives, it may matter a great deal exactly where the edges go, and the complexities involved can be surprisingly challenging to deal with (see Fischer, 2004). Think, for instance, of the familiar example of a street network (see Figure 6.1). At a high level of abstraction, only the center lines of roads are included, and vertices in the graph are the street segment intersections (Figure 6.1a). Augmented with a little information about what level of the road hierarchy (residential street, local road, major road, state highway, and so on) each edge in the graph belongs to, such simple data can be used to automatically generate useable road maps. However, much more information is needed to support the automated generation of detailed 3

Mathematicians sometimes refer to directed edges as arcs and may change the associated notation so that the set E of edges {ei j } becomes the set A of arcs { ai j }.

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Figure 6.1. Schematic representation of possible levels of detail in a network representation of a street network: (a) shows a simple undirected graph representation, (b) includes allowed directions of travel, and (c) includes detailed information about lanes and allowed lane changes and turns.

turn-by-turn directions. In this case, a directed graph that represents allowed directions of travel on each road segment is required, and vertices become points at which a selection can be made among the available options for onward movement (Figure 6.1b). Depending on the level of detail required, this network could be augmented further so that individual stretches of vehicle lane are represented as edges, and vertices are decision points where a driver can make any one of a range of maneuvers such as lane changes, left or right turns, or perhaps even U turns (Figure 6.1c). Whereas the simple representation can be an undirected graph, the more detailed versions must necessarily be directed. It is important to note here that the relational nature of a graph means that in each of these cases, what a vertex or edge represents is inherently related to what the other represents. A vertex in the simplest case represents a street intersection, which can only really be meaningful in combination with the edges in that version of the graph, not with edges in the more detailed representations.

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Similar complexities apply to the detailed representation of any realworld network. Often, what seems at first glance to be a simple network is less amenable to straightforward representation as such than might be thought. For example, the nodes in a transit network are station stops, that is, the short periods of time when a train or bus can be boarded by a passenger at a particular time and place. In between these periods the network is not really present at that location, and it is clear that time has to be explicitly considered for an adequate representation to be built (see Chapter 7), and for transit-based accessibility to be properly understood (Farber et al., 2014). Similar challenges arise when we consider how to represent the network available to pedestrians in dense urban environments, where legal and illegal crossings of streets may be available depending on traffic, and where exactly the edges are across areas of open ground is unclear. Stepping back from the details of particular cases, a mathematical graph G = ⟨V , E⟩ can only be an approximate representation of what might be a highly complicated real-world network consisting of many entities, both material (actual physical stuff) and immaterial (protocols or rules governing behaviors and interactions). The approximate nature of a graph representation is even clearer when they are used to represent conceptual or transient connections of one kind or another, such as friendship ties in a social network, or flows of goods, materials, people, or money in (say) a trading network. Regardless of these layers of complexity, even in the simplest form, the need for two sets of entities, vertices and edges, makes for surprising complications in the computational representation of graphs. Whereas a data table with each row representing an entity and each column an attribute of the entity is the standard approach for data that treat each entity as an independent thing unto itself, there are a variety of approaches to storing graph data. Two tables, one of vertices and one of edges, each with any associated attributes, and with care taken to ensure that the cross-referencing between the identifiers of edges and vertices map on to one another is the obvious approach. But it is also possible to store only edges, since each edge includes identifying information about vertices. Such edge list approaches only work well if there is no

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relevant or interesting attribute information to be stored concerning vertices, but it is notable for drawing attention to the primacy of the edges in a graph: It is the relations among vertices rather than the vertices that are the essence of a graph representation. Another approach is an adjacency matrix, a square matrix with rows and columns corresponding to vertices, and each row-column entry recording the existence, or perhaps weight, of any edge relating the relevant vertices. A weakness of this approach is that many graphs are sparse, with only a small proportion of all the possible edges between all vertices that might be present actually present, so that many entries in the adjacency matrix are null or zero and thus redundant. In any case, there is no agreed standard approach to storing, handling, and manipulating graph data, certainly not in a giscience context. The development of graph databases (see §Graph Databases, Chapter 2) suggests that this may change, although such databases are often associated with semi-structured data rather than enforcing rigid requirements on the entities in a dataset, which may hinder uptake in bureaucratic settings where GIS is commonplace.

Relations Do Not a Network Make Once we start to approach things relationally, and think about recording both the internal or intrinsic attributes of things and their external relations to other things, it can be easy to start thinking that everything is a network. Philosophically, perhaps everything should be represented this way. But it is important also to think about the transitivity among things when considering whether to represent their relations in a graph structure. Perhaps more accurately, it is important when considering methods discussed later in this chapter to think carefully about their applicability to particular relations in a specific context, and whether pairwise relations imply the existence of network structure or not. For example, consider commuting or travel-to-work data that records the numbers of regular commutes among some set of areas (either transport analysis zones or census units). The first-order origin-destination linkages in such data can readily be recorded as a set or directed edges

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Figure 6.2. Commutes into Upper Hutt Central for work and education based on data from Statistics New Zealand.

in a graph. Such a graph can immediately yield maps of the travelto-work/study catchment of particular places (see Figure 6.2). A more interesting example showing the relations between properties owned, and where their owners reside, is found in Shelton (2018), who clearly draws inspiration from earlier work by Bunge (1971) and the Detroit Geographical Expedition and Institute (1971). However, taking either of these examples, although they can be rendered as graphs, care must be taken before assigning meaning to second-order relations. Places A and B might be connected to place C, because there are some commutes starting in A or B and ending in C, or because property owners living in A and B own land in C. What does the existence of the directed relations A → C and B → C imply for relations between A and B? The only answer, in general, is that it depends on the nature of the relations in question, and the questions we want to ask. For example, if there are large numbers of commuters in A and B who all work or study in C, then when it comes to (say) spread of a disease, this would imply a relatively high risk of infection spreading between A and

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B via workplace or school encounters at C. On the other hand, if there are also some commutes starting in C traveling to a fourth location D, then there is no particular reason to consider the second-order relations A → C → D and B → C → D given the directionality, and in this sense the set of origin–destination relationships do not necessarily constitute a network per se. With regard to the other example, of land ownership relations, we are even less likely to expect such second-order effects. Either way, the existence or not of a network is highly context-dependent. Another setting where the notion of the existence of a network arising out of a set of relations has perhaps been unhelpful is in actor-network theory (ANT). This perspective arose in the context of the social science of science, where the effects in the world of nonhuman things, such as devices, ideas (referred to as “inscriptions”), and so on are prominent (Law & Lodge, 1984). In the context of a biology lab, everything from the objects of study themselves (say viruses), to microscopes and other equipment, the published research literature, laboratory protocols, buildings, along with the scientists themselves, might act on or have effects in the world around it. Intentionally or not, this framework for how to conduct research on science, by paying close attention to the varied elements affecting how science is done, morphed into a more general ontology of social phenomena as ANT (Latour, 1987; Muniesa, 2015), where anything with effects in the world is an actant involved in relational interactions (translations) with other actants. But not long “after ANT” (Law & Hassard, 1999), leading thinkers in its development were regretting the network label suggesting that, [w]hile twenty years ago there was still some freshness in the term as a critical tool against notions as diverse as institution, society, nation-state and, more generally, any flat surface, it has lost any cutting edge (Latour, 1999, p. 15).

Law is more specific, arguing that thinking of a network “tends to limit and homogenize the character of links [. . . ] the character of possible relations, and so the character of possible entities” (1999, p. 7). Whereas researchers in this field wanted to emphasize relations, the network idea can lock in place the identity of the actors (its nodes), and

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instead of considering a distinction between actors (that act) and networks (which actors form among themselves, in order, for example, to act collectively), the ‘actor-network’ is both the ‘networkthat-acts’ and the ‘actor-that-springs-from-a-network’ (Muniesa, 2015, p. 83).

Whatever the merits of a more fluid actant-relational theory might have been, this case again shows that thinking that relations alone define a network structure may not always be helpful. ANT is an important precursor to a number of approaches considered in Chapter 8 (see especially §Related Strands in Geographical Thought). The reason why such questions matter is that many network analysis methods operate on the totality of all relations and on linked sequences of relations, and it is important to consider carefully which are relevant in different situations, and not assume that a collection of pairwise relationships implies the existence of a network structure proper. The techniques discussed in the next section are not attuned to these ontological and interpretive questions—many of them require only an adjacency matrix to work—so it is important to take such questions seriously before adopting these methods.

NETWORK SCIENCE In whatever way a graph is assembled from some geography of interest, network science (Newman, 2018) opens up a wide array of methods for understanding the resulting network structure. Interpreted spatially, as is usual in geographical contexts, the insights gleaned might shed light on the structure of the spaces in which the geographies of interest unfold. The structures revealed (if any) are static, and so not consistent with more dynamic or process-relational views on space (see Chapters 7 and 8), but may still be of interest. Following a number of previous surveys (Wassermann & Faust, 1994; Boccaletti et al., 2006; Barthélemy, 2011; Phillips et al., 2015; Andris & O’Sullivan, 2019), it is helpful to consider the analytical possibilities in network science under a number of headings—local

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properties, distance, centrality, connection (and disconnection), functional aspects, and small world effects—as we do below.

Local Properties Although the main interest in studying a graph is in uncovering overall global properties of a system, the local properties of a network may still be of interest. With respect to vertices, the edges incident at a vertex connect it to a set of neighbors in the network. The set of neighboring vertices is often referred to as its neighborhood, although this term may be taken to include the connecting edges also. A vertex may be considered part of its own neighborhood or not, depending on context, although it is more common for it not to be. The size of a vertex’s neighborhood, known as its degree, is the number of vertices it contains, or equivalently the number of edges incident on it. A preliminary evaluation of network structure may simply be concerned with identifying the vertex with the largest degree, or perhaps more holistically with the average degree of the whole system, or at a more detailed level the overall distribution of vertex degree. Is there a single dominant vertex with by far the highest degree? Or do all vertices have similar degree, with only a little variation among them? Consider, for example, a network based on scheduled air connections between airports. Whether all airports have similar numbers of flights or only one or two dominate will have important implications for how sequences of connecting flights through the network are routed. Networks with only one or two large hubs of high degree may be more vulnerable to disruption— because one of those large hubs is out of action—than less-hierarchical networks with many medium-sized hubs. Closely related to the degree of a vertex is the question of how interconnected are its neighbors. The most useful measure of this property is the vertex clustering coefficient, which is the proportion of all possible edges between neighbors of a vertex that do exist, relative to the number that could possibly exist (Watts & Strogatz, 1998). A vertex with, say, five neighbors could have anywhere between no edges among those five neighbors, and 10 edges, if all were mutually connected. The former case

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Figure 6.3. Clustering coefficient of a vertex, shown increasing from top left to bottom right from 0 to 1, when successively more edges connecting neighbors of the central vertex are added from none to the maximum, in this case of 10. Potential edges connecting vertices are shown in light gray. The change in local structure from starlike to a dense knot of connections is apparent.

would be a star arrangement of vertices and the latter a dense local knot of connections (see Figure 6.3). An alternative way of thinking about the clustering coefficient is as a local edge density. This is a measure that can be calculated for a graph as a whole in the same way, that is, as the actual number of edges in the graph expressed as a fraction of all possible edges in the graph. Most graphs are relatively sparse because the number of possible edges increases with the square of the number of vertices, whereas in real-world systems it is likely that the number of connections will grow at a similar rate to the number of vertices, that is, linearly. So, for example, if one graph of a particular kind of system (say an electrical power grid) has 10 times as many vertices as another, it is unlikely that the larger graph will have 100 times as many edges, which would be required for the two to be of similar overall density.4 On the other hand, it is always possible for graph density measured locally at particular vertices to remain high. 4

In planar graphs, which loosely speaking are graphs that can be drawn on a sheet of paper without any edges crossing one another, it can be shown that the number of edges e, the number of vertices v, and the number of facets the graph edges divide the space into f , are related according to the equation e = v + f + 2. This places further restrictions on how dense a planar graph can be, and is often applicable (at least approximately) to real-world infrastructure networks. See Andris & O’Sullivan (2019) for more detail on this feature of planar graphs, which was proven by Leonhard Euler in the 18th century.

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Network Distance and Path Lengths The connections in a network promote or hinder movement between locations (i.e., nodes). If edges indicate the presence of a connection between two nodes, then sequences of edges in the network can be chained together, forming a path between any two nodes. Formally, a path is a sequence of nodes v1 , v2 , v3 , . . . visited in turn by traversing the connecting edges e12 , e23 , . . ., and the path length is some total accumulated along those edges. In the simplest case path length is determined just by counting the number of edges in the path. In an airline network this would be the number of flights in an itinerary. If some weight is associated with each edge in the path, then these can be summed to give the path length. If weights are the lengths of edges in either distance or travel time, then path lengths will reflect total distance or time taken to get from the first to the last vertex of the path. For any pair of vertices in a network there may be many possible paths connecting them. In the example shown in Figure 6.4, three possible paths between vertex A and vertex B are shown (there are many

Figure 6.4. Three possible paths in a network from vertex A to vertex B. The shortest path in terms of the number of edges in this example is the path of only four edges shown in a heavy black line, compared to two others also shown in black, each of which has five edges.

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more possibilities). Among all the possible paths, some will be the shortest, depending on how we measure their length, by counting the number of edges, or based on accumulating some edge weight. In the illustrated example, the path marked in the thickest black line is shortest based on counting the number of edges. It is difficult, effectively impossible, once a graph gets beyond a relatively small size to enumerate all the possible paths between vertices because their number becomes exponentially large.5 This would make it difficult to find the shortest path between two vertices, if it was necessary to first find all paths, but fortunately reliable algorithms have been developed to find the shortest path between specified vertices (Hart et al., 1968), or alternatively to find all the shortest paths between every possible pair of vertices (Dijkstra, 1959; Floyd, 1962; Warshall, 1962), and these have been widely implemented. Determining all shortest paths in large graphs can still be computationally challenging, but in general shortest path is a solved problem. This is the basis for a vast number of locationbased applications which rely on routing algorithms to optimize pickup and delivery times across a range of services. In broader network science terms, the shortest paths are an important starting point for many other structural analyses, particularly those focused on evaluating centrality.

Centrality To the extent that any graph represents a system of relations through which flows pass—of people, goods, money, information, and so on— the question naturally arises of which locations are most central to those flows. Where in the graph are the most critical vertices and edges? This 5

Counting how many paths there are between two vertices in a graph is hard because there are so many of them. In a graph with n vertices where every vertex is connected to every other, that is, the complete graph of size n, the number of possible paths between Ín−2 n−2
two vertices Pn is given by k=0 k k! (see Biondi et al., 1970, and also http://oeis.org/ A000522). For graphs size n from 2 to 10 this gives us 1, 2, 5, 16, 65, 326, 1,957, 13,700, and 109,601, paths between two vertices. In other words the number of paths increases very rapidly! For example, P20 is 17,403,456,103,284,421. The numbers increase more slowly for sparser graphs, but the general nature of the problem is apparent.

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is the motivation behind a variety of ways of measuring the centrality of vertices or edges in a network. We illustrate some concepts of centrality using an example network derived from world city network data available at the Globalisation and World City Research network website,6 which is described in detail by Taylor et al. (2002). Here, we use a reduced version of the dataset by restricting attention to the 72 cities with at least one corporate headquarters or major regional office present. An edge exists between two cities if they both contain an office of the same firm. These data were collected in 2000, and so they don’t show much evidence of the rapid rise of China in recent decades. Conventional geographical views of the network are shown in Figure 6.5, where the challenge of dealing with global data of this kind is apparent. A naïve presentation of the relations among cities in Figure 6.5a on a conventional global projection shows all the network edges spanning the world as straight lines from one city to the other. Even connections that might be more correctly drawn across the Pacific Ocean (between say Australia and the west coast of North America) are drawn across the center of the map. A better approach determines the paths of these connections as geodesics on great circles, although again, projections (see Chapter 3) can impede effective visualization, as the edges are discontinuous in the projected space when they cross the dateline at ±180° longitude, as seen in Figure 6.5b. With some care this can be corrected as in Figure 6.5c. A potentially more geographically informative view is provided by Figure 6.6. There are not many edges crossing the Pacific, but they are more reasonably represented in this perspective. These difficulties of geographical visualization aside, the point of network analysis of such data is to ignore (at least to begin with) the geography. Returning to the question of network centrality, we have already seen a potential simple measure of vertex centrality, namely, degree. In general, the more edges that are incident at a vertex, the more influence it has over flows in the system. This is obvious in a case such as the network of regularly scheduled airline flights, where the most important locations 6

See https://www.lboro.ac.uk/microsites/geography/gawc/datasets/da11.html.

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Figure 6.5. The world city network derived from the data described by Taylor et al. (2002). (a) edges are straight point-to-point lines, (b) edges follow the geodesic (great circle) shortest paths between cities but projection difficulties at the dateline produce artifacts, and (c) great circle paths have been cut at the dateline to assist in the visualization.

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Figure 6.6. The world city network visualized to give a clearer sense of its geography.

are those airports that serve the largest numbers of routes. In the example network, based on vertex degree, the most central cities are London and New York ( jointly), followed by Paris, Madrid, Hong Kong, Milan, Frankfurt, Singapore, Tokyo, and Toronto. Vertex degree is a local measure—local in graph terms, not geographically, since some edges span the globe. More subtle approaches rely on the shortest path analysis discussed in the previous section. For example, one answer to the question of which city is most central is to determine which is on average closest to all other cities in the system. Given all shortest paths in the graph, closeness centrality can be readily calculated for any vertex, based on any chosen measure of edge length. Here, if we simply count the number of jumps from one city to another, the 10 most central cities are more or less unchanged, with Los Angeles replacing Toronto in the top 10. Another approach is betweenness centrality, which identifies the vertices that appear most often on the shortest paths between all pairs of vertices. More than closeness measures do, betweenness measures emphasize potential control over flows from place to place by counting how often each vertex appears on all shortest paths. Again, this doesn’t change the

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rankings much, but the change is significant: Brussels enters the top 10 in place of Toronto/Los Angeles, due to its important role in the European Union. The betweenness approach is applicable to edges in exactly the same way. While in this case the different approaches do not affect the overall picture that emerges, in general, closeness centrality depends greatly on the spatial extent and geometry of the system. In a well-connected system the most central vertices measured by closeness will often be those near the middle of the system, because they are likely to have the shortest mean path lengths to all other vertices. In more sparsely connected systems, or ones where the relevant measure of edge length is only loosely dependent on Euclidean distance, the structure of the network will often mean that the betweenness center and closeness center are different. There are many other measures available for characterizing the centrality structure of networks (see Newman, 2018, for details).

Connection, Disconnection, and Communities Centrality measures focus on how the structure of a network connects the system together. Another broad category of structural measures focuses attention more closely on how variation in the connectivity of the system leads to regions that are more strongly connected internally than they are externally to the rest of the network. The origins of network science in social network analysis have led to tightly connected subgraphs being termed communities.7 Like clusters (see §Regionalizing Space, Chapter 5), communities in network science are poorly defined and in practice a community is any subgraph in a system that is detected by a community detection algorithm. This circular definition means that it is important to understand how such algorithms work, at least in general terms. Unfortunately, this is no small task, because there are many algorithms available. Good overviews are provided by Fortunato (2010) and Fortunato and Hric (2016). 7

Another term that comes up in this context is clique, which is also derived from social network analysis.

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We can get a sense of the issues that arise by considering a popular class of algorithms developed in recent years, under the general heading of modularity maximization. Development of these algorithms was spurred by the challenge of community detection in very large graphs (Girvan & Newman, 2002; Newman & Girvan, 2004; Newman, 2004; Clauset et al., 2004). The idea is simple: A modularity statistic is defined that tells us how good a particular partition of a network into communities is (how modular it is). Modularity is based on counting the number of edges internal to communities relative to the number of edges between communities, and evaluating this with respect to what we would expect if the graph were randomly partitioned into communities of the same sizes. High modularity indicates a good partition, and algorithms are therefore focused on searching for high-modularity partitions. The problem, as is usual with graph methods, is that there are astronomically large numbers of possible partitions of even small graphs. For example, a graph with just 10 vertices can be partitioned into five communities in 45,525 different ways, while 20 vertices can be partitioned into five communities in 749 billion ways, and 30 vertices can be similarly partitioned 7.7 quintillion ways, or 7,713,000,216,608,565,075 to be exact.8 Such enormous numbers of possibilities rule out true maximization of the modularity of network partitions in practice, since it is impossible to measure the modularity of every possible partition. Instead, various heuristics can be used to progressively create a good partition. A relatively easily understood approach is described by Newman and Girvan (2004). If we start with the network under investigation and progressively remove critical connecting edges until the graph starts to break into disconnected subgraphs, these would, we assume, be good candidate partitions. We need to determine which edges are critical, and one option is to rank edges from the most central to the least central by any convenient method—betweenness centrality is a good option. We remove the most central edge, then recalculate the remaining edges’ centralities and again remove the highest-ranking edge. We repeat this process until the graph 8

These numbers are known as Stirling numbers of the second kind (see https://oeis.org/ A008277) and show up in other areas of combinatorial mathematics.

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starts to break into disconnected subgraphs. The resulting sequence of partitions can be assessed, based on the modularity statistic, to determine good candidate solutions for the original network’s community structure. The intuition is that high-betweenness edges are critical to tying together the graph into a connected whole, and removal of just a few such edges should cause it to break apart into distinct, tightly internally connected subgraphs. This is a loose sketch of one modularity-based approach, and modularity maximization algorithms are themselves just one class of approach (see Fortunato, 2010, for others).9 Community detection methods are potentially of great interest in geography. Most obviously, communities in a network can plausibly map on to much longer established concepts such as regions. A simple example is shown in Figure 6.7, where a community detection algorithm run on a network of trade flows identifies major continental blocs as distinct communities. However, smoke and mirrors are at work here—the particular partition shown turns out to be sensitive to exactly how the network is defined. Here it is based on trade flows above US$2.5 billion only, whereas sparser networks constructed with a higher threshold did not partition quite so neatly, and different community detection algorithms failed to identify the grouping shown. Less significantly, while the layout of the image was largely automatic, the choices underpinning this particular presentation were far from it. Nevertheless, this general idea underpins a recent ambitious and interesting attempt to empirically derive urban mega-regions from commuting data by Nelson and Rae. Tellingly, these authors note that it becomes clear that the dream of a regionalization based purely on statistical analysis is unviable; any division of space into unit areas will have to take into account a ‘common sense’ interpretation of the validity and cohesion of the regions resulting from an algorithmic approach (2016, pp. 16–17).

9

It is important to realize that modularity methods all face the significant challenge that different network partitions with different implications for interpretation and explanation may have similar modularity scores (see Good et al., 2010).

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Figure 6.7. World trade network partitioned into communities, denoted by different gray levels. Node locations are roughly geographical but shifted to cope with crowding in Europe. Edges are bilateral flows of more than $2.5 billion value in 2014 with widths reflecting relative scale of the flow, colored by the origin region of the flow. Data from https://correlatesofwar.org/wp-content/ uploads/COW_Trade_3.0.zip; see Barbieri et al. (2009) for details.

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Similar to statistical clustering methods that underpin geodemographic analysis (see §Regionalizing Space, Chapter 5), expert human interpretation of the results produced by such techniques is needed, if they are to be useful in geographical analysis. Other examples are provided by Farmer and Fotheringham (2011) and Guimera et al. (2005).

Functional Roles and Blockmodels The idea behind a network representation of the relations among entities is not only to capture the immediate relations among entities, but also to understand the combined effect of all the relations across all entities, both locally and at several removes. Both centrality and community detection approaches demonstrate the potential of the graph representation for revealing underlying structure in a system, and stick closely to themes familiar in geography of distance and connectivity. Network analysis methods also allow us potentially to uncover more subtle structure by identifying recurring motifs or patterns of relations. The easiest way to think of this is perhaps in terms of contrasting styles of transportation network. In a hierarchical network, some network nodes are high-level hubs with many connections to other hubs in the network, along with connections to nodes lower in the hierarchy. At lower levels in the hierarchy, nodes are connected to their peers locally, and to some lower level nodes, but to only a few of the hub nodes higher in the hierarchy. Network analysis methods can distinguish this kind of structure from more linear structures on the one hand, or from everywhere-toeverywhere flat structures on the other. Equally, it is possible to identify which nodes are hubs and which are at the ends of spokes. Measures of centrality already perform this role to some extent, as do community detection methods. A third category of structure relies on the intuition that functionally different locations in a network will exhibit different patterns of connectivity between them. One example of this idea is a stochastic blockmodel which posits the idea that the graph is composed of k different blocks or groups, and that the probability of connection between vertices in groups r and s, prs , varies based on block membership (Doreian, 2009). It is helpful to step back a little here and consider

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two extreme cases. Imagine, on the one hand, a graph that consists of two completely disconnected subgraphs, and on the other, a bipartite graph where the same two subgraphs have no internal connections, but instead vertices are connected only to vertices in the other subgraph. This contrast is illustrated in Figure 6.8a and b. The graph with distinct communities has all the connections on the main diagonal of its adjacency matrix, while the bipartite graph has all the connections off the main diagonal. A third simple example in Figure 6.8c can be classified into three blocks. The clear-cut contrasts in these simple examples are rare in practice, but in real-world networks, approximations to these kinds of structure might be observed. An adjacency matrix with strong on-diagonal groupings has a strong community structure. When off-diagonal groupings are also strong, it may be indicative of more structural or even functional aspects of the network. The example shown in Figure 6.9 features a

Figure 6.8. Contrasting structures of (a) a graph with 10 vertices in two completely connected subgraphs (or communities), (b) a graph with 10 vertices in disjoint bipartite subgraphs, and (c) a graph with two hubs and second- and third-tier nodes. The corresponding ordered adjacency matrices are shown with gray colored squares indicating connection between the corresponding vertices.

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Figure 6.9. The trade network data from Figure 6.7 with the upper panel an adjacency matrix where every flow over $2.5 billion is a black square, and row-column order is alphabetical by country name. After blockmodeling, the matrix in the lower panel is reordered and more structure emerges. The core region is the small densely connected group at top left, while two other levels in a global trade hierarchy are also apparent. Country names before and after are shown on the left- and right-hand sides, respectively.

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strongly connected set of core countries: China, France, Germany, India, Italy, Japan, Netherlands, South Korea, the United Kingdom, and the United States. A second level block includes Canada, Australia, Singapore, Russia, and Switzerland, along with 25 others. These might be considered an intermediate level. Smaller economies are included in the remaining large group of 80 or so countries. To some extent this partitioning is based on the size of the economies, although this is not the sole driver, since we have dropped the dollar value of the trade flows and replaced it with a simple binary 0 or 1 indicating if a flow of sufficient magnitude exists. Crucially while the partitioning shown in Figure 6.7 is clearly geographical, the blockmodel partitioning in Figure 6.9 exhibits aspects of function in the economic order. Again, it is important to note the significant interpretation required to make sense of this kind of analysis, and also the large number of choices that must be made to produce even a simple result like this. The computational demands of blockmodeling are substantial given the combinatorial issues already mentioned, and the methods remain less well developed than other tools for network analysis, in spite of recent progress (Peixoto, 2014; Newman & Peixoto, 2015; Karrer & Newman, 2011).

Small Worlds Another aspect of graph structure that deserves closer scrutiny is the so-called small world effect. This refers to the familiar situation when, on meeting an ostensible stranger, we discover mutual acquaintances, at which point it is obligatory to comment “small world!”10 This is one of those everyday occurrences that may or may not require explanation, depending on your take on probability. It can be shown that in a random graph of n vertices where each vertex has on average k neighbors, the expected diameter of the graph (the length of the longest shortest path between any two vertices) scales with ln n/ln k (see Newman, 2018, pp. 360–63). Roughly speaking, this is because at each step out from a vertex in such a graph the number of vertices reached increases by a factor 10A

wry grin is optional.

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k, so at x steps there are k x vertices included. When k x ≈ n, then the whole graph has been reached, giving us a radius from any vertex to the edge of the graph that scales, as stated, with ln n/ln k. If every person has (on average) 100 acquaintances (probably an underestimate), then we might expect a chain of acquaintances to reach the whole planet within around only five steps, thus accounting for the famous six degrees of separation observation, and also making the small world phenomenon of bumping into a stranger less surprising.11 Where this reasoning breaks down—making small world encounters seem unexpected—is where many acquaintanceship networks are tightly interconnected. Many of the people we know also know many of the other people we know, so the actual number of new people reached as we move outwards through a social network is not multiplied by k at each step, but by a smaller number. Seen from the perspective of tightly clustered local acquaintanceship networks, it may not be so unreasonable after all to be surprised by small world encounters. The apparent contradiction can be expressed in terms of the relationship between the global graph property of average path length, and the local property of clustering coefficients. A simple exploration of the small world phenomenon is described by Watts and Strogatz (1998). Starting from a regular lattice in one dimension, in effect a ring of vertices, randomly selected edges are broken and reconnected or rewired to randomly selected other vertices in the graph. Each rewiring potentially connects a vertex to an otherwise remote vertex on the other side of the graph, introducing shortcuts, where previously all the intervening vertices had to be visited on the shortest path. The rewiring process is illustrated in Figure 6.10. It turns out that only a few edges need to be rewired for there to be shortcuts from everywhere to everywhere else in the graph. Crucially, the local clustering coefficient of vertices remains high, but the number of degrees of separation—the diameter of the graph—rapidly becomes surprisingly small. Such small world structure enables a network to be locally dense yet still have every node be easily reached from any other. 11 When

the likely similarities of class, origin, and so on of so-called strangers in most contexts are accounted for, small world encounters begin to seem almost inevitable.

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Figure 6.10. Progressive rewiring of a one-dimensional small world graph of 50 vertices. Between each panel and the next the probability of an edge being rewired is 10%.

An example of this using a two-dimensional lattice is shown in Figure 6.11 along with a plot showing how clustering coefficient remains high while the mean path length from every vertex to every other falls rapidly. The geographical implications of this behavior are profound. They go a long way to explaining, in general terms, how many infrastructure, transport, and logistic networks—along with the accompanying social, economic, and political networks—are structured. Even so, the small world problem has not been much studied in geography (although, see Stoneham, 1977), perhaps because shortcuts are not possible in many kinds of physical network. However, taking into account combinations of multiple networks—road, highway, rail, air, telecommunications, and internet— shortcuts in real and virtual space are possible, and developing intuitions about their effects is important. One area where this seems particularly relevant is understanding the complexities of scale, not as a neatly nested hierarchy of levels, but perhaps as a complex relational structure with local coherence and global connection (see Chapter 3). The small world is an accessible example of models of network formation. The earliest such model was the random graph commonly attributed to Erdös and Rényi (1959) (but proposed in the same year by Gilbert, 1959), and used by mathematicians until relatively recently as a null model for graph structure. The mathematical simplicity of this model lends itself to analysis of basic statistical features of graphs, but has limited relevance to networks in the real world. Other useful examples of network growth models are discussed by Barthélemy (2011) and also in early work by Haggett and Chorley (1969).

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Figure 6.11. The small world rewiring process in a two-dimensional lattice. Typical graphs produced by the process are shown along the top. Empirical results showing how mean clustering coefficient and path length vary with the rewiring probably are shown in the lower plot. The large region where the two measures diverge might cause the shortest paths from place to place to be surprisingly short.

GRAPH DRAWINGS AS (POSSIBLE) PROJECTIONS This chapter has featured drawings of graphs throughout. Key to the idea of a graph is that we can render a given graph in many different ways without changing its essence, that is, the structure of the relations it represents. This is shown in Figure 6.12 where the most obvious version of the graph, in the center, has been redrawn eight different ways. To provide an orientation to the graph structure, vertices are colored according to their closeness centrality, with the most central vertices darker.

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Figure 6.12. Nine alternative redrawings of the same graph. The graph was constructed by rewiring some edges in a 20-by-20 lattice as seen in the center drawing. The layouts used are respectively (a) random, (b) circular, (c) multidimensional scaling based on the distance matrix, (d) tree, (e) radial tree, (f) distributed recursive layout (DrL; see Martin et al., 2011), (g) the Kamada and Kawai (1989), and (h) the Fruchterman and Reingold (1991) forcedirected methods. Vertex closeness centrality is colored from black (high) to white (low).

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Figure 6.13. The world city network visualized as a graph. Vertex size scales with degree and edge width with the number of corporate offices in common. Vertex positions determined by the Fruchterman–Reingold algorithm (Fruchterman & Reingold, 1991).

Different redrawings of a graph may emphasize different aspects of its structure and some algorithms rely on graph structure to determine an appropriate layout (Tutte, 1963; Di Battista et al., 1999; Jünger & Mutzel, 2004). For example, the two layouts in Figure 6.12d and e treat the graph as a tree-like hierarchy, and choose as root vertices those determined to be most central, arranging others either in a series of layers or

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circles at progressively increasing distances from the root. Other algorithms such as those which produced layouts in Figure 6.12g and h rely on the mathematics of systems of springs and masses to allow a tangle of nodes and links to settle into a stable arrangement. Another example of this approach is shown in Figure 6.13 where the world city network data from Figure 6.5 has been redrawn using such an algorithm. The details of any particular graph drawing algorithm are not relevant here, and many options are available (Di Battista et al., 1999; Tamassia, 2014). Two parallels are relevant. First, like clustering and community detection, a good drawing depends on subjective interpretations in combination with an array of algorithmic options that can provide starting points for further exploration. Second, like map projection, there is no true or correct redrawing, just a range of options that emphasize different aspects of the structure. The parallel with map projections also highlights the potential in graph drawing to rearrange the geography of a collection of spatially embedded vertices yielding what is potentially a novel map projection that recognizes relationality in space. This aligns well with arguments made by Waldo Tobler concerning map projection in geography when he argues that the purpose of “geographical and analytical cartography is the development of geographical theory” (Tobler, 2000, p. 189). As a very rough and ready example of how this might work, Figure 6.14 shows a conventional map of the road network of Santa Barbara, California. Below, the network is redrawn reflecting estimated relative travel times from a central location based on the street network structure. In principle, this redrawing could also inform the remapping of other data layers associated with this space to present a different perspective on the city’s geography (see also Sugiura, 2014).

NETWORKS ARE FLOWS FROZEN IN PLACE Networks are interesting because they represent relations between things, not things in themselves. Because the conceptual groundwork for the relevance of relational geography has been a recurring theme (see

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Figure 6.14. Santa Barbara street network and a redrawing of it based on relative travel times over the network, from a central location.

Chapters 2, 4, and 5, where the relational nature of space and place was discussed at length), this chapter has focused on networks as computational objects of inquiry in themselves. This has (at least) two side effects.

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First, the impression may be given from the examples in this chapter that giscience is farther along in engaging with networks as representations than is the case. None of the examples shown was produced using standard geospatial tools. This is because the network tools provided in standard giscience platforms do not handle networks well, except in the special case of transport networks, particularly road networks. The data table format, which assumes that each row in a table is a complete representation of an entity, entire unto itself, cannot easily accommodate networks, where the relationships among entities are essential to the representation. Even in the case of road networks, the analytical necessity for tightly binding together two sets of spatial data, the point data representing vertices (street intersections) and the line data representing edges (sections of street) requires an unwieldy layer of additional data management to create network datasets (see, e.g., Okabe & Sugihara, 2012). APIs and tools specifically tailored to managing graph data do a little better than this, although they are uneven in their handling of attributes that might be associated with vertices and edges. For example, because graphs are not spatially located by necessity, and because many network analysis tools redraw networks on demand, it can be difficult to retain consistent spatial locations for vertices as data are moved from one tool to another. The relatively unsettled state of tools and data formats for handling network data can be frustrating and demands sustained attention to even trivial questions about location that are taken for granted in GIS settings. Developments in graph databases (see §Graph Databases, Chapter 2) mean that these problems might not persist forever, although the motive of understanding geography relationally is unlikely to be a strong driver of uptake, compared to the more mundane question of managing logistical infrastructures. Second, it is easy, having adopted a network representation, and taken relationality seriously at least to that extent, to lose sight of what is still missing from these representations. A relational perspective demands consideration of dynamics, which graph representations do not provide. Relations are not fixed, static connections, but ongoing relations between participating entities. Relations are maintained by exchanges of information or people or materials or energy, by the flow of something; they do not

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exist in fixed, concrete form. Even infrastructure networks such as roads only approximate the relations that they are built to sustain and advance. This perspective has come to the fore in recent years, in the guise of the mobilities paradigm (see Urry, 2007; Sheller & Urry, 2006; Adey, 2017; Cresswell, 2011, 2012, 2014, among many others), which emphasizes the essentially dynamic nature of relational systems. The mobilities paradigm, Urry suggests, “focuses upon movement, mobility and contingent ordering, rather than upon stasis, structure and social order” (2007, p. 9). Network analysis, while it is underpinned by a relational perspective, tends to emphasize the latter properties of geographical systems. The movements, exchanges, and flows that constitute relations are frozen into a fixed, static structure. While this is strongly preferable to models that treat entities as distinct and unrelated, a broader computational ontology encompassing dynamics, time, change, and process is called for, if Urry’s suggestion is to be taken seriously. We consider some possibilities in Chapters 7 and 8.

Chapter

Time and Dynamics iscience has tended to struggle with time and dynamics, not least because the wider discipline of geography also struggles with time. This partly stems from a notional academic division of labor between history, centrally concerned with time, and geography, centrally concerned with space. Although historical geography is recognized as a distinct subdiscipline, all geography is historical, and necessarily concerned with past, present and potential future times. Events always unfold in space and place, and spaces and places unfold through time. It is obvious that no neat separation of space and time is possible or even particularly coherent, although we broadly accept this separation for now, deferring more thoroughly dynamic, space-time, processual thinking to Chapter 8. In spite of its obvious failings, a conceptual separation of space and time is a persistent feature in scientific thinking generally, and geography as a would-be (at least some of the time) “science of space” is perhaps particularly prone to making this distinction. One framework for thinking about time in geography that is closely related to work in quantitative geography has been available for almost half a century, namely, Hägerstrand’s time geography. Time geography held considerable sway in the early 1970s, and is perhaps the last big idea in geography considered relevant today in both giscience and in the

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discipline more generally. Even so, time geography disappeared from view to a great extent from the mid-1980s onward. In recent years with the advent of commonplace GPS tracking of people (and other organisms) the concepts of time geography have experienced a revival in giscience. This development and its potential for the discipline more widely will be examined, particularly in light of the mobilities paradigm (Adey, 2017; Waters, 2013; Urry, 2007) in recent human geography, and movement ecology (Nathan et al., 2008).

TIME AND SPACE: A COIN WITH TWO SIDES The notion that time and space are separable aspects of reality is deeply embedded in Western thought. It is closely related to the absolute conception of space central to Newtonian physics (see §The Nature of Space, Chapter 2), and became more deeply embedded through Kant’s metaphysics where time and space are posited as distinct, synthetic a priori concepts intrinsic to how we perceive and understand the world. This division made its way into geography via various pathways, most influentially through Richard Hartshorne’s reading of German geographers such as Ritter and Hettner. For example, quoting Hettner (1927, p. 114) at length, Hartshorne argues that, [r]eality is [. . . ] a three-dimensional space, which we must examine from three different points of view in order to comprehend the whole [. . . ] From one point of view we see the relations of similar things, from the second the development in time, from the third the arrangement and division in space (translated by Hartshorne, 1939, p. 140).

Later,1 wrapping up his extended consideration of The Nature of Geography, Hartshorne (1939) returns to this framework, positing a division of labor: There is, therefore, a universal and mutual relation between them [geography and history], even though their bases of integration are 1

Much later. . .

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in a sense opposite—geography in terms of earth spaces, history in terms of periods of time (1939, p. 463).

Building on this logic, Hettner (and Hartshorne) argue that geography’s proper concern is with “spatial arrangement and division” on Earth’s surface. This emphasis can be misrepresented as a narrow regional geography, concerned solely with assembling fact-laden, descriptive accounts of regions. This misinterpretation of Hartshorne became received wisdom following a revisiting by Schaefer (1953), which was espoused by many early quantitative geographers as a call for a more theoretical geography, in spite of a comprehensive point by point rebuttal by Hartshorne (1955; see also Martin, 1989). In fact, Hartshorne’s account of regions is more nuanced than the critics suggest, while also being limited in its own way. Hartshorne recognized that regions are not actual things, but are subjectively defined as required, for particular purposes (compare Gould, 1997, discussed in the introduction to Chapter 6). This makes them effectively ambiguous and potentially porous, when we consider the many ways they can be defined. They might even be relational entities, so that [j]ust as the historian is concerned with the historical association of phenomena not only more or less contemporaneous, but also those rather widely separated in time [. . . ] so the geographer is concerned with the spatial connections of things not only close together in a single area, but things as far apart as a dairy farm in New Zealand and a grocer’s shop in London (1939, p. 284).

This perspective on regions might be read (a little generously) as prefiguring more recent perspectives on place and region (see Chapters 4 and 5) but falls well short of a fully relational perspective on space since the implication seems to be that even if there is no single definitive collection of regions out there in the world, in any particular case a region or regions is defined in absolute space. Smith (1989) provides a more convincing critique than Schaefer’s rousing but clumsy effort, and in noting the embedding of regions in absolute space returns attention to the limitations of the Kantian space-time-entity perspective Hartshorne adopts.

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The Kantian space-time-entity perspective also underpins quantitative and computational geography by way of Berry’s geographical matrix (1964, pp. 5–8), itself based on a reading of Hartshorne. The geographical matrix slices the world into spaces, times, and phenomena, emphasizing a tabular data perspective, where time is reduced to a series of snapshots, an idea hinted at by Hartshorne when he suggested that [t]o combine them coordinately [space and time] involves difficulties which, as yet [. . . ] appear to be beyond the limitations of human thought. Possibly one approach [. . . ] can be made in geography by the lantern-slide method of successive views of historical geographies of the same place. An attempt to develop a motion picture would produce a continuous variation with respect to both time and space which would, of course, represent reality in its completeness (1939, p. 284).

While the difficulties of combining space and time “coordinately” are no longer a problem, the rigid conceptual separation of space and time, as well as their distinctive characters, remain challenging.

Cartography and Giscience’s Problem With Time Numerous approaches to incorporating time into geographical computing have been discussed, far too many to cover in any detail here. A comprehensive survey by Siabato et al. (2018) both organizes the wide variety of approaches into coherent categories and provides a detailed map of the literature.2 This chapter instead attempts to convey only a general idea of the challenges. In a later section, one more-specific approach, time geography, is considered, while in Chapter 8 simulation modeling, a rather different set of approaches to dynamics in space-time, is the focus. Standard giscience representations of the world struggle to deal with time (Peuquet, 1994, 2003; Yuan, 1999). The origins of GIS in automated cartography go some way to explaining this difficulty, along with 2

At the time of writing (October 2022) this work is accompanied by an interactive timeline bibliography at http://spaceandtime.wsiabato.info.

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the particular reading of Hartshorne via Berry discussed above. In any case, maps are an essentially static medium. Where the surveys and other data that come together in a map might have been collected over years, the map synthesizes and flattens them into a singular snapshot view, freezing everything into a static representation. While it has been argued that maps are processual (Kitchin & Dodge, 2007), the current outcome of ongoing processes, and the same can be argued for geospatial databases, actual maps, as artifacts, at any particular moment, are static. The same is true in large measure of GIS, and these assumptions are deeply embedded in the underlying data structures. The centrality of the relational database to standard geospatial architectures has reinforced this tendency. Relational databases are centrally concerned with data integrity and the careful management of changes to data records, which tends to make changing data difficult. Even seemingly simple tasks such as representing how land parcels change ownership over time have proven challenging for GIS developers and researchers (Langran, 1989b; Moudon & Hubner, 2000). The difficulty is not so much updating records over time, but in reconstructing the history or dynamics of a series of changes over time. The current state of things tends to become a timeless present, unless regular snapshots of prior states of the database are retained. On the one hand, regular snapshots are likely to be wasteful of resources if one must be retained for every small change in the data, but on the other, if we wait until enough changes have accumulated to merit a new snapshot, then temporal resolution is lost as many changes are bundled together in a single database update. Thus, even when snapshots are retained, it may be difficult to trace when and why particular changes occurred. Fundamental data structures that allow for change over time are surprisingly difficult to devise. Time, like space—it turns out—is complicated (Frank, 1998) ! We are accustomed to thinking about past, present, and future time, but there’s something more than a little strange about how we only experience time as a present moment, forever turning into the next moment, and the next moment after that (see Chapter 8). We also experience time differently at different moments, and at different stages in life. Time can fly by, or it can drag. In many cultures time is

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understood not as proceeding from one moment to the next, but as cyclical (Reid et al., 2020; Mackenzie et al., 2020). This makes complete sense given how deeply embedded cycles are in how our planet works. Clock faces are circular for exactly this reason—there really is nothing unsophisticated or irrational about thinking of time as cyclical, not linear. In fact, the opposite is true, and even under capitalist modernity, daily, weekly, monthly, quarterly, and annual cycles are recognized as meaningful (but see Crary, 2014). Setting to one side such fundamental questions about the nature of time, and accepting for now a unidirectional, measurable, unchanging time, we face questions of datums, time zones, daylight savings systems, and so on. The computing infrastructure that surrounds even the seemingly mundane task of time stamping files in a computer is formidable. Universal Coordinated Time (UTC) is an internationally maintained reference time dependent on atomic clocks, and precise calculation of the Earth’s rotation and its orbital progress, to allow for the insertion (or deletion) of leap seconds. Computers in turn have time datums, with Unixbased system time referenced from January 1, 1970; Windows system time from January 1, 1601; and Apple system time from January 1, 2001. Generally, these behind-the-scenes details are invisible to computer users, but anyone who has ever done even a small amount of data analysis dealing with data pertaining to time in a spreadsheet, for example, will appreciate how these and other technical details can be troublesome. Assuming such niggly problems solved, trickier, more substantive questions await. What kinds of temporal thing are we interested in? We might want to know when something happened—forgetting for now what the something is. This would be a time stamp. For something that more or less straightforwardly happens at a particular instant in time (say a digital photograph) a time stamp can be attached. But many other happenings are much less clear-cut. I was born in Ireland, but live in New Zealand. When does my birthday begin? The time of my birth in Ireland was such that it was a different calendar day in New Zealand when it occurred. Of course birth is often a protracted event rather than an instantaneous occurrence. My older son took a seemingly endless 24 hours to be born, yet we celebrate his birthday as if it were instantaneous. More generally,

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most happenings, or events, have a start time, a duration, and an end time (boundaries in time, if you like). Even this rather loose discussion of the problem makes clear how complicated dealing with something as simple as time stamping data can be. While complicated, none of this is a new problem, and most of the complexities are worked out in a paper by Allen (1984). An interesting approach to visualizing time intervals in two-dimensional space was proposed by Kulpa (1997) and has even been implemented as part of an exploratory query interface for time-stamped geographical point data by Qiang et al. (2012). Nevertheless, when the intricacies of time stamps are combined with the variety of happenings that might occur in relation to spatially extended entities, the dimensions of the challenge increase dramatically. Much of this book is about the severe limitations of simple constructs such as points, lines, polygons, and raster surfaces for representing geographical reality, but nevertheless, for the sake of argument, let’s briefly consider the ways in which they can each change. Points are relatively simple, and can come into existence, move, or disappear. Line segments (formed of two points) can appear or disappear, move in some way with one or both points moving, or if one point disappears, they mutate or collapse into a point. Adding a point to a line segment changes it into a polyline or perhaps, if the line is offset from that connecting the original two end points, it can become a polygon! Furthermore, some changes to a line segment may alter its length, while others may preserve it. The range of changes available to a polygon is greater still (some are illustrated in Figure 7.1). Turning to raster surfaces, if we assume that the cell structure of the raster is unchangeable, then we are left only with the values assigned to each cell changing (and of course the same is true of any or all of the attributes associated with any of the vector data types). In itself, a change in the values of cells in a raster is not particularly complicated, although the coordinated change in value across a connected collection of cells in a raster surface may occur in a rich variety of ways (Mennis et al., 2000; Bothwell & Yuan, 2012). Of course, a classic geospatial object has not only geometric characteristics, but also attribute values. A complete picture of the dynamics of a

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Figure 7.1. Some ways in which a polygon can change between snapshots. The original polygon is shown in the center. Possible changes shown are (a) rotation, (b) translation, (c) skew, (d) uniform contraction, (e) uniform expansion, (f) shrinkage by removal, (g) growth by addition, and (h) the appearance of a hole. This is not an exhaustive list, depending on how change is defined.

changing system must therefore keep track of what changes are happening to which objects spatially (effectively geometrically), temporally, and in their attribute values (Hornsby & Egenhofer, 2000). When the objects are changing in these ways, difficult questions about the identity of objects arise. Whether it is even possible to consider a somewhat corresponding element in a later snapshot to be the same object but changed is unclear. This problem arises even in routine situations such as the definition of census zones from one census to the next. How much can census zones change between consecutive censuses for it to no longer be meaningful to

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consider one a slightly changed version of the other, rather than a wholly new object? This problem can become even trickier when the objects in question are derived from underlying data such as in classified imagery (Cheung et al., 2015). Combining this array of possibilities with the temporal dimensions of those changes, their ordering in time, start times, and durations, and the complications are evident. Just how complicated can be seen in work by Worboys and Hornsby (2004), by Jiang and Worboys (2009), and by Campelo et al. (2011, 2012), among others. In the first two of these examples a notion of events as things in themselves, rather than as differences detectable between snapshots of objects, is introduced. In their geospatial event model, Worboys and Hornsby (2004) separate out the geospatial setting of objects and events from the things (objects or events) themselves. A setting, because it can be spatio-temporal, is more complex than a geospatial geometry, and instead is a history or trajectory, a record of spatial form over time. A complete representation of any entity then consists of its object attributes, its setting, and events with which it may be involved. Importantly, the setting of an object or event is incidental to this model, which is very different from standard GIS data models, where the spatial aspect of data is primary. Approaching the problem differently, and drawing on earlier work on topological relations (Randell et al., 1992), Jiang & Worboys (2009) describe a way to record changes in the geometry of objects over time so that the object can maintain its identity as its geographic realization changes. Broadly, the spatial structure of objects is represented as a tree of the topological relations among its parts, and changes are recorded in terms of how they alter the tree. This scheme allows for four different kinds of changes to the tree—insertion of a node, deletion of a node, merging of trees, or splitting of a tree—each with corresponding topological changes in the spatial structure of the object. Finally, Campelo et al. (2011) propose a model where the atomic element is a triple ⟨a, g , s⟩ where a is an attribute or bundle of attributes, g is a geometry, and s is a time stamp that may be an instant or an interval. This framework by contrast with the previous two does not consider events, and is much closer to the snapshot approach that is the de

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facto standard, because it emphasizes traditional geometries and records them as they change as part of the triple, at given time stamps. The authors outline an implementation architecture and elsewhere show how the framework might allow geographical processes (see Chapter 8) to be inferred from data (Campelo et al., 2012). Many details remain to be worked out, such as extending the approach to a wider range of geometry types, including three-dimensional entities.

The Trouble With Snapshots What’s so wrong with tackling spatio-temporal data using the snapshot approach? The problem, as it is with actual snapshots as a record of events, is that we don’t know what happened between the snapshots. “How did the situation at time t change into this different situation at time t + 𝛿t?” is an unanswerable question in the absence of any concept of change or the processes that lead to change (again, see Chapter 8). The classic work addressing this issue is Gail Langran’s dissertation (1989b; see also Langran, 1989a, 1992), which proposes an explicit representation of changes in the state of records held in geospatial databases. This approach is the most obvious way to extend GIS systems to handle change over time, but there is still no concept of a change per se. Andrew Galton (2004, p. 40) calls it a “three-plus-one” dimensional approach. Entities are conceived as endurants that persist through some period of time, undergoing changes along the way. Events cause changes to occur, and by recording these and granting them status as things in themselves, a record of an object’s history can be developed. Depending on the other capabilities developed for a system based on this approach, we may be able to derive snapshots of a system over time from some starting state combined with a record of the changes that occurred, or conversely to derive a sequence of events or changes that occurred given a series of snapshots.3 However, this presupposes “that there is a clean separation between (spatial) objects and (temporal) events” (Galton, 2004, p. 41). 3

There may even be a role here for solutions akin to software version control systems.

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Depending on the frequency and scale of changes relative to the lifetime of entities, this may be a natural-seeming model. But what about an object like a storm? A storm at any moment has location and extent, but is constantly changing over time. Treating a storm as a fully four-dimensional hyperobject, a perdurant in space-time might be a better approach. Perdurant hyperobjects do not change; rather we perceive them differently through time. This is a very different perspective than that adopted in conventional GIS platforms. It is also important to recognize that viewed at an appropriate scale (spatial and temporal) all entities are four-dimensional hyperobjects! Relative to its lifetime, the number and extent of the changes that occur with respect to (say) a building may be limited, and certainly not continual as in the case of a storm. It is also important to recognize that a hyperobject only becomes the fixed unchanging thing I am describing after it is gone. While it persists, as time unfolds it continues to change, to the extent that sensing systems in place are able to record its ongoing evolution. The various complexities and relations among these perspectives are outlined in some detail, in an accessible way, by Galton (2004). An important insight is that there really is no right or wrong way to deal with these complexities.4 In some situations, more or less enduring, more or less unchanging computational objects, subject nevertheless to more or less instantaneous changes, are a reasonable approximate representation of the world. This is the case in many mundane applications of GIS. Think, for example, of a city government maintaining lamp posts or fire hydrants across its jurisdiction. These assets need to be repainted or have parts replaced from time to time. Less often, new lamp posts or fire hydrants will be added or old ones decommissioned and removed. In terms of the overall lifetime of the system, or of any individual element in the system, changes are infrequent, and more or less instantaneous. In other situations, change is continual, constantly updated by streaming data—the example of a storm system again comes to mind. It is tempting to consider some kind of artificial-natural world divide here, with natural 4

See Peuquet (1994) and Wachowicz (1999) for other approaches, and Peuquet (2003) for an extensive survey.

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world objects more often falling into the continuously changing category. This would be a mistake, however, particularly in light of the increasing prevalence of continuously updated monitoring of so many aspects of day-to-day life, most obviously in logistical contexts where people and things are in transit from place to place, and geographical computing platforms manage their movements. There is a loose consensus that the emergence of a standard model of fully spatio-temporal entities akin to the point-line-polygon vector and/or raster models of established GIS platforms is unlikely. From an ontological perspective, there may not be a readily generalized and implemented formal way to represent dynamic geographical phenomena, or at any rate none that is widely considered adequate (O’Sullivan, 2005, p. 754).

More pragmatically, Goodchild (2013) identifies seven distinct potential uses of a space-time GIS—tracking, temporal snapshots (raster or vector, considered separately), cellular automata, agent-based models, events or transactions, multidimensional data—and argues that each likely demands different computational representations and platforms. He then argues that “a number of distinct forms of STGIS [spatiotemporal GIS] are likely to evolve, based on distinct data types and suites of scientific questions” (2013, p. 1076). Surveys of progress tend to support this view. In an extensive review, Pelekis et al. (2004) identified progress toward implementation only in the areas of object tracking and the maintenance of property records.5 A more recent extensive survey (Siabato et al., 2018) uncovers few examples of working software, and only a few more proof-of-concept implementations of approaches. Yet those implementations that have been presented tend to be specific and certainly not the general-purpose STGIS that a few continue to hope for.

5

This might be an interesting reflection on late capitalist society’s priorities.

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HÄGERSTRAND’S TIME GEOGRAPHY In spite of, or perhaps because of, the challenges, grappling with the complexities of time has bequeathed geography one of its few home-grown systematic frameworks, with significant uptake in giscience, and notable theoretical impact within the discipline, and more widely. Time geography was first presented by Torsten Hägerstrand (1970) in near-complete form, with a few additional concepts added in a later paper (Hägerstrand, 1982). For many years prior, Hägerstrand worked on diffusion models (Hägerstrand, 1968, the translation of the Swedish original published in 1953).6 Diffusion necessarily focuses attention on movement, whether of people or things or ideas, and time geography is principally concerned with how things in motion are able (or not) to interact with one another across time and space. Central to the appeal of time geography is its inclusion from the outset (see Hägerstrand, 1970) of a compelling visualization framework, the space-time diagram, sometimes referred to as the space-time aquarium. Good overviews of the essentials have been provided by Thrift (1977a) and Dijst (2009). It is easy to get distracted by space-time diagrams7 and lose sight of the ideas behind time geography. The key concepts are space-time paths and constraints. Individuals (whether persons or things) follow a continuous path in space-time, such that at any given moment they must be at a particular, singular location.8 Central to time geography is the notion that social life can be investigated in terms of how multiple paths relate to one another in space-time. Interrelations among space-time paths are governed by constraints, which Hägerstrand groups into three categories: capability constraints, coupling constraints, and authority constraints. Capability constraints relate to the ability of an individual to traverse space .

6

7 8

This work was a significant influence in the early years of the quantitative revolution (Morrill, 2005), and Hägerstrand himself was also instrumental in ensuring the publication of Bill Bunge’s Theoretical Geography (1962). See the next subsection, where I lean into the distraction. This seems obvious, but communications and virtual technologies increasingly call it into question, at least a little—see Adams (1995).

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through time, and depend critically on access to different modes of transport: A person who must walk everywhere is more constrained spatially than someone with a car—even if a person on foot can access locations that a person in a car cannot. Coupling constraints refer to the need for individuals to be present in the same place at the same time so that certain activities can occur, or as Hägerstrand puts it, “the individual has to join other individuals, tools, and materials in order to produce, consume, and transact” (1970, p. 14). These constraints are often expressed through clock time, subject to conventions around the working day, working week, opening hours of services, and so on. Coupling constraints become challenging to navigate when individuals are participating in multiple projects and roles, and are greatly clarified in space-time diagrams. Finally, authority constraints pertain to how power is expressed spatially, dictating in which regions or places and at what times various activities can occur, and which people are permitted or required to be present in what roles. This is the realm that we associate with political geography, and notions of in-place and out-of-place activities (see Chapters 4 and 5, especially §Everything in Its Place). The inclusion of authority constraints acknowledges the importance of power relationships in time geography, although it does so in a curiously apolitical way. The constraints on individual paths are simply there—how they came to be there, or how they might change, is not really a concern, although there is no intrinsic reason for it not to be, particularly if spatial or temporal scale is changed from the (typically) diurnal focus of many time geography studies. As some have commented, given how entangled with one another capability, coupling, and authority are, these distinctions are rather fluid (see, e.g., Gell, 1992, pp. 192–93).9 The particular constraints faced by an individual arise out of their position in society. This is likely to mean that in societies with significant imbalances in power relations, the relatively powerless will be more constrained than 9

When I first wrote these words in March 2020 and lockdowns were being imposed in a number of countries in the face of the COVID-19 pandemic, the importance of understanding how coupling constraints arise out of authority constraints became very clear.

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the powerful, even as these constraints appear as merely capability or coupling constraints, and are naturalized by that appearance. In this respect, of course, time geography is no different from any framework that starts with an emphasis on documenting and presenting how things are, rather than how they came to be.

The Space-Time Aquarium Time geography without the accompanying diagrammatic methods does not sound like much more than some rather obvious statements about the constraints on everyday lives. A simple example of a space-time path for a typical day in the life of someone leaving home, going to work, doing something at lunchtime, and going out to a movie in the evening before returning home is shown in Figure 7.2. Geographical space is the floor of this three-dimensional view, while time is a third dimension, usually portrayed with time advancing in an upward direction. It bears emphasizing that in its conception this is an absolute space model, even if the later focus on the relations between paths pushes it a little in the direction of relative space.

Figure 7.2. A simple space-time path showing one day’s activity.

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All space-time paths can only move in an upward direction from bottom to top, and movement is not instantaneous. The connection from home to work is sloped slightly upwards, because it takes time to get from one place to the other. When a person or thing is not in motion, the space-time path becomes a vertical line in the aquarium. Rapid transit yields less steeply sloped paths, because larger distances (horizontal) are traversed in shorter times (vertical). Furthermore, while the diagram shown indicates straight connections from place to place, there is no reason that these cannot follow streets or other connections actually used to make the journeys in question (see Figure 7.6). An individual path in space-time is rather uninteresting, although it may reveal surprising choreographic intricacies in everyday activities. It is when other paths are added to the picture, so that how constraints shape paths may become apparent, that things get interesting. Figure 7.3 is a schematic space-time representation of a meeting in physical space. Multiple paths converge into a bundle of co-presence, for the duration of

Figure 7.3. Convergence of space-time paths for a physical meeting, showing the bundling associated with this or similar collaborative projects in the physical world.

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the meeting, before the paths of the meeting participants diverge back to their places of origin. Charted in this way, collective social life is an endlessly complicated set of interwoven individual paths, with convergences and dispersal as people participate in the various projects with which they are involved. Hägerstrand refers to the patterns traced out by many paths variously as a “net of constraints,” a “socio-economic web” (1970, p. 11), and a “time-space web” (p. 20), thus emphasizing the importance of the relationships between paths through coupling constraints. Capability and coupling constraints govern what is possible (or impossible) for individuals given their various commitments in a way that is nicely illustrated by space-time diagrams. It is easier to illustrate some aspects by reducing the space-time diagram to two dimensions, one of space and one of time (see Figure 7.4). Here we get a clearer idea of how capabilities affect the area in space

Figure 7.4. Capability and coupling constraints in a two-dimensional spacetime diagram. Space is reduced to a single dimension on the horizontal axis for clarity. In the left-hand panel, individuals using faster transport modes have access to larger potential path areas. In the right-hand panel, given a particular mode and successive commitments at locations A and B, the dark region is the prism in space-time potentially accessible to an individual. The prism results from intersection between the potential path area forward in time from A, and the constraint imposed backwards in time by the requirement to be at location B by a certain time.

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potentially accessible from a given starting location, the potential path area. The forward (future) potential path area defined by a capability constraint in combination with fixed locations in space-time where an individual is required to be, and their associated backward (past) potential path areas combine to produce a space-time prism actually accessible to an individual under these coupling constraints (Figure 7.4). Note that the prism shown in this figure would be a complicated three-dimensional volume in space-time which schematic illustrations such as in Figure 7.5 can only give a general impression of. There has been significant technical progress in delineating such constructs with respect to realistic movement paths along street or transport networks (see, e.g., Neutens et al., 2008; O’Sullivan et al., 2000), although the conceptual content of the representation remains unchanged. Thinking with these visual tools, it is clear how if the locations A and B are closer together, or available transport options are more efficient, the space-time prism and potential path areas increase in spatial extent. It is

Figure 7.5. The space-time prism in a three-dimensional space-time diagram. The projection of the prism into two-dimensional space is the potential path area of locations reachable by an individual within the capability and coupling constraints imposed by events at A and B.

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also easy to see how complicated juggling multiple commitments—each with associated space-time extents and limitations—is for individuals, or across a social order. The space-time aquarium provides a visual language for thinking about how everyday life is lived. This picture of people tracing paths inside constrained space-time prisms that are the complex outcome of overlapping demands prompted Gell to suggest that “daily prison” might be a better label (1992, p. 193). In the two key papers describing time geography (Hägerstrand, 1970, 1982), it is paths and constraints, and the resulting prisms, that dominate. In the later of these papers, Hägerstrand introduces the diorama as a setting within which paths and prisms unfold. It is surprising that he prefers this new term (new for geography) and not any of many other possibilities, most obviously place or landscape, but also not any of region, site, situation, setting, or locale which might fit equally well. In opting for diorama, there is an unmistakable air—at least for me—of the model railway about the time geographic worldview. Constraints are not so much constraints as the regular timekeepers of a well-regulated and ordered world.10 This is unfortunate given that for a period in the 1970s and well into the 1980s, there was vibrant discussion of time geography. Time geography was an important influence on the turn to behavioral geographies focused on the lifeworld (Buttimer, 1976). The potential to speak directly to longstanding debates in social theory concerning structure and agency (see especially Giddens, 1985) was important in connecting geography to wider currents in the social sciences. Influential scholars worked diligently at this overlap (Thrift, 1977b,c; Pred, 1981, 1984). Particularly important were detailed considerations of the emergence of clock time and national systems of timekeeping under industrialization (see chapters in Parkes & Thrift, 1975, 1980). Hägerstrand’s bundles of converging space-time paths were extended and generalized by others as

10Some

might also be reminded of imaginary worlds like Trumpton, Mister Rogers’ Neighborhood, or Richard Scarry’s Busytown.

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projects, which might set in motion many space-time bundles in multiple locations over long periods.11 The notion of geographical places as extensive space-time projects contributed to a new take on the region as a dynamic entity rather than a stable, clearly delineated region in space (Thrift, 1983). There are also unmistakable (if unspoken) echoes of time geography in Massey’s wish for “a fuller recognition of the simultaneous coexistence of others with their own trajectories and their own stories to tell” (2005, p. 11), in her argument for “space as a simultaneity of stories-so-far” (2005, p. 9) over 30 years after time geography’s first appearance.

LIMITS TO TIME GEOGRAPHY Whatever its promise and wide-ranging impacts, time geography does not exert much direct influence in contemporary geographical thinking. Geography is forever moving on, so there is no single clear reason for this. Before considering the reappearance of time geography—in some aspects—under the guise of human dynamics, it is instructive to consider some limitations that contributed to its retreat from the forefront of geographical thought from the mid-1980s on. I have already suggested that time geography—certainly as it was widely taken up—is guilty of a kind of naively empiricist model railway approach to the world. This tendency was criticized even when time geography was widely considered a central contribution to geographical theory and practice (Thrift & Pred, 1981). Although the collection Social Relations and Spatial Structures12 (Gregory & Urry, 1985) includes several chapters drawing on time geography, there is also a complex critique by Derek Gregory (1985) bemoaning its “physicalist” tendencies. The argument links time geography to social physics and to logical positivism—not necessarily fatal criticisms in 1985, but certainly not 11 The

precise origin of the concept of a project is unclear. Thrift (1977a) locates it in a conference paper presentation by Hägerstrand (1974) which is now hard to find. 12 This collection impresses for the evidence it provides of still active engagement in the mid-1980s of theoretical work in geography with quantitatively derived underpinnings, something not much in evidence only a few years later.

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points in its favor either. The deeper dimension to Gregory’s concern is how time geography, in spite of an avowed focus on movement and change, emphasizes repeated patterns and the packing of activities and projects in space-time, so that relatively static structures become a dominant theme. Furthermore, the emphasis on the essentially biophysical capability and coupling constraints—the indivisibility of individuals, time and space as resources, packing as a geometric problem—over authority constraints, which are politically contestable, ironically yields a static view of the world. Physicalism may have particularly bothered Gregory writing in 1985, when critical realism (Bhaskar, 1975) with its emphasis on abstraction and real, but nonempirical mechanisms was beginning to impinge on cutting-edge geographical thinking.13 This failing is less evident in the wake of materialist geographies (Whatmore, 2006), and Thrift gives time geography some credit for reducing the “distinction between humans and other objects” (2005, p. 338), an early harbinger of that tendency (see also Schwanen, 2007, and Chapter 8). Even if time geography added nonhuman objects to the ontology of human geographers, it is the space-time path that is perhaps its lasting legacy. This turns a dynamic, unfolding process into a static, essentially geometric object (compare how networks tend to render dynamic processes as static, as discussed in Chapter 6). It also brings to mind Galton’s perdurant hyperobjects. Of course, space-time paths or trajectories can be subjected to all kinds of interesting analyses, but the curious way they change the living, thinking, active human beings tracing that path into an inert object was noted even by Hägerstrand himself: There are other, less tangible, factors which influence the sequence of situations within the limits set by what is physically possible. Outstanding among these are human intentions. The fact that a human path in the time-geographic notation seems to represent nothing more than a point on the move should not lead us to forget that at its tip—as it were—in the persistent present stands a living body subject, endowed with memories, feelings, knowledge, imagination 13The

first edition of Sayer’s influential Method in Social Science (1992) appeared in 1985.

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and goals—in other words capabilities too rich for any conceivable kind of symbolic representation but decisive for the direction of paths. People are not paths, but they cannot avoid drawing them in space-time (1982, pp. 323–24).

The most enduring impact of time geography thus balances awkwardly on this failure of “symbolic representation,” as is persuasively argued by Gillian Rose in a chapter of her Feminism and Geography entitled “Women and Everyday Spaces” (Rose, 1993, pp. 17–40). On the one hand, by foregrounding the complicated daily choreography of everyday life, time geography draws attention to previously neglected subjects: Examining the lives of women requires attention to the ordinary, to the unexceptional, because women are excluded from arenas of power and prestige; and time-geography, its proponents claim, is ‘admirably suited to this type of “bottom-up” study’, both theoretically and methodologically (Rose 1993 22, quoting Miller 1983, 85).

Rose discusses a number of examples taking up this idea (Hanson & Hanson, 1980, 1981; Miller, 1982, 1983; Dyck, 1990) in various ways, although for the most part the detailed travel diaries necessary for specifically time geographic analysis do not appear; rather it is a focus on the spatiality of women’s everyday lives that distinguishes the work. The edited collection Women in Cities (Little et al., 1988) emphasizes the importance of this perspective, although as Tivers notes “the complexity of the gender role constraint [. . . ] seems much greater than the simple idea of having to be at certain places at certain times in order to attend to the needs of children” (1988, p. 85). So time geography seems to have offered a perspective that was at least somewhat aligned with the concerns of feminist geographers which had previously been neglected by geography more widely (Monk & Hanson, 1982). Even so, few of the early studies deploy time geography explicitly. An example that does examines the lives of housespouses dependent on public transport in four suburbs in Christchurch, New Zealand (Forer & Kivell, 1981). This paper cleverly scales back and forth between details of individual everyday lives, and how these might be

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understood as societal constraints at a more urban or region-wide scale. It was not until Mei-Po Kwan’s work almost two decades later (Kwan, 1998, 1999a,b, 2000), which pushed GIS tools to their then limits, that similarly detailed feminist time geographical analysis at scale was attempted. That work has subsequently been significant in establishing links between feminist geography and giscience (Kwan, 2002), so was important to the emergence of critical GIS (Pavlovskaya, 2009), and also to starting conversations between quantitative and qualitative work in geography more generally (Kwan & Schwanen, 2009; Schwanen & Kwan, 2009). But returning to the awkward relationship between time geography and a feminist perspective, as Rose notes, “time-geography and feminism are not entirely congruent” (1993, p. 18). She goes on to outline how time geography’s insistence on a singular space is at odds with a feminist awareness of the separation of public from private space. This is effectively the limitation spelled out by Hägerstrand himself when he recognizes the “living body subject, endowed with memories, feelings, knowledge, imagination and goals” (Hägerstrand, 1982, p. 324), and also related to the limits of an absolute space model. But Rose is more specific, decrying the absence of emotions and affect, relationships, and the bodily from time geography. It is also telling that most illustrative time geography paths (including my Figure 7.2) present a home location as the start and end point of each day, so that the emphasis is on public spaces outside the home where paths may intersect at places of (paid) work. An interesting point of comparison here is Marston’s (2000) call for geographers’ considerations of scale to acknowledge social reproduction and the domestic sphere (see §Scale as Socially Constructed, Chapter 3) In sum, the body in time geography “virtually disappears [. . . ] reduced to its movement” (Rose, 1993, p. 30) and space once more becomes a neutral container where public activities unfold, wherein, other than the constraints of public life, individuals are free to go anywhere. This is sharply at odds with many women’s (and not only women’s) experiences, where places are inaccessible for reasons such as fears for bodily safety (see especially Rose, 1993, pp. 34–38). Reflecting on Rose’s critique, Latham sums up: “time-geography presents a mechanical, lifeless, profoundly masculinist, picture of society”

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(2003, p. 2009; see also Buttimer, 1976). Torrens (2022) has recently proposed space-time trajectories vastly enriched by data from the numerous sensors of ubiquitous mobile computing—principally smartphones, at least for now—although the presentation of this idea in the context of retail data science points to a rather narrow focus. Perhaps more fruitfully for geography generally, Latham goes on to suggest that, reinterpreted through these critiques, and if the final research text is itself considered as a kind of performance, it is possible to imagine ways of working with narrative devices like time-space graphs that recognize both their productiveness and their partiality (2003, p. 2009).

Latham also presents interesting collages in space-time of images, words, and so on. Recent work by Moore et al. (2018) points to the possibility for productive and creative collaborative work by geographers and giscientists in this space (see also Latham & Wood, 2015).

BEYOND TIME GEOGRAPHY: MOBILITIES AND HUMAN DYNAMICS The continuing importance of grappling with time and movement is apparent albeit in the more contemporary clothing of mobilities and human dynamics. Although many proponents downplay the relevance of time geography as a precursor to the mobilities paradigm, it is often hard to discern the differences between the perspectives in practice, beyond the widerranging, self-proclaimed remit of mobilities research, and an emphasis on qualitative methods. Mobilities has been enthusiastically taken up in geography, since it was named as such in the subtitle of John Urry’s Sociology Beyond Societies (2000).14 Most introductions to the topic begin with statements like “everything is on the move” (not a quotation, but see, e.g., 14Robin

Law’s earlier (1999), more modest call for a cultural turn in transport geography seems an equally important inspiration for mobilities research, suggesting that it was a change in emphasis already afoot before Urry’s book appeared.

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Adey, 2017; Cresswell, 2011; Urry, 2007; Sheller & Urry, 2006). These slightly trite statements belie a deeper recognition that the world cannot reasonably be considered a collection of more or less fixed and stable entities. Rather, everything is in motion, albeit at wildly varying speeds, so that the world presents itself as a shifting collection of entities of varying degrees of permanence. Urry’s book is a reaction to the inadequacy of fixed categories—in geography examples would include the nation-state or region—for properly examining the world. This stance is taken to its extreme by Merriman (2012) who argues that all stable things are illusory and that a necessary processual perspective on the world requires us to set aside space and time as fundamental categories and focus on “movement-space” instead (see also Chapter 8). In any case, the tools of time geography not taken up by researchers in the mobilities paradigm nevertheless seem to hold potential for the approach, and might reasonably be added to the “mobile methodologies” described in Adey’s (2017, pp. 272–316) wide-ranging discussion. Meanwhile, the entirely separate world of human dynamics analyzing the proliferation of large datasets tracking movements of people is more respectful of a time geographic heritage, without much advancing the conceptual thinking underlying it (Dodge & Nelson, 2023; Yuan, 2018; Shaw & Sui, 2018). An example that uses time geographic concepts and tools to consider segregation of populations in everyday life as a dynamic space-time phenomenon is provided by Farber et al. (2015) and starts to recognize that space and population are not static and fixed (Kwan, 2013). Even so, most work in human dynamics seems more focused on the technical challenges of dealing with large spatiotemporal datasets, or on the possibilities of novel (social media) datasets, than with advancing or extending concepts for thinking about time and space. A sense of the possibility of time geographic analysis in this setting is provided by even cursory study of examples such as those in Figures 7.6 and 7.7. The latter in particular points to possibilities at the intersection of time geography and movement ecology (Nathan et al., 2008) especially the extensive recent work on the analysis of movement data (Dodge

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Figure 7.6. Space-time diagram for 100 Beijing taxis for a one-week period. Data available from https://www.microsoft.com/en-us/research/publication/tdrive-trajectory-data-sample/ (Yuan et al., 2010, 2011) pertain to the period February 2 to 8, 2008, including Chinese New Year. This probably accounts for the unexpected pattern in the week’s activity, which does not follow a weekday/weekend rhythm as might be expected.

et al., 2016; Laube, 2014). It feels like there simply must be geographical insights to be found in such rich data. What kinds of insights these might be is less clear. One influential thread of research in this area directly links human dynamics and smart cities (Shaw & Sui, 2018), an enterprise

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Figure 7.7. Coordinated space-time paths derived from a simple flocking simulation model (see O’Sullivan & Perry, 2013, 121–25, and §Agent-Based Models, Chapter 8). Compare the coordination of these paths with that of the taxis in Figure 7.6.

that appears less focused on geographical understanding and more on optimizing cities.15 It seems reasonable to wish for more than this. In a thoughtful reflection on time geography, Dan Sui (2012) suggests the potential for richer ways of combining space and time that move beyond the absolute space and time embedded in space-time diagrams (and by extension human dynamics). Richer models of space and time might enable a more ambitious human dynamics engaged with wider currents of geographical 15 “Status

quo theory” in Harvey’s damning phrase (1972, p. 41).

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thought. He suggests that Hägerstrand was working toward a broader formulation of time geography, but unlike the much cited earlier work never organized his thinking into a coherent framework easily taken up by others. A hint of the evolution in Hägerstrand’s thinking is provided by his turn to landscape or diorama over absolute space (Hägerstrand, 1982), and Sui suggests that his thinking on time was also moving “from symbolic to embedded time” (2012, p. 8). Taking this idea further, Sui (2012, pp. 9–12) goes on to suggest that up to nine versions of time geography are conceivable, depending on their representation of time (as absolute or experienced, or both) and space (as space or place, or both). For example, Time Geography V would characterize geography as both absolute spatial and embedded place-oriented, and time as absolute. Whether or not Sui’s suggestions are the place to start, deeper engagement with questions about how space, place, and power geometries (Massey, 1991a) are made and remade by the kinds of data flows central to the pursuit of human dynamics, is surely necessary for real progress. Taken together, mobilities and human dynamics research could be poster children for this book. The concerns central to mobilities research also underpin the datasets that human dynamics researchers work with. But the latter community approach their analysis with entirely different questions and the former are mistrustful of the shallowness of the data gathered by and for human dynamics researchers. There are serious challenges to the two communities engaging one another’s work, both philosophical and methodological in nature, and it is much easier to suggest collaboration than to pursue it. Nevertheless, the possibilities of such collaboration hold promise for geography.

FROM TIME TO DYNAMIC PROCESSES Taking time seriously presents difficult challenges for giscience and for geographical thought. Perhaps even more clearly than other themes and concepts in this book, it demonstrates how focusing on low-level questions of representation in giscience risks missing the point. Adding time to long-established spatial data structures, file formats, or databases does

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not seem likely to be as productive as thinking carefully about conceptual aspects of what it would mean to extend geographical computation to routinely handle time. Hägerstrand’s time geography is much more fertile ground for engaging geographical thought than developing the best new data structure to add to GIS tools. It is also interesting to think about why GIS was built on cartography and static maps rather than on time geography; or to speculate on what GIS would look like today, had it been built on time geography.16 For now, it is apparent that such a platform would still have limits, albeit different ones than today’s. A limitation revealed by this discussion, and in the consideration of networks in Chapter 6, is that processes are missing from both approaches. Relations among places and things, and the unfolding of things over time, are both underpinned by dynamic processes. Neither network representations nor most of the approaches to adding time discussed in this chapter take process seriously. Movement or change may be captured in some sense, but how or why movement happens or change occurs is not the focus, because the processes driving change are absent. Similarly, relations among things and events through processes remain elusive. Network representations tend to reduce the relationships and flows among elements, driven by processes, to static structures, while many representations of time freeze change over time into fixed data structures or visualizations. Taking processes more seriously as on a par with things, perhaps even taking precedence over them, is the focus of the next chapter.

16This

is left as an exercise for the reader.

Chapter

Process and Pattern he last two chapters have shown that we need to think carefully about process. Network representations of relations among entities render the dynamics of interacting processes as static topological structures. These are convenient to analyze but discard process information. On the other hand, when we explicitly consider change through time, but ignore the driving processes, we may be unable to account for change effectively. In this chapter we address these omissions by considering process thinking in relation to geography, and how it might enhance computational representations of geographical phenomena. We first explore process philosophies. As elsewhere, we will stick to the shallow end of these deep waters. The key idea is that we replace the assumption of a world of more or less stable entities—the assumption that underpins the data tables of giscience—with a world of processes, change, and events, where stable entities, understood as patterns of repeated occurrence (see Galton, 2018), become something we must explain, not something pre-given. Under the guise of complexity theory, this idea is consonant with thinking in the sciences more broadly, although geography along with many other disciplines continues to emphasize substance philosophy thinking in many of its tools and methods. Some of the computational tools most directly relevant to this worldview are

T

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simulation models, which have become commonplace in some subfields in geography. Simulation models bring with them an array of technical, methodological, and even philosophical problems, some of which we also consider. Many of these technical issues relate to a longstanding preoccupation in geography, particularly its more quantitative branches, with the relationship between pattern and process. I will suggest that whereas this preoccupation has at times been accused (not unfairly) of oversimplifying geographical thought, appropriately reinterpreted it can again be an important motif in the discipline.

PROCESS PHILOSOPHIES Process philosophies have been a minor strand in Western philosophy since Ancient Greek times. Heraclitus is famously credited with saying something along the lines of “no one ever steps in the same river twice.”1 The point is that the river is not a fixed stable thing, but an ongoing constantly changing process. In some versions it is further suggested that both the person stepping into the river and the river are constantly changing. Notwithstanding this venerable tradition, process thinking has been overshadowed in Western thought by substance and object philosophies. Yet, as Seibt (2018) notes, there is a continuous, if stuttering, line of development from Heraclitus, through Leibniz’s monadology, and Hegel’s dialectics to the authors central to contemporary process thinking, Peirce, James, Bergson, and Whitehead. This history of marginality is by contrast with mainstream Eastern philosophies, such as Daoism (see Chen, 2018), and also many Indigenous modes of thought (Sundberg, 2014), where processual thinking is often dominant (see e.g., Stewart, 2020). It is clear that Western process philosophies have borrowed

1

It is unclear that Heraclitus ever said anything as direct as this (see Graham, 2019). If process thinking were more central to Western thought, it is hard to imagine that the source of Heraclitus’s dictum would be quite so obscure.

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heavily from both Eastern and Indigenous sources, and that this has been underacknowledged. It would be presumptuous of me to generalize about diverse Indigenous and other non-Western philosophies. Having said that, and instead to generalize about Western science, it is not a stretch to suggest that its characteristic mind/body, human/nonhuman, local/global, time/space, and related dualisms are atypical among worldviews. For example, in te ao M¯aori (the M¯aori world), “[t]ime cannot exist without space, and space cannot exist without time” (T Smith, 2000, p. 56), “truth is not an objectified, definitive truth but a recognition of relationships and interconnectedness which defines the uniqueness of things and individuals” (2000, p. 59), and “all things are living” (CW Smith, 2000, p. 45). Or again, focusing on space and time to develop an alternative spatio-temporal ontology integrating Cree temporalities, Reid et al. note that, 1. Time can be a repeating cycle instead of a line; 2. The past and the future have agency, which contrasts with the positioning in the present; 3. Geographic entities are dynamic processes rather than fixed physical objects; 4. Time is inseparable from a place rather than merely a fourth dimension added to a three-dimensional space model (2020, p. 2335).

Elsewhere, Reid and Sieber (2020) rightly ask, “Do geospatial ontologies perpetuate Indigenous assimilation?” so it is important to be clear about my reasons for plotting what will be a Western course through process philosophy. Given my position as a P¯akeh¯a scholar within the Western tradition, I have chosen to emphasize process philosophies in that tradition, particularly the work of Alfred North Whitehead. This is not because I consider this particular iteration of process philosophy to be “best in class.” Nor is the point to suggest that such ideas do not exist elsewhere—they clearly do. Rather I focus on this body of work because it explicitly seeks to correct dominant substance philosophy traits in Western metaphysics—traits firmly embedded in giscience. In this way, I hope that Whitehead’s philosophy can provide pathways for giscience toward a diversity of approaches that are “open to conversing with and walking alongside other epistemic worlds” (Sundberg, 2014, p. 33).

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The most complete description of Whitehead’s process philosophy is set out in Process and Reality ([1927] 1978), where he proposes understanding reality as constituted by processes, and not in terms of things at locations in space-time. Bluntly, there are no such things as “things,” only processes, or events, referred to as actual occasions. Even phenomena that appear to be concrete, stable things are constantly remaking themselves in processes of becoming. The dominance of substance/object thinking in the Western philosophical mainstream and in everyday language can make this simple idea seem willfully obscure and difficult. This impression is reinforced by Whitehead’s propensity for coining new and unfamiliar terms like “concrescence” or “actual occasions,” and for using familiar terms like experience and society in novel ways. Whitehead acknowledges this difficulty in Process and Reality when he suggests that “[w]ords and phrases must be stretched towards a generality foreign to their ordinary usage” ([1927] 1978, p. 4). Seibt (2018) notes that “Whitehead’s process metaphysics is terminologically somewhat difficult to digest.” Certainly Isabelle Stengers’ enthusiasm for Whitehead’s “free and wild creation of concepts” (2011) is not universally shared! With this in mind, an easier place to start is through secondary accounts, and Mesle’s (2008) introduction is very approachable. He argues that, far from being difficult, process philosophy is intuitive: Process philosophy is an effort to think clearly and deeply about the obvious truth that our world and our lives are dynamic, interrelated processes and to challenge the apparently obvious, but fundamentally mistaken, idea that the world (including ourselves) is made of things that exist independently of such relationships and that seem to endure unchanged through all the processes of change (2008, p. 8).

Or again: Some things change very slowly, but all things change. Or, to put it better, the world is not finally made of “things” at all, if a “thing” is something that exists over time without changing. The world is composed of events and processes (2008, p. 8).

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In other words: We experience the world as a continuous flow of events and change, so why then would we take seriously arguments of philosophers that the world consists of static, fixed entities? For some process philosophers this concern extends beyond the external world “out there,” to the individual perceiving, experiencing subject. Not only you and me, and any other conscious entity, including animals, but even in some iterations of process thinking, seemingly inert entities like rocks. Mesle (2008, pp. 31–41) designates this perspective, “experience all the way down.” Process philosophies therefore not only emphasize process but usually also dissolve Western thought’s habitual privileging of the conscious human mind over inert matter, with its accompanying centering of the individual. It is here where process philosophy most obviously overlaps with spiritual worldviews that emphasize the “oneness” of all being. Regardless of how far one is prepared to go along with these corollaries of process philosophy, seeing the world as composed of events and processes raises questions for geography in general, and giscience in particular. Whatever flavor of process philosophy we adopt, viewing events and change as fundamental makes entities we observe as more or less constant patterns of occurrence (Galton, 2018) that which demands to be explained, and not simply taken for granted. The entity–attribute model can at best only offer a dim reflection of a world of unending flux, and at worst completely misrepresents reality. Whitehead is utterly scathing about the error of forgetting that the true nature of things is unending flux. He terms this “the Fallacy of Misplaced Concreteness” ([1925] 1967, p. 52), and considers it responsible for many of the ills of the modern world. Systematizing knowledge by simplifying it, so that it is expressed through the behavior of more or less static and enduring entities, when the reality is ongoing flux, change, and interaction among processes, leads to all kinds of problems. Scientific knowledge is impoverished by its balkanization into disciplinary silos studying different things, in denial of the interrelatedness of everything. In parallel, public policy revolves around systems of professionalized knowledge reliant on abstractions treated as real—the economy, unemployment, inflation, and so on—rather than as complicated

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ongoing outcomes of interacting processes. Abstractions are useful, even necessary; the trouble arises when we start believing that they really exist. Importantly, Whitehead does not deny that working with concrete abstractions has been highly effective in advancing scientific knowledge. Until recently, such apparent progress probably contributed to the marginalization of process philosophy. In the 21st century faced with accelerating anthropogenic climate change and multiple interrelated other crises,2 it is perhaps easier to take seriously his warnings about misplaced concreteness. Whitehead makes not many (if any) recommendations about how to proceed differently. His philosophy is a metaphysics, an ontology describing the nature of the world. He doesn’t offer advice on how to understand the world—epistemology—beyond urging us to recognize its processual nature, and our oneness with that nature. Others, drawing on Whitehead and other sources, such as complexity science (Prigogine & Stengers, 1984) and poststructuralist thought (Latour, 2004), have argued for new approaches to science, whether postnormal (Dankel et al., 2017; Funtowicz & Ravetz, 1993), real (Ziman, 2000), or slow (Stengers, 2018; Lane, 2017). All of these are congruent with process thinking. The recognition of “wicked problems” (Churchman, 1967; Rittel & Webber, 1973) where the complicated interconnectedness of problem-solving science with the messy worlds of policy, governance, and society is central, also aligns well with Whitehead’s perspective.

Process, Space, Place, and Pattern In Chapter 2 we noted Whitehead’s ([1925] 1967) dismissal of the notion of “simple location” as uninteresting, but it’s much worse than that! Simple location is not only boring, it is also central to the fallacy of misplaced concreteness:

2

As I write, most obviously, the COVID-19 pandemic. Recall, too, that Whitehead was writing in the 1920s, when sounding an alarm about the downsides of scientific progress was still a minority, contrarian perspective.

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Of course, substance and quality, as well as simple location, are the most natural ideas for the human mind. It is the way in which we think of things [. . . ] The only question is, How concretely are we thinking when we consider nature under these conceptions? My point will be, that we are presenting ourselves with simplified editions of immediate matters of fact. When we examine the primary elements of these simplified editions, we shall find that they are in truth only to be justified as being elaborate logical constructions of a high degree of abstraction ([1925] 1967, p. 53).

Considering the world as a collection of objects with various attributes at various locations in space may seem natural, but it is an elaborate abstraction. The apparently obvious notions embedded in giscience representations of space, place, region, and so on, and embedded in GIS, are baroque and misleading abstractions (Fisher, 1997, is one author who recognized this). How then can we think about space, without reducing it to “the locus of simple locations” (Whitehead, [1925] 1967, p. 53), as giscience does? One starting point is Jim Blaut’s paper “Space and process” (1961), which emphasizes how there can be no such thing as space devoid of process: “every empirical concept of space must be reducible by a chain of definitions to a concept of process” (1961, 2, emphasis in the original). On this basis, Blaut finds wanting a range of methodological approaches in geography that he argues rely on nonprocessual notions of space. Of particular relevance to giscience is that “[a]ll of these views assume that structure and process are two different things, which they are not; structures of the real world are simply slow processes of long duration” (1961, 4, emphasis added). While Blaut refers to Whitehead only in passing, a more sustained engagement is found in David Harvey’s Justice, Nature, and the Geography of Difference (1996, pp. 207–327), where he develops a relational account of space, time, and place. Of central importance is that “[s]pace and time are not, therefore, independent realities, but relations derived from processes and events” (Harvey, 1996, p. 256), so that “an understanding of process must precede or parallel an understanding of space and time” (1996, p. 258). This leads to the conclusion that

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the traditional dichotomies to be found within the geographical tradition between spatial science and environmental issues, between systematic and regional (place-bound) geographies appear totally false precisely because space-time, place, and environment are all embedded in substantial processes whose attributes cannot be examined independently of the diverse spatio-temporalities such processes contain3 (1996, pp. 263–64).

For our purposes the key is that space, time, and place are inseparable from process. Zigzagging through Whitehead as Isabelle Stengers recommends,4 the aspects of process philosophy that jump out at me are its notions of what constitute things and how they can be characterized. It is striking from a geographical (and giscience) perspective that both spatial continuity and pattern are central to Whitehead’s understanding of what we would in everyday language call things or objects or beings. For Whitehead all of these are “societies” of events, where events occur together in association (“extensive connection”) with one another, to continually become a persistent thing, recognizable as such: Thus the theory of objects is the theory of the comparison of events. Events are only comparable because they body forth permanences. We are comparing objects in events whenever we can say, ‘There it is again.’ Objects are the elements in nature which can ‘be again’ (1920, p. 144).

In later work he stops referring to objects, and focuses on how events endure: 3

4

Disappointingly, he continues, “[t]he implications for the philosophy of geographical thought are immense, but I do not here have the space or time to make a place to explore them in any detail” (Harvey, 1996, p. 264) The scrupulous inclusion of space, time, and place suggests that Harvey is making a (rather dry, not especially funny) joke. There really ought to be a footnote leaving the details as an exercise for the reader. “[Y]ou cannot read Process and Reality from the first to the last page, in a linear manner, but must zigzag, using the index, being lured to come back to something you recollect but which had remained mute and now takes on a new importance, taking the leap that you have just felt is possible” (Stengers, 2008, p. 109).

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Endurance is the repetition of the pattern in successive events. Thus endurance requires a succession of durations, each exhibiting the pattern ([1925] 1967, p. 127).

Still later, pattern is also critical to how entities (understood as societies of related events) may be internally structured in more or less complex ways: The notion of a society which includes subordinate societies [. . . ] with a definite pattern of structural inter-relations must be introduced. Such societies will be termed ‘structured’ ([1927] 1978, p. 99).

With these ideas in mind, it is worth revisiting the relationship between spatial patterns and processes (see §Relative Space in Quantitative Geography, Chapter 2). Quantitative geographers have always emphasized spatial pattern, although pattern is an ill-defined and slippery concept.5 Geographers are not alone in failing to define the term: According to mathematicians Grünbaum and Shephard, “[t]here seems to be not a single instance in the literature of a meaningful definition of ‘pattern’ that is, in any sense, useful” (1987, p. 261). Those mathematical approaches that do exist, rely on the idea of the symmetries of an arrangement of geometries. Symmetries are the transformations— the translations, reflections, or rotations—of the geometries that map them back on to themselves. This definition depends on precise repetitions of the elements in an arrangement, and is applicable to settings like tiling (Grünbaum & Shephard’s focus) or the design of patterns like wallpapers. In the empirical world—whether natural or social—precise repetition is rare. Rather, we observe recurrent similarities such that “we can say, ‘There it is again’ ” (Whitehead, 1920, p. 144) and identify those similarities as things, amid what would otherwise be random noise or 5

We avoided providing a clear definition several times in Geographic Information Analysis (O’Sullivan & Unwin, 2010). The lack of a clear definition of pattern is shared with cluster (see §Regionalizing Space, Chapter 5) and the concepts have a great deal in common: Both are repetitions in observations, the former based on geometry or spatial arrangement, the latter on qualities or measured characteristics.

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flux. Whitehead is not offering a definition of pattern with this “there it is again” formulation, but it is a workable concept for our purposes, and also fits well with Galton’s notion of processes as “patterns of occurrence, whose realizations are states or events exemplifying those patterns” (2018, p. 41). Accepting that a precise definition is elusive, it is still possible to characterize patterns in the spatial configuration of things. Early work in quantitative geography pursued this goal (Dacey, 1964), often inspired by the central place theory of Christaller (1966).6 The idea, since developed in much more detail in spatial analysis, is that patterns are departures from randomness, where randomness is defined as the absence of spatial biases in the locations of events or their spatial relations to one another. Bias in the locations of events are termed first-order effects, while biases in their relative locations are second-order effects (see O’Sullivan & Unwin, 2010, pp. 106–8). Respectively, these reflect overall spatial trends in the occurrence of events, and in the interactions between events whether these are mutualistic or competitive. This framework is most easily understood in the context of point patterns, where points are formally referred to as events, and patterns are produced by mathematically or computationally defined point processes. The central concern of point pattern analysis and other branches of spatial analysis is the question, “what (posited) kinds of process could yield this kind of (observed) pattern?” Thus, while spatial analysis is often criticized for a naïve emphasis on instantaneous snapshots of the world (i.e., patterns), it is actually much more concerned with the kinds of processes that may or may not give rise to observed spatial configurations of events. The important thing, as already noted (see Chapter 2), is that the purpose of characterizing patterns is not the identification of patterns for patterns’ sake, but for the clues to underlying processes that might have led to those patterns being observed.

6

Apparently oblivious to more sinister aspects of Christaller’s work in its relationship to the ideologies of Nazi Germany (see Barnes & Minca, 2013; Kobayashi, 2014).

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For some years in the 1960s, relating particular patterns to unique processes that must have produced them was a holy grail of quantitative geography. But it turns out not to be so simple: In general the same or similar processes unfolding in different contexts may yield similar, or very different patterns; conversely, very different processes can yield similar (static) patterns (Olsson, 1969). This means—unsurprisingly— that there is no simple one-to-one relationship between processes and patterns. However, we can reasonably, if less ambitiously, expect there to be recurrent relations between processes and patterns, since, if this were not true, it would be hard to conceive of a geography (or any other science) that would be of any use at all for understanding the world. If there are no somewhat coherent relations between processes and patterns, then all would be chaos and all explanation would be impossible. To the extent spatial analysis and modeling are part of giscience, materials for processual computational representations (however abstract) might then already be available. The injunction that the “[attributes of] substantial processes cannot be examined independently of the diverse spatio-temporalities [they] contain” (Harvey, 1996, p. 264) must be taken seriously here: It is after all why no one-to-one mapping between processes and patterns exists. The key is that the spatio-temporalities of processes are diverse not singular. Singular, reductive approaches in giscience have tended to attract the strongest criticism of other geographers, their skepticism often motivated by understandings of the world grounded in more plural process-oriented perspectives. Picking out single sets of attributes for spatial analysis is to unpack processes in a way that holistic process philosophies argue against. Processes may exhibit many spatiotemporalities, and it is necessary to recognize this in any attempt to examine processes through spatial analysis. Local spatial statistics were not developed with this critique in mind, and it is important not to overstate their accomplishments, but it is nevertheless worth noting their potential for revealing the multiple scalar spatio-temporalities of processes (Fotheringham, 1997; Johnston et al., 2014), especially if diverse distance metrics are deployed, including metrics that are not geometry-based (Deza & Deza, 2016).

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Related Strands in Geographical Thought Perhaps because of its terminological difficulties, perhaps because of its slightly jarring theological overtones,7 or perhaps for its lack of any suggestions on how to proceed, Whitehead’s process philosophy remains relatively obscure. I have emphasized it for its thoroughly processual “process all the way down approach” which shows that it is possible to think of the world as composed only of process. It also demonstrates that doing so requires thinking relationally, and also recognizing that space and time are bound up with one another. It would be wrong to suggest that Whitehead’s process philosophy carries much sway in geography. Nevertheless, an important inference from Whiteheadian and other process philosophies that is shared with other, more influential frameworks, is the dissolution of any clear distinction between the human and nonhuman. The human and nonhuman are the same kinds of entities, each capable of acting in the world in various ways—or if not acting, then at least of having effects. More broadly, this notion dissolves the nature–culture and mind–matter dualisms, foundational to modernist and postmodernist thought alike. Moving beyond unproductive stand-offs between rationalist modernism on the one hand, and relativist postmodernism on the other, in We Have Never Been Modern (1993) Latour suggested it was more useful to recognize that these share a commitment to the human–nonhuman dualism, and that this is where the problems of modernist rationality lie, a claim similar to Whitehead’s diagnosis of the ills arising from the fallacy of misplaced concreteness. Whether or not we accept the agency of nonhuman entities is a distraction here (see, e.g., Kirsch & Mitchell, 2004). Instead, I want to briefly explore another dimension to breaking with nature–culture dualisms, the notion of flat ontology, which we have already encountered (see §The End of Scale? Chapter 3). Assemblage theory (de Landa, 7

Sample text: “It is as true to say that God is one and the World many, as that the World is one and God many” (Whitehead, [1927] 1978, p. 348). This aspect of Whitehead’s thought kept theologians interested in his philosophy when few others were. In an odd coincidence, a major advocate of process theologies grounded in Whitehead’s thinking was philosopher Charles Hartshorne, brother to geography’s Richard.

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[2006] 2019, drawing on Deleuze & Guattari, 1987), object-oriented ontologies (Bryant et al., 2011; Harman, 2018), new materialisms (Bakker & Bridge, 2006; Bennett, 2010; Kirsch, 2013), along with actor-network theory (see §Relations Do Not a Network Make, Chapter 6), earlier work by Donna Haraway (1991), and Indigenous thought (e.g., Stewart, 2020) can all, to some degree (rightly or wrongly), be characterized as flat ontologies (Ash, 2020). A flat ontology perspective argues that things can exist and interact and act on one another regardless of their type or scale or mode of existence. As Bryant puts it, “entities at all levels of scale, whether natural or cultural, physical or artificial, material or semiotic are on equal ontological footing” (2011, p. 279). In a flat ontology ideas and concepts, technologies, people, collectives, inert matter, places, and so on should be treated as having equality of being, and can be studied and deployed in explanatory accounts on an equal footing with one another. This can sound strange at first, but it is consistent with how we develop accounts of how things come to be. When, for example, we seek to explain the (perhaps surprisingly rich) coffee culture across Australia and Aotearoa New Zealand, we might end up considering (among other things) the large-scale irrigation schemes on Australia’s Murray River in the 1950s; U.S. restrictions on immigration from Southern Europe after the early years of the 20th century; the invention of the piston-driven espresso machine in 1945; the Melbourne Olympic Games of 1956; along with various specific local characters, cafés, and places. Each of these, whether people, machines, events, large-scale movements of people, or whatever is equally a thing that can have effects in the world and contribute to an explanation. In some other context, where something else is to be explained, we might assemble a different set of things, and emphasize a different set of relations and effects, even in the same spacetime setting—again, diverse entities may exist amid multiple unfolding processes. The provisional nature of any particular, context-specific, flat ontology might be a sticking point for anyone keen to develop universal explanations. In some frameworks, such as assemblage theory, each assemblage of interacting entities is unique, and not representative of a class of similar things: “the ontological status of assemblages, large or small,

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is always that of unique, singular individuals” (de Landa, [2006] 2019, p. 29),8 reflecting that perspective’s origin in theory grounded in difference (Deleuze, 1994). This may also make more generalizable theorizing difficult. Flat ontologies can also be questioned if they are construed as a refusal to recognize imbalances in power among entities seen as operating on some kind of level playing field (see Amin & Thrift, 2005; Smith, 2005). These wider, broadly political arguments are not a primary concern here. More immediately relevant is whether entities in flat ontologies possess internal structure. If not, then it is hard to see how they evade accusations of a willful refusal to recognize complexity in the world, or for that matter how we can approach explanation of different phenomena in the same setting by developing context-specific flat ontologies, as suggested above. Returning to Whitehead, societies of actual occasions (i.e., entities) can be intricately internally structured, since as we have seen, they may include “subordinate societies [. . . ] with a definite pattern of structural inter-relations” ([1927] 1978, p. 99). Furthermore, he continues, they provide an environment in which their constituent entities can persist, and may also exist in an environment that allows for their own persistence: A structured society as a whole provides a favourable environment for the subordinate societies which it harbours within itself. Also the whole society must be set in a wider environment permissive of its continuance ([1927] 1978, p. 99).

Whitehead’s metaphysics envisages an intricately, often hierarchically structured world. Given that societies are systems of extensive connection, the implication seems to be that hierarchical structure will be expressed spatially. Assemblage theories are also clear on this point. For example, in A New Philosophy of Society, de Landa argues that assemblage theory, “starting at the personal (and even subpersonal) scale, climbs up one scale at 8

Page references for A New Philosophy of Society, first published in 2006, are to the 2019 Bloomsbury Academic edition.

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a time all the way to territorial states and beyond” ([2006] 2019, p. 5), which is seemingly at odds with the notion of flat ontology (see also the discussion in §The End of Scale?, Chapter 3). De Landa is careful to explain that scale is not only to be interpreted geometrically, that is, extensively in his work, but may also relate to other intensive properties of assemblages than their geographical extent. This distinction is set out in more detail in earlier work (de Landa, 2002; see also Escobar, 2007). As de Landa is setting out a philosophy of society, while Whitehead is describing an ontology of the material world, some divergence on this might be expected (compare Cox, 2021), given the spatial discontinuities across which social relations may nevertheless hold.9 In any case, in both systems, ontological flatness is among entities or assemblages, not necessarily within them. Meanwhile, other flavors of flat ontology are more ambiguous on the matter of hierarchy and internal structure (Ash, 2020, references wider debates on this question).

Postscript: Process in General and Process in Particular Much of this overview has been of a rather general nature. Maybe it is not so hard to accept the idea that all is process, and that permanent features are illusions. But, in practice, many things of interest are permanent enough—thing-y enough—that it is pragmatically useful to treat them as such. But while an earth scientist, meteorologist, or economic geographer might welcome geographical computing tools that take process seriously, it is hard to imagine a local government administrator tasked with maintaining street furniture getting excited about the idea that lamp-posts are really slow-moving processes. It may still be useful then to recognize things and processes as different aspects of geographical phenomena, even if—on some level—it is wrong. Put another way, we may accept as true the proposition that all is process, that the only enduring thing is flux. But in particular contexts at particular times and places, we can consider particular processes as acting 9

Or perhaps, since even virtual relations are constituted by physical connection via wires, optical fiber, electrons, photons, and so on, the apparent macroscopic discontinuities in social assemblages are connected from a Whiteheadian perspective.

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on more or less enduring objects to change their properties while their identity persists. While accepting process in general, we investigate particular processes and their effects in contexts defined both by processes and collections of interrelated entities. This perspective underpins the simulation modeling approaches discussed in later sections.

THE PLACE OF COMPLEXITY THEORY The title of this section refers to a paper by Nigel Thrift who suggests that complexity is “a body of theory that is preternaturally spatial” (1999, p. 32). It is thanks to this aspect of complexity theory that geographers of a computational bent may be surprisingly well placed to take on board the abstract metaphysical ideas discussed above. Loosely speaking, complexity theory is a set of concepts and approaches that aims to understand the shared characteristics of complex systems. What makes a system complex remains poorly defined. Roughly speaking, a system is complex if it is composed of many interacting elements of several kinds. The terms “many” and “several” are vague, but complex systems are not like gases, composed of extremely large numbers of similar elements; nor are they small systems with only one or two elements. Rather they are systems of middling to large size characterized by “organized complexity,” which Warren Weaver (1948) prophetically suggested might be amenable to analysis using novel computing methods. An outgrowth over subsequent decades from dynamical systems theory (von Bertalanffy, 1950), cybernetics (Wiener, 1948), and related fields such as artificial intelligence, complexity theory aims to understand how complex systems can be more than the sum of their parts, or as Anderson (1972) pithily puts it, how “more” is not simply more, but can become “different.” The notion of systems of organized complexity maps nicely onto Whitehead’s societies of actual occasions or de Landa’s assemblages. For example, immediately after describing assemblages as (potentially, perhaps even often) hierarchically structured by (geographical) scale, de Landa goes on to say that “[i]t is only by experiencing this upward

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movement, the movement that in reality generates all these emergent wholes, that a reader can get a sense of the irreducible social complexity characterizing the contemporary world” ([2006] 2019, p. 5). It is clear from his book’s subtitle, Assemblage Theory and Social Complexity, and earlier work (see de Landa, 1997) that what de Landa means by complexity relates to the nonlinear dynamics of complex systems. Or again, Robinson (2005) suggests that Whitehead’s process philosophy and de Landa’s inspiration, Deleuze’s philosophy of difference, could form a basis for a “metaphysics of complexity” (see also Shaviro, 2009; Connolly, 2011).10

Getting to Grips With Complexity I suggested two decades ago that “[c]omplexity is hard to pin down” (O’Sullivan, 2004, p. 283). It hasn’t gotten any easier in the meantime. Good general overviews include Melanie Mitchell’s Complexity: A Guided Tour (2008), and Coveney and Highfield’s Frontiers of Complexity (1995), or for more critical accounts see Helmreich (1998), Williams (2011), and Li Vigni (2022). For present purposes, complexity is probably best understood through the recurring characteristics of complex systems that have been uncovered, some of which are considered below. This list does not aim to be definitive, and the definition of a complex system remains fuzzy (Ladyman et al., 2013). Complex systems exhibit self-organization or spontaneous order without any top-down centralized control (Phillips, 1999; Kauffman, 1993; Allen, 1997; Portugali, 2000). Although a system is composed of many elements relationally interacting in various ways, the overall outcome is comprehensible as a unified system. Whatever order enables the system to be perceived as coherent in this way is not imposed centrally but emerges from the varied interactions among elements. Such emergence is sometimes accorded a somewhat mystical status, but it’s easy to get past this when we consider that the alternative is a world of unending chaos where nothing coherent of any kind would exist. 10Other metaphysics

Byrne (1998).

are available! For critical realist takes, see Harvey & Reed (1996) and

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If spontaneous order and emergence give us coherent entities, then adaptivity is required for them to persist. The environment of any entity is unlikely to be stable, so it is necessary for entities to adapt and change so that they persist. The combination of spontaneous order with adaptivity gives us a complex adaptive system often considered the paradigmatic object of study in complexity science (Levin, 1998). All kinds of things from cities, to people, to species, to markets, to storms can usefully be considered complex adaptive systems, and the focus of interest is often what processes or behaviors they engage in to maintain their existence. A complex adaptive system is effectively one of Whitehead’s permanences or a society of actual occasions. A commonly observed dynamic in complex systems is the existence of positive feedbacks. These are changes that a complex system causes, which are amplified when they occur, causing further changes of the same kind. Positive feedbacks may be important to the maintenance of environments in which a particular complex adaptive system can persist. Negative feedbacks are also observed, but tend not to be emphasized in complexity science, given their association with equilibrial steady states, which are central to less dynamic scientific approaches. Even so, balancing positive and negative feedback effects is usually vital to the persistence of any complex adaptive system. Positive feedbacks are often associated with path dependency, where once a system sets off down one development path, the future is a function of the previous history of that path (Arthur, 1994). The immediate future of simple (noncomplex) systems, by contrast, is determined only by the immediate state of things, not by a whole history. In geographical contexts, path dependency is often also place dependency, and is most easily understood in terms of examples like Silicon Valley where the accumulated technical expertise concentrated in one place positively reinforces a tendency for more expertise to accrue in that place. In his engineering perspective on complexity Holland (1998) emphasizes spontaneous order and emergence, but then argues that emergent entities will further organize into nested hierarchies of more complex entities. This is strongly reminiscent of de Landa’s account of assemblages ([2006] 2019) and closely related to Herbert Simon’s The Architecture of

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Complexity (1962) (see §Scale as Hierarchy, Chapter 3). It also relates to the idea of complex systems as “middle-sized,” since large, highly complicated systems necessarily consist of smaller collections of middle-sized systems.

Reflecting on Complexity Baldly listed like this, the characteristics of complex systems, and hence of complexity science, may not seem to amount to much. What phenomena in the world aren’t complex in one or more of these ways? And if everything is complex, is complexity science anything more than the study of “interesting stuff” (see Horgan, 1995) ? In an important sense the value of complexity science is not ontological, but epistemological. Where much scientific effort over centuries has been dedicated to a reductionist program, often based on crude simplifications,11 complexity science signals an intention to take more seriously the messiness of real systems. While much work in complexity science, seemingly contrary to this high-level goal returns to simplified models, the focus of attention is on how complicated behaviors can arise even in such simple systems. Even when abstracting away some complication, complexity science welcomes the messiness in, making it the subject of study. As noted, this list of patterns of behavior or properties of complex systems is not definitive or exhaustive. Nor are any of these properties unambiguously defined. This is not surprising, given the rather fuzzy realm in which complexity theory operates, across disciplines. What matters is the commitment to exploring these kinds of behaviors, focusing on dynamic behavior rather than on fixed sets of measured attributes of given entities. These complex system properties also have recognizable counterparts in the process philosophy metaphysics we have been exploring and in empirical phenomena in branches of geography and other disciplines. Self-organization, emergence, and adaptivity are necessary precursors to the existence of entities we can study. Landforms, cities,

11 Memorably lampooned in the phrase “consider a spherical cow.” See also Stellman (1973).

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regions, cultures, neighborhoods, and so on can all be thought of as complex adaptive systems that self-organization, emergence, and adaptivity combine to produce. Taken together, complexity behaviors can explain— or at least describe—how such permanences persist. The attempt in complexity theory to take these behaviors seriously helps account for how successfully it has traveled between disciplines (Thrift, 1999). It also helps make a case—rhetorically at least—for the universality of the patterns of behavior complexity theory aims to explain. Yet we must be cautious in the face of often overly ambitious claims of complexity theory. Things have calmed down since the early 1990s hype, with much of the excitement of that period since passed down to network science, big data, and data science. It is certainly possible to argue that complexity promises more interesting geographical insights than big data (O’Sullivan, 2018), but more than anything what complexity theory offers is a warrant for the panoply of approaches and methods so characteristic of geography. This should not be surprising, given that geography as a discipline also aims to be holistic and range across scales, processes, and relations. While simulation models remain a dominant approach in work on complexity (and are the focus of the next section), they are evidently insufficient to the kinds of questions complexity theory raises. If processes that matter can range from the microscopic to the global, and from the chemical through the biological, to the social and cultural, then while simulation models can potentially provide an overview, understanding the details will always require deeply grounded empirical work too.

SIMULATION MODELS Complexity’s origins in the more mathematical sciences have meant that even when the subjects of study are far removed from physics, the preferred approaches are mathematical, or most often, computer simulation models. Simulation modeling is a huge topic in itself, well beyond our present scope. The topic of simulation and its relation to contemporary science and indeed contemporary life more broadly is vast—think of

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the role of global circulation models in relation to climate politics, macroeconomic models in relation to government economic policies, or model-based forecasts of the impacts of COVID-19 to pandemic response. A comprehensive consideration of simulation modeling would have to cover topics including model verification and validation, other forms of model evaluation, and the social contexts in which models are developed and used (Weisberg, 2013; Winsberg, 2010; Edwards, 2010). My narrower focus here is on simulation models as representations of geography, particularly in the context of the reflections on process philosophies and related ontologies earlier in this chapter. A wide diversity of types of simulation model exists from conceptual models, through physical, and empirical (or statistical) models, to more dynamic simulations encompassing systems dynamics models, and complex spatially explicit simulations (see O’Sullivan & Perry, 2013, pp. 1–11, for a discussion). I consider only the last of these categories, spatially explicit simulation models—specifically cellular automata and agent-based models—in any detail as these seem to hold the most direct relevance for geography.

Cellular Automata The paradigmatic representation of space as an always unfolding process is the cellular automaton (CA). CAs rely on a fixed model of space, although it is worth considering whether that space is absolute, relative, relational, or even something else again (see §Prospects for Relative/Relational Giscience, Chapter 2 and also Takeyama & Couclelis, 1997; Couclelis, 1997). A CA is a discrete representation in space and time of a spatially extensive system of elements called cells (Burks, 1970; von Neumann, 1966; Wolfram, 1983). Cells are arranged in a regular lattice, most often in geographical cases in a two-dimensional grid. The lattice defines for all cells some neighborhood of other cells. Typically, the neighborhood of a cell is some number of other cells nearest to it in the lattice. In a twodimensional grid this will usually be either the four orthogonal neighbors or the eight immediate neighbors (four orthogonal, and four diagonal).

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A CA also has a set of defined, allowed cell states, one of which every cell is in at any moment in time. A set of transition rules determines what will be the next state of that cell, based on the current state of a cell and the current states of its neighbors. Time, like space, is discretized so that cell state transitions occur as clock time in the CA advances. Cell state updating may be simultaneous (synchronous), or sequential, according to some ordering principle (asynchronous). Either way, the overall system state is fixed between updates. As a CA runs, it produces a series of snapshots, but stepping back a little it can be viewed as a continuously unfolding dynamic process. Crucially, recurrent structural or aggregate features of the system are usually of more interest than the states of particular cells. The simplest possible CA is a one-dimensional line or ring of cells, where each cell has two neighbors, one on each side, and the allowed cell states are 0 or 1 (dead or alive, off or on, or however we wish to label them). This structure yields eight possible configurations of a cell and its neighbors,12 and a deterministic transition rule defines for each of these states what the next state of the cell will be. Since each of the eight neighborhood states can lead to the next cell state being either 0 or 1, there are 28 or 256 possible CAs with this structure. If we consider only cases that are different under symmetry, and which do not have the neighborhood state 000 (which Wolfram, 1983, calls “quiescent”) transitioning to cell state 1, this number reduces to 32. One-dimensional CA are easily illustrated in static two-dimensional form as seen in Figure 8.1 where all 32 of the possible CAs with this structure are shown. The initial system state in each panel is a random sequence of 0s (in white) and 1s (in black) arranged vertically at the left-hand side, and each model tick produces a new system state from left to right. Even these simple examples yield surprisingly varied behavior, such as the triangular (space-time) regions seen for rule 122 among others. The rich behavior of such simple, deterministic systems is intriguing and surprising (Couclelis, 1988), and the unpredictability of the state of any specific cell at a chosen time after initialization is also unexpected. 12 A

neighborhood consists of three cells, the cell itself and two neighbors. Each may be in one of two states, giving 2 × 2 × 2 or 23 possible neighborhood states.

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Figure 8.1. Evolution of the 32 one-dimensional cellular automata studied by Wolfram (1983). Orientation is such that evolution of the system state is from left to right. Labels are the decimal number formed from the binary code also shown, which is the transition rule as a series of binary output bits for each input neighborhood state 111, 110, 101, and so on down to 000. This notation is due to Wolfram (1983).

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Figure 8.2. Evolution (from left to right) of the one-dimensional cellular automata with transition rule 110, which has been shown to be capable of universal computation (Cook, 2004).

In fact, mathematicians have shown that at least one such simple system is capable of universal computation (Cook, 2004; see Figure 8.2). This means that arbitrarily complicated behavior can arise depending on the initial state and size of the system, and also that while the general evolution can be anticipated, local prediction of its state over time is impossible: The system must be run to observe what happens in detail. For geographers, who are usually concerned with phenomena in (at least) two spatial dimensions, the patterns produced by one-dimensional CA are of limited interest, although they might potentially represent advancing fronts of fire, infection, erosion, or other contagion. Unfortunately, moving to two dimensions makes illustrating simulations on the page difficult, as only snapshot views can be provided. Simple examples of two-dimensional CA systems are Conway’s Game of Life (see Gardner, 1970; Berlekamp et al., 1982, and Figure 8.3) and voter models (see Kimura, 1953; Weidlich, 1971; Clifford & Sudbury, 1973, and Figure 8.4). The game of life is a two-state CA, where cells change state depending on their current state and the state of their eight neighbors in the lattice. A cell currently dead comes alive if it has three alive neighbors, otherwise it remains dead. A cell currently alive remains alive if it has two or three alive neighbors, otherwise it dies. State changes are synchronous. The resulting dynamics are richly varied. A game of life configuration often

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Figure 8.3. Twenty consecutive time steps of the Game of Life CA on a 50by-50 lattice, reading from left to right, top to bottom. A glider circled in the first panel moves along the line shown in each panel, advancing one lattice position northwest every four ticks.

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Figure 8.4. Twelve consecutive time steps of a three-state voter model CA on a 50-by-50 lattice, reading from left to right, top to bottom.

includes spontaneously emergent blinkers and spaceships. These are small localized patterns of live cells that regularly cycle through a repetitive sequence of configurations, respectively, in place, or while moving across the lattice.13 The existence of such higher-order entities in the game of life is not immediately apparent from a description of the transition rules, but the rules sustain their emergence and persistence. John Conway, the mathematician who devised the life CA, was searching for a simple set of rules that would exhibit this kind of rich behavior, so it is inaccurate to claim that there is something mystical about these phenomena given the

13A

simple demonstration of the operation of these rules, which is also rather moving if you have spent much time observing game of life configurations, can be seen at https: //xkcd.com/2293. This example features a glider like in Figure 8.3.

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explicit intention of a designer. Even so, the persistence of recurrent patterns and motifs amid what at first glance appears as chaos is in tune with the processual worldview, where all things are processes unfolding. The game of life can be loosely linked with ideas in population ecology where survival depends on space being neither too crowded nor too sparsely populated. The generally interesting behavior of systems built on similar “Goldilocks” transition rules has been confirmed by other examples (de la Torre & Mártin, 1997; Evans, 2003; Peña & Sayama, 2021). The game of life isn’t an attempt to represent anything so much as it is a thing in itself. Voter models are a better example of a class of CA that offer a starting point for direct representation of competition across space. Here cells may be in a number of states (the example in Figure 8.4 has three states). Each cell changes state to match that of a neighbor picked at random. Variants may feature synchronous update or random update of only some cells each generation, or allow different neighborhood sizes (perhaps at greater distances), or different strengths of different states in competition with one another. The snapshot progression in the figure does not convey well the fluid, dynamic nature of the evolving map that the iterative updating of cells produces. In its simplest forms the voter model can be mathematically analyzed in great detail (see O’Sullivan & Perry, 2013, 78–83 for an accessible discussion), but for present purposes the emphasis is on how regions of uniform state in the lattice persist while changing over time. Voter models can be readily interpreted as representations of real geographical processes, most obviously competition and succession in ecological systems (Itami, 1994), or even the diffusion of ideas in social systems (the origin of the voter designation). Applications of these and other CA as representations of actual geographical systems tend to be much more complicated than these examples (although, see Wesselung et al., 1996). Available cell states are likely to be more varied. In a land-use context, for example, various densities of commercial, industrial, and residential development might be represented, along with agricultural, parkland, and infrastructure designations (White & Engelen, 1997). The rules governing how cells transition between states can easily become very complicated. In fact,

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often, where we might hope for transition rules that encode socioeconomic and political processes, model builders have gravitated toward rules based on empirical statistical analysis of recent historical change in the system under study (Zhou et al., 2020; Mustafa et al., 2018; Aburas et al., 2017). Thus, relative probabilities of transition from a given initial state to a variety of possible new states, contingent on the nearby presence of cells in various other states, may define CA transition rules. While this may make sense in the representation of physical landscape processes (e.g., landslides), it feels like a loss in the potential of such models to represent geographical processes more deeply, especially relative to early optimism about the prospects for bottom-up land-use models (Batty, 2005). I have suggested elsewhere how “human agency is in danger of becoming a ‘ghost in the machine’ ” (O’Sullivan, 2002, p. 271) in these cases. Other variations on the rigid constraints of classic CA models are possible. In geographical systems, of particular interest are possibilities that depart from a regular lattice. Instead of identical sites on a lattice, cells might be parcels of land, with a range of sizes and shapes (Lu et al., 2019; Stevens & Dragićević, 2007). Cells might also be organized into a hierarchy of levels (Vliet et al., 2009; Crols et al., 2015). In these less uniform spatial structures, it may be appropriate to think of the systems not as a lattice, but as a graph (O’Sullivan, 2001). Further, it may be that some cell state changes might rewire the neighborhood structure of that graph (see, e.g., O’Sullivan, 2009; Semboloni, 2000, and also §Small Worlds, Chapter 6). The boundary between such models and dynamic models of graph or network growth and change is a fuzzy one (Gross & Blasius, 2008).

Agent-Based Models The ghostly (non)presence of people and other (nonhuman) actors is an inherent feature of CA, when we consider that key active agents of change—people, institutions, and other actors—are missing from a grid-cell representation, appearing only implicitly as state changes of the

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cells on which they act. Agent-based models (ABM) are a more intuitively satisfying model architecture that can potentially address this absence. ABMs are much more loosely defined than CA. In an ABM the central concept is an agent. But the notion of an agent is a capacious one. In computer science a software agent is any piece of computer code capable of autonomous action in some computational environment (Wooldridge, 2002). A software agent has some internal state, and some set of behaviors that it enacts depending on the context in which it finds itself. Web crawlers, deployed by search engine providers to map hyperlinks among internet pages, are an example. Web crawler agents can read, store, and transmit information about websites, and also follow links on websites to visit other websites. In an ABM, software agents with similar capabilities represent entities in the world that taken together constitute the system to be modeled. These representational agents are endowed with states and behaviors that encapsulate our understanding of the possible states and behaviors of the entities they model. Overall, collections of software agents model collections of entities in the system of interest. This is not so different from a classic GIS representation except that agents have behaviors, and the capacity to change state as a consequence of their own behaviors and the behaviors of other agents in the model. But what does an agent represent exactly? The short answer is, “anything we want it to.” In the simplest of cases an agent might be a mobile organism with an (x, y) coordinate location (i.e., state) executing a random walk that results in changes in its state over time. A simple instance like this can be made more complicated by incorporating more state variables, such as age, size, available energy, and associated other characteristics like a home location. Movement behavior could then be motivated not randomly, but in response to an environment containing available food sources. The environment might also include other agents, and these might be immobile, like plants, or mobile like themselves, including agents of the same or other kinds (Boyer et al., 2012; Okuyama, 2009). In a different context, agents might be individual pedestrians navigating an urban environment (see Haklay et al., 2001, for an early example). In both these cases, the spatial character of agents might be

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represented purely by (x, y) coordinates, but the spatial aspect of agents is also entirely open-ended and agents might be regions, segments in a network, or have any other spatial realization deemed appropriate (Hammam et al., 2007), or perhaps none at all. To make things more concrete two simple canonical examples can be briefly described—not because they are necessarily good examples, but because they are easily described. First, is the Schelling model (Schelling, 1969, 1971; Sakoda, 1971, and see Figure 8.5), perhaps more correctly referred to as the Schelling-Sakoda model (Hegselmann, 2017) of segregation. This model posits agents of two different types positioned at sites on a regular two-dimensional lattice, with some vacant lattice sites available. In turn, agents decide if they are happy at their current location based on the mix of types of agents in their neighborhood, and if they are unhappy, they move to a vacant location. The usual formulation is some simple rule for determining happiness such as “at least a third of my neighbors must be like me,” that is, of the same type. When the model runs are based on this kind of preference for like neighbors, the collective outcome is often a strongly segregated pattern of the two different agent types. This behavior is robust under many elaborations, such

Figure 8.5. The Schelling-Sakoda segregation model. The initial random state (left panel) takes two rounds of relocations to segregate via the stages in the middle and right panels. Solid outlined agents are unhappy and move. Locations with dotted outlines were either vacated or have had a different agent move in since the previous step. In this example agents require half their neighbors to be the same as themselves to be happy.

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as relating available choices to household incomes, or introducing agents of more than two different types. The Schelling-Sakoda model is sometimes rather casually used to make arguments that strong patterns of urban ethnic segregation are not evidence of antipathies among groups or of systemic discrimination in housing markets (Fossett, 2006). It is safer to say that the model suggests that more evidence than a segregated pattern of residential housing is required to sustain arguments about housing preferences and discrimination. This is highly relevant to thinking about relationships between process and pattern in geography, a topic we considered earlier in this chapter. Whatever its (limited) merits as a realistic simulation of residential segregation, the Schelling-Sakoda model is often presented as an example of emergence, based on the supposed difficulty of predicting that strong aggregate segregation would occur based on “reasonable” levels of intergroup tolerance, although this is questionable (see Forsé & Parodi, 2010). Even so, and as intended, the model allows consideration of the relationship between individual motives and collective outcomes, or per the title of Schelling’s (1978) book, Micromotives and Macrobehavior. It also demonstrates the rhetorical power of simple models, and the linguistic slipperiness of the relationships between processes and their outcomes: In most accounts of this model, agents are said to “choose” to move to “preferred” locations. But when an agent moves out of a location with large numbers of unlike neighbors to a location with more like neighbors, this could as easily be interpreted as an outcome of discriminatory exclusion rather than an exercise of choice, and different kinds of conclusions would surely be drawn. A second simple model is the boids model of flocking behavior (generally attributed to Reynolds, 1987, but see Okubo, 1986 for earlier work). In this model mobile agents attend to the movement direction and speed of their near neighbors in the group, and in time, agents initially moving in random directions form coherent flock-like movement (O’Sullivan & Perry, 2013, 121–25, provides more detail). An example of the space-time trajectories produced by a model like this was shown in Figure 7.7. Variants of this model have been heavily used in simulating animal flocking, schooling, and herding movement, along with the

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movement of human crowds in various settings (Schellinck & White, 2011; Torrens, 2012). In these models, the notions of emergence and permanences are both relevant. Individual agents have no concept of a flock to which they belong, but acting only locally, the more or less permanent collective entity of the flock emerges. An apparent difference from the Schelling-Sakoda case is that the outcome is not a static pattern, but a mobile formation. However, variants of the Schelling-Sakoda model are capable of producing segregated regions with shifting boundaries, and the perception of emergent mobile formations is more one of spatio-temporal scale than a model feature per se. ABMs have been widely taken up in geography (Heppenstall et al., 2012). Given the flexibility of the approach, broad topical coverage might be expected, but applications have been dominated by land-use change (Matthews et al., 2007), residential choice (Huang et al., 2014), socioecological systems (Schulze et al., 2017), transport (Maggi & Vallino, 2016), and public health (Bian, 2004; Tracy et al., 2018). For the most part, these are planning settings, where there is a general trend toward complicated multicomponent simulations. Neither of the simple examples above includes detailed representation of an environment, unlike applied examples, when GIS datasets are often used to represent the environment in which agents interact. As simulations become more complicated, it can be increasingly difficult to understand their behavior in detail, and the promised broader insights from ABMs can seem elusive, replaced instead by specific findings in relation to specific places (O’Sullivan et al., 2016). This reflects the challenge of coming to general conclusions based on studies of specific places—one of geography’s core challenges—while also highlighting the limitations of single method approaches. An important consideration in geographical ABMs is the question of scale, obviously spatio-temporal, but also as in de Landa’s ([2006] 2019) formulation “intensive,” that is, in terms of groups or organizations of agents. For example, a would-be realistic model of residential relocation built on the basis of the Schelling-Sakoda model, in addition to a more representative geography based on streets and neighborhoods, requires close attention to time. It quickly becomes unwieldy to manage

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relationships between the timescales on which households make location choices, new developments are built, and neighborhoods change. The question also arises of the kinds of agents to include. Perhaps households are agents, but what about individuals within households, with differing priorities? And what about government agencies, real estate firms, developers, major employers, schools, and so on? Should each of these be represented, and if so, should they be collective agents or collections of many agents playing roles in the various organizations they collectively produce? There is a strong tendency in ABMs to assume that individual people are the atomic elements out of which all other actors are composed, but the logic of this position is rarely pursued, and in practice it is more common for various corporate actors to manifest as constraints on the choices of the agents explicitly represented in the model (O’Sullivan & Haklay, 2000). Thus, for example, in a model of land-use change, farmers managing their holdings might be agents, but the government agencies whose decisions create the context in which farmers act are controls on the model, the settings of which may be changed to explore different regulatory settings. From a flat ontology perspective, it might make more sense to represent corporate actors at various scales as agents, although this brings questions about how to model complicated organizations to the fore.

CA and ABMs as Geographical Process Models There are many simulation styles and approaches, only two of which I have considered here. In practice, simulation models in the real world— even in academic research settings—are complicated interconnected networks of many models of various kinds. ANT scholars would add that simulation models are only one actant in a network that governs the effects of particular simulation models in the world. But even naïvely considering a simulation model as a stand-alone representation of some slice of the world, they rarely exist in isolation. A statistical model of local climate might govern aspects of a model of land-use change that also includes cellular automata mechanisms to represent landscape change,

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an agent-based model to represent farmers, network elements to represent relationships among farmers, and systems of linked equations to represent macroeconomic effects. Single-mode models that are pure CA or pure ABM models are rare. Even so, it is reasonable to ask if CA or ABMs really take us beyond representing things and toward representing processes. In CA, we endow fixed spatial units (grid cells) with the capacity to change state over time, but otherwise, they are not that different from raster GIS. In ABM, we allow spatial entities to change state, to move around, perhaps even to mutate spatially, but again, we are dealing with spatial entities with added behaviors, not pure process. Overall, it might be argued, we have standard GIS entities with the capacity to change over time, contingent on their relations to other entities. On a more positive note, there is an act of representation in both cases where some things are collectively represented as process outcomes. The clearest example in the previous two sections is the flock that arises out of the representation of many individual agents and their behavior. The flock is not explicitly represented, but is an outcome of setting in motion a collection of agents representing other things. So this model can be understood as processual, but only after we take some entities as given—in the flocking model, the individual animals of which it is composed. This entity-based core is particularly apparent in ABMs. Some things (agents) are assumed to exist as things (not processes), but if we think of the simulation model not as representing those entities, but the collective behaviors, patterns, and outcomes that those entities may produce, then the ABM is processual. In the case of CA, where the substrate for things is an array of state variables, the case that the simulation is a process representation is perhaps stronger, and CA might be considered as spatial substrates in which processes unfold. If we attend to the representational acts involved in developing either kind of model, then the interesting change relative to other giscience representations is that the focus is on what interactions cause change in entities. Emphasizing change and interaction is very different from the data modeling work in deciding which attributes to record to describe more or less static entities in a GIS database. Furthermore, it is important

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to acknowledge that while process philosophies hold that everything is a process in continuous states of becoming, they also recognize that at particular scales, some processes manifest as more or less permanent entities—the permanences “that can ‘be again’ ” (Whitehead, 1920, p. 144). These considerations direct our attention to the salience of scale in thinking about the kinds of representations of what kinds of things in geography CA and ABM can be. In an ABM some chosen spatial and temporal scales that we are working at will tend to imply the existence of more or less persistent entities that will be represented as agents. While these agents are endowed with the capacity to change, we typically don’t question, once the model has been built, the persistence of the agents themselves. If it is the patterns of relations among agents that we are interested in, then this is useful, but from a more thoroughly process-oriented worldview, where the persistence of more or less coherent structures amid constant change is the thing to be explained, ABMs are assuming this question away. CA, being less assertive about the notion of entities, are more akin to a medium in which process unfolds, and might therefore be considered a more fully processual representation. In both cases, central to any question of the nature of the representations are questions of the intention of the various users, and contingent on those intentions, the scale and level of the intended representation, given the focus of any particular study (see also §Scale in Giscience, Chapter 3).

PROCESS AND PATTERN REVISITED Much more could be said about the merits of various simulation approaches in relation to process philosophies. Rather than disappear down that rabbit hole, I want to return to the role of pattern in learning from simulations. As we have noted, any hope that one-to-one matches between particular processes and particular patterns can be found is delusional. Yet, complexity theory, in posing broad questions about persistent emergent entities (complex adaptive systems), leans heavily on the observation of regularities across diverse systems. At the same time, process

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philosophies make clear that for things to be perceivable as things in the world they must endure, which requires “the repetition of the pattern in successive events” (Whitehead, [1925] 1967, p. 127), so that “we can say, ‘There it is again’ ” (Whitehead, 1920, p. 144). Thus, many of the epistemological challenges of simulation models boil down to questions of evaluating models via the patterns they produce relative to the empirical systems they claim to represent. One approach, originating in ecology, is pattern-oriented modeling (POM, Grimm et al., 2005; Grimm & Railsback, 2012). POM effectively engages the diverse spatio-temporalities of the processes in a simulation, by testing model outcomes with respect to multiple patterns: statistical (distributions of measured properties), temporal (time series of summary statistics), and spatial (configurations of outcomes). This is an important step forward from seeking one-to-one matches between processes and patterns, and as elsewhere in this chapter, it points to a need to investigate geographical phenomena of interest using diverse methods. From this perspective simple simulation models might appear more compelling than large, complicated, and messy ones. After all, simple models can convincingly demonstrate how little is needed to produce ordered, patterned outcomes: The self-organizing tendencies of matter at all scales are strong (Kauffman, 1995; Ball, 2011). The aphorism “everything is the way it is because it got that way,” often attributed to Thompson ([1942] 1992),14 is telling here. The intuition behind the aphorism is that spatial form reveals process, and, indeed, Thompson’s On Growth and Form ([1942] 1992) was one inspiration for early quantitative geographers’ enthusiasm for seeking explanation in spatial form (see Werritty, 2010). While such simplistic explanations from form are clearly unsustainable, an important lesson from taking process seriously must surely be that geographers still have much to learn from patterns across many space-time scales. 14The

phrase is an apt summation of On Growth and Form, but doesn’t appear anywhere in Thompson’s work! See Cosma Shalizi’s blog at http://bactra.org/notebooks/darcythompson.html. An example of the phrase being wrongly attributed is found in This Explains Everything (Brockman, 2013, pp. 172–73).

Chapter

Doing Giscience Doing Geography If you have made it this far, you’ve earned some brief reflections on all that has gone before.

COMMON GROUND: A SPACE TO THINK he principal conceit of this book is that geography and giscience share common ground in the shape of an array of big ideas (see also Thatcher et al., 2016). However differently these ideas have been taken up in giscience and in subfields of geography, because they are shared they create a space where conversations can take place and new ideas and understandings emerge. This is true even—perhaps especially—when it is clear that little beyond a word is actually shared, and the idea itself has been taken in dramatically different directions. I have explored some parts of this common ground—space, scale, place, borders and regions, relationality and networks, time, and process and pattern. For the most part it is clear that the giscience takes on these are less rich than those in geographical thought. This is hardly surprising.

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Human language with its fluid relations between words and meaning is a much more supple medium for exploring ideas in nuanced ways than is computer code. Further, once software is written, it is anything but soft. Systems are built on systems, and the engineering dictum “if it ain’t broke, don’t fix it” prevails. Belying the shiny newness of computers, there are parts of present-day GIS platforms whose original code was written in the 1970s.1 So space is implemented as coordinates and Euclidean distances; scale as a representative fraction; place as the difficulty of associating a label with coordinates; territory as polygons; and so on. And once the associated tools exist, they are used, and if they are good enough for many purposes, then why change? “In short,” as Eric Sheppard notes, “GIS as we know it is the end result of a particular evolutionary path that may or may not be the best possible path” (2001, p. 546). These effects are particularly powerful when they become sedimented into general purpose platforms in widespread use—as today’s geospatial platforms did three or four decades ago, leading to highly routinized kinds of geographical computing. While the dominance of the classic desktop GIS has been eroded in the last decade or so by web mapping platforms, many elements of the underlying architecture, associated data structures, and assumptions remain. I hope it is apparent that the common ground of shared ideas between geography and giscience is teeming with opportunities for developing and extending computational representations of geography. Some of those opportunities seem clear enough: Relational space and networks, and methods for visualizing approximations to their complex high-dimensional topologies, are well known. In fact, earlier quantitative geographers have been here before (Gatrell, 1983; Forer, 1978; Tobler, 1961). It mystifies me that such work has receded from the geographic mainstream, given its possibilities. I am not alone in thinking this: Miller and Wentz argued that [t]hrough the vehicle of GIS, many researchers are adopting the Euclidean model and its related analytical possibilities without realizing its assumptions or its alternatives (2003, p. 574). 1

To be fair, the same is true of all sufficiently old computing platforms.

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and that, [r]econsidering and expanding the geographic representation model underpinning both SA [spatial analysis] and GIS is an unexplored avenue for improving analytical capabilities of both (2003, p. 574).

Similar rich possibilities exist with respect to all the big ideas we have examined. It is unlikely that such exploration will lead to a new, generalized geospatial platform, a so-called “GIS/2” (Sieber, 2004), or really geographical information system, but we already have a generalized geospatial platform, and don’t really need another one.2 It would be great to fold some new ideas into the general platforms where this can be easily done (non-Euclidean space seems very feasible; see Bergmann & O’Sullivan, 2017), but this need not be a priority. The more urgent priority is that having once made tools for working with computational representations that offer more to geographers than geodetic precision and simple location, then through collaborative exploration still richer possibilities might emerge. Like others (see Cope & Elwood, 2009), Marianna Pavlovskaya emphasizes the importance of enhancing the capacity of platforms for handling qualitative relations for such developments, [t]he challenge is to open up GIS to qualitative research so that complex relationships, nonquantifiable properties, unprivileged ontologies, and fluid human worlds can be represented and better understood (2006, p. 2016).

I agree, but I also think that this position overemphasizes the qualitative versus quantitative dimension of the limitations of geospatial platforms (see also Sheppard, 2001; Plummer & Sheppard, 2001) over their more hidden, underlying inflexible geometric (cartographic) defaults. I am convinced that the task of “[r]eimagining and reconstructing GIS as a flexible tool for creating diverse human geographies” (Pavlovskaya, 2

Digital humanities scholars lacking a standard platform have found this lack to be a spur to creativity (Drucker, 2009).

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2006, p. 2016) —and not only human geographies—will depend on GISers taking geographical thought much more seriously than they have hitherto.

DOING GISCIENCE: REPRESENTATION AS PROCESS AND PRACTICE A major stumbling block for many critics of giscience is its failure to take seriously the problematic nature of representation. Refuting the notion that maps are in any way simple, unproblematic representations of the world lies at the heart of critical cartography, and getting to grips with the nature of the representational acts involved in geographical computing should be similarly central to any would-be critical giscience. The critique of giscience most conveniently encapsulated in the collection Ground Truth (Pickles, 1995) and the associated debates around that time led to the emergence of critical GIS (Schuurman, 1999). As I argued in the opening chapter, critical GIS has led to many projects that have demonstrated the viability of GIS as a platform for diverse geographic research, but this has happened without changing the computational tools and representations central to doing GIS. In Chapter 1, I tried to deflect or at least postpone this criticism by making clear first that there is no such thing as a perfect representation, and second that a better way of thinking about representations in giscience is as propositions (Krygier & Wood, 2009; Wood, 2010b). Alternatively (but relatedly) Kitchin and Dodge (2007) suggest that the important question is not what a map is (a spatial representation or performance), nor what a map does (communicates spatial information), but how the map emerges through contingent, relational, context-embedded practices (2007, p. 340).

Similarly, computational representations in geography—some of them maps, but many of them not—are constantly in a state of becoming, as practitioners grapple with how best to represent their ideas computationally.

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A substantial technical literature has emerged around “how maps work” (MacEachren, 1995) as representations, even as critical cartography has questioned the status of maps as representations. If we accept that the important thing about maps is how they emerge though practices (of data collection and collation, design, production, and so on), then similar ideas surely apply to computational representations of geography. If cartographers can develop guidelines for what kinds of visual variables, or color schemes, or fonts (and so on) work well or badly for conveying various kinds of geographical information (Bertin, 1967), then it is surely long past time for giscience to move beyond the limitations of the raster–vector debate (Couclelis, 1992),3 in reflecting on its representational practices. Other representations are possible, and while some of them have even been implemented, still more possibilities remain to be invented. But beyond raster and vector, few have been mainstreamed, and the advent of desktop GIS has narrowed the scope for making different kinds of representation while doing giscience, even in the face of vastly increased computational capacities (Gahegan, 2018). Changing giscience surely requires making different kinds of GIS, such as “geographical imagination systems” (the “gis” of Bergmann & Lally, 2021), not only using the same old GIS to do different things. There are few things more likely to date a book than setting out a research agenda, so I am wary of providing a list of desiderata for a more geographical giscience, nor is it my place to do so. Rather the collective efforts of geographers, GISers, and giscientists will determine what comes next. Even so, skimming over the preceding chapters, and without cross-referencing them directly, since they recur regularly in many places, some persistent themes emerge. We might start with one of the shibboleths of giscience, its First Law, that “everything is related to everything else, but near things are more related than distant things” (Tobler, 1970, p. 236). Instead of emphasizing the urge to simplify of 3

The doggerel Yes raster is faster / But raster is vaster / And vector. . . / Just seems more correcter attributed to Dana Tomlin by Clarke (2011, p. 77) is not wrong, as far as it goes, but the discussion of data models in giscience sometimes seems like it doesn’t get much further than this—at any rate, not in educational settings.

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this dictum’s original context, we might interrogate more closely possible meanings of “related,” “near,” and “distant.” Relative/relational space dominates geographical thinking, and is essential to any serious consideration of place, boundaries, and processes, yet relational models remain second-order representations in giscience. Dropping the insistence in many geospatial platforms that particular geodetic coordinate reference systems be rigidly applied, and allowing instead for user-determined coordinates (and the projections they imply), could greatly expand the variety of visualizable and computable spaces. Finding ways to recognize the fuzziness, ambiguity, porosity, and uncertainty of boundaries, and explore the implications of the fiat/bona fide distinction in geographical entities, has potential to open up new and different ways of seeing geographies. Good starting points already exist for all of these. Taken together, they might also set the stage for ways that processes, events, and patterns can be explicitly represented and described, so that the familiar entities of giscience become emergent, not fixed and pre-given. In sum, there is considerable scope for rethinking giscience as a kind of speculative geographical metaphysics. To repeat myself, many materials for enlivening the practice of computational representations of geographies already exist in the common ground between giscience and geography. There is plenty to work with in many corners of giscience as it already exists, albeit around the edges,4 and not conveniently at hand in standard platforms. None of this is to deny the insight that GIS is much more than the computer on the desk. It is simply to say that ideas that are implemented and embedded in code have particular force when it comes to doing GIS. The countermappers’ dilemma of only being able to operate in the terms that the system permits stands in the way of real alternatives. If platforms remain unchanged, then it will be hard to ask different questions.

4

Corners are where edges meet, so this may be a tautology. . .

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TOWARD DOING DIFFERENTLY The phrase “doing GIS” appears no fewer than 22 times in a paper by Wright et al. (1997a) which, read alongside a negative commentary by John Pickles (1997) and a crestfallen response from the authors (Wright et al., 1997b), emphasizes the challenge of taking both giscience and geography seriously. The question of what constitutes doing GIS is revisited by Matt Wilson (2017), who rightly argues, [l]oaded in that question is a series of assumptions about what it means to practice, and I think we can do more to broaden our vision of that practice as both technical and critical. This, of course, necessitates a shift in undergraduate and graduate programming (2017, p. 2).

I hope I’ve shown that one way to develop that “technical and critical” vision is to take the geographical in giscience more seriously, and for geography to take giscience more seriously also. As Wilson suggests, and as my own educational experience confirms (see Chapter 1), this will require new approaches to teaching.5 Outside isolated pockets, we have been at an impasse over this for decades. Wilson (2017) goes on to quote Pickles, writing of the 1990s that GIS students were rarely introduced to the prevalent debates about philosophies of science, social theory, and cultural studies [. . . ] In parallel, the technical possibilities for larger data-sharing and analysis were not taken up by most Marxist, feminist, and humanistic geographers (Pickles, 2006, p. 765).

Wilson wryly adds, “this reflection could be as easily made about our current moment” (Wilson, 2017, p. 8). Whatever is to blame for such “lines drawn, divisions articulated and reinforced” (2017, p. 8), Wilson’s concern is well-founded. Unsurprisingly, little has changed in the short time since, so it is high time to approach teaching giscience and geography differently. The doing of giscience and the doing of geography will 5

Perhaps even approaches that find this book useful!

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not change if we continue to teach them as fields apart. This applies with particular urgency to giscience, which should really “never again be quite the comfortable retreat for the technically minded” (Goodchild, 2006, p. 687), which it remains, in spite of the best efforts of critical GIS scholars. As I have noted, the representational palette of existing platforms is narrow, and tends to force all projects down particular paths, regardless of original intentions. But broadening the palette of available representations to enable new kinds of projects will only make a difference if we also broaden the training, both technical and critical, of would-be giscientists, so that they don’t (like me) have to write a book to get there! If the GISers, who become part of the overall GIS infrastructure of machines, ideas, practices, and modes of thought, remain unchanged, narrowly trained (as I was), it will not much matter how different the tools become.6 The narrowness of giscience has recently abated a little as libraries for handling the basics have developed in open computing environments— in “sandboxes” such as R, Python, and most obviously the web— enabling mixing, matching, remixing, and even “playful mapping” (Wilmott et al., 2016). These more open environments can foster more playful approaches to teaching giscience, perhaps even assisted by increasingly powerful coding agents. Purposeful play, exploring possibilities beyond the routinized geospatial requirements of states and corporations, requires engaging with ideas from across the whole gamut of geography, and expanding the kinds of questions we ask of students in their learning. Whether playful or serious (or both), it was just such explorations that led to community mapping by way of the Detroit Geographical Expedition and Institute (Warren et al., 2019) and feminist GIS (Timander & McLafferty, 1998; McLafferty, 2002) and its descendants, which remain the most sustained examples of doing GIS differently, along with closely related efforts in participatory GIS and countermapping. Again geographical thought can be a rich source of prompts to such creativity, alongside the increasingly fertile ground at the intersection of art, cartography, and visualization (Lally, 2022). 6

Anyone who has taught GIS will be familiar with the genius of students for framing every question as an overlay problem. They have learned too well!

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FINALLY. . . Astute readers will realize that these three reflections are alternative takes on the same argument. Geography and giscience curricula at all levels should explore the common ground that they share. There is no reason why an introductory GIS class cannot also be a class that critically examines fundamental ideas in geography, doing so beyond focusing only on the technical issues that arise in working with existing representations. Such exploration can be deeper and more extended at more advanced levels, but should be included from the outset. Questioning and changing the default geographical representations of giscience should be core to education in giscience, critical GIS, and geography. Ultimately, the goal should not be separate worlds of giscience, critical GIS, and geography but a giscience that is technical and critical, and above all, thoroughly geographical. Such a giscience would not need bridging to geography, it would be right there at the heart of it. At the end of the first chapter I suggested that geographical thought and giscience “can mutually inform one another to enliven a more thoroughly geographical computing.” I am excited to see what we come up with, together.

References Numbers in brackets following each entry are pages where the work is cited. Aburas MM, YM Ho, MF Ramli & ZH Ash’aari. 2017. Improving the capability of an integrated CA-Markov model to simulate spatio-temporal urban growth trends using an analytical hierarchy process and frequency ratio. International Journal of Applied Earth Observation and Geoinformation, 59, 65–78. [238] Adams B, G McKenzie & M Gahegan. 2015. Frankenplace: Interactive thematic mapping for ad hoc exploratory search. In Proceedings of the 24th International Conference on World Wide Web. International World Wide Web Conferences Steering Committee, 12–22. [99] Adams PC. 1995. A reconsideration of personal boundaries in space-time. Annals of the Association of American Geographers, 85(2), 267–285. [193] Adey P. 2017. Mobility. (2nd edn). Routledge. [180, 182, 204, 205] Agnew J. 1994. The territorial trap: The geographical assumptions of international relations theory. Review of International Political Economy, 1(1), 53–80. [119] Agnew J. 2011. Space and place. In DN Livingstone & J Agnew, (Eds). The SAGE Handbook of Geographical Knowledge. SAGE, 316–330. [101, 108] Agre PE. 2003. Hierarchy and history in Simon’s “Architecture of complexity.” Journal of the Learning Sciences, 12(3), 413–426. [50] Alexander C. 1965. A city is not a tree. Architectural Forum, 122(1), 58–62. [51]

257

258

REFERENCES

Allen JF. 1984. Towards a general theory of action and time. Artificial Intelligence, 23(2), 123–154. [187] Allen PM. 1997. Cities and Regions as Self-Organizing Systems: Models of Complexity. Gordon and Breach. [227] Amin A & NJ Thrift. 2005. What’s left? Just the future. Antipode, 37(2), 220– 238. [224] Anderson J & I Shuttleworth. 1994. Sectarian readings of sectarianism: Interpreting the Northern Ireland census. The Irish Review, 16(Autumn-Winter), 74–93. [129] Anderson PW. 1972. More is different: Broken symmetry and the nature of the hierarchical structure of science. Science, 177(4047), 393–396. [226] Andrews J. 1996. What was a map? The lexicographers reply. Cartographica, 33(4), 1–12. [113] Andris C & D O’Sullivan. 2019. Spatial network analysis. In MM Fischer & P Nijkamp, (Eds). Handbook of Regional Science. Springer. doi: 10.1007/978-3642-36203-3_67-1. [156] Arthur WB. 1994. Increasing Returns and Path Dependence in the Economy. University of Michigan Press. [228] Ash J. 2020. Flat ontology and geography. Dialogues in Human Geography, 10(3), 345–361. [223, 225] Ash J, R Kitchin & A Leszczynski, (Eds). 2019. Digital Geographies. SAGE. [8] Atkin RH. 1974. Mathematical Structure in Human Affairs. Heinemann Educational. [147] Atkin RH. 1981. Multidimensional Man. Penguin. [147] Bailey TC & AC Gatrell. 1995. Interactive Spatial Data Analysis. Addison Wesley Longman. [31] Bakker K & G Bridge. 2006. Material worlds? Resource geographies and the “matter of nature.” Progress in Human Geography, 30(1), 5–27. [223] Ball P. 2011. Nature’s Patterns: A Tapestry in Three Parts: Shapes. Oxford University Press. [246] Banai R. 1999. A methodology for The Image of the City. Environment and Planning B: Planning and Design, 26(1), 133–144. [85, 105] Barabási A-L. 2014. Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life. Basic Books. [147] Barbieri K, OM Keshk & BM Pollins. 2009. Trading data: Evaluating our assumptions and coding rules. Conflict Management and Peace Science, 26(5), 471–491. [167]

REFERENCES

259

Barnes TJ. 2001. Lives lived and lives told: Biographies of geography’s quantitative revolution. Environment and Planning D: Society and Space, 19(4), 409– 429. [3] Barnes TJ. 2003. The place of locational analysis: A selective and interpretive history. Progress in Human Geography, 27(1), 69–95. [3] Barnes TJ. 2004. The rise (and decline) of American regional science: Lessons for the new economic geography? Journal of Economic Geography, 4(2), 107– 129. [3] Barnes TJ. 2006. Geographical intelligence: American geographers and research and analysis in the Office of Strategic Services 1941–1945. Journal of Historical Geography, 32(1), 149–168. [3] Barnes TJ. 2008. Geography’s underworld: The military–industrial complex, mathematical modelling and the quantitative revolution. Geoforum, 39(1), 3– 16. [3] Barnes TJ. 2009. “Not only . . . but also”: Quantitative and critical geography. The Professional Geographer, 61(3), 292–300. [v] Barnes TJ. 2014. Geo-historiographies. In R Lee, N Castree, R Kitchin, V Lawson, A Paasi, C Philo, S Radcliffe, SM Roberts & CWJ Withers, (Eds). The SAGE Handbook of Human Geography. SAGE, 202–228. [3] Barnes TJ & C Minca. 2013. Nazi spatial theory: The dark geographies of Carl Schmitt and Walter Christaller. Annals of the Association of American Geographers, 103(3), 669–687. [220] Barnes TJ & MW Wilson. 2014. Big data, social physics, and spatial analysis: The early years. Big Data & Society, 1(1), 1–14. [3] Bars I & J Terning. 2010. Extra Dimensions in Space and Time. Springer. [46] Barthélemy M. 2011. Spatial networks. Physics Reports, 499(1–3), 1–101. [156, 173] Bartlett A, B Penders & J Lewis. 2017. Bioinformatics: Indispensable, yet hidden in plain sight? BMC Bioinformatics, 18(1), 311. [2] Batty M. 2005. Agents, cells, and cities: New representational models for simulating multiscale urban dynamics. Environment and Planning A, 37(8), 1373– 1394. [238] Batty M. 2018. Digital twins. Environment and Planning B: Urban Analytics and City Science, 45(5), 817–820. [72] Batty M & PA Longley. 1994. Fractal Cities: A Geometry of Form and Function. Academic Press. [3] Baudrillard J. 1994. Simulacra and Simulation. University of Michigan Press. [72]

260

REFERENCES

Beaumont JR & AC Gatrell. 1982. An Introduction to Q-Analysis. CATMOG 34. Geo Abstracts. [147] Bennett B. 2001. What is a forest? On the vagueness of certain geographic concepts. Topoi, 20(2), 189–201. [122] Bennett J. 2010. Vibrant Matter: A Political Ecology of Things. Duke University Press. [223] Berg LD & RA Kearns. 1996. Naming as norming: “Race,” gender, and the identity politics of naming places in Aotearoa/New Zealand. Environment and Planning D: Society and Space, 14(1), 99–122. [98] Berger S. 2010. The study of enclaves — some introductory remarks. Geopolitics, 15(2), 312–328. [126] Bergmann LR. 2016. Toward speculative data: “Geographic information” for situated knowledges, vibrant matter, and relational spaces. Environment and Planning D: Society and Space, 34(6), 971–989. [41] Bergmann LR & N Lally. 2021. For geographical imagination systems. Annals of the American Association of Geographers, 111(1), 26–35. [1, 251] Bergmann LR & D O’Sullivan. 2017. Computing with many spaces: Generalizing projections for the digital geohumanities and GIScience. In Proceedings of the 1st ACM SIGSPATIAL Workshop on Geospatial Humanities. ACM SIGSPATIAL. ACM Press, 31–38. [27, 31, 249] Berlekamp ER, JH Conway & R Guy. 1982. Winning Ways for Your Mathematical Plays. Academic Press. [234] Berry BJL. 1964. Approaches to regional analysis: A synthesis. Annals of the Association of American Geographers, 54(1), 2–11. [184] Bertin J. 1967. Sémiologie Graphique: Les Diagrammes, Les Réseaux, Les Cartes. Gauthier-Villars. [251] Bhaskar R. 1975. A Realist Theory of Science. Leeds Books. [201] Bian L. 2004. A conceptual framework for an individual-based spatially explicit epidemiological model. Environment and Planning B: Planning and Design, 31(3), 381–395. [242] Biondi E, L Divieti & G Guardabassi. 1970. Counting paths, circuits, chains, and cycles in graphs: A unified approach. Canadian Journal of Mathematics, 22(1), 22–35. [160] Bittner T. 2011. Vagueness and the trade-off between the classification and delineation of geographic regions — an ontological analysis. International Journal of Geographical Information Science, 25(5), 825–850. [122] Black JL & J Macinko. 2008. Neighborhoods and obesity. Nutrition Reviews, 66(1), 2–20. [100]

REFERENCES

261

Blaut JM. 1961. Space and process. The Professional Geographer, 13(4), 1–7. [217] Boccaletti S, V Latora, Y Moreno, M Chavez & D Hwang. 2006. Complex networks: Structure and dynamics. Physics Reports, 424(4–5), 175–308. [156] Bothwell J & M Yuan. 2012. A spatiotemporal GIS framework applied to the analysis of changes in temperature patterns. Transactions in GIS, 16(6), 901– 919. [187] Box GEP. 1979. Some problems of statistics and everyday life. Journal of the American Statistical Association, 74(365), 1–4. [14, 26] Boyer D, MC Crofoot & PD Walsh. 2012. Non-random walks in monkeys and humans. Journal of the Royal Society Interface, 9, 842–847. [239] Branch J. 2014. The Cartographic State: Maps, Territory and the Origins of Sovereignty. Cambridge University Press. [114, 115] Brassel KE & R Weibel. 1988. A review and conceptual framework of automated map generalization. International Journal of Geographical Information Systems, 2(3), 229–244. [73] Brenner N. 1997. State territorial restructuring and the production of spatial scale. Political Geography, 16(4), 273–306. [53] Brenner N. 2001. The limits to scale? Methodological reflections on scalar structuration. Progress in Human Geography, 25(4), 591–614. [54] Briceño S & S Mumford. 2016. Relations all the way down? Against ontic structural realism. In A Marmodoro & D Yates, (Eds). The Metaphysics of Relations. Oxford University Press, 198–217. [146] Brindley P, J Goulding & ML Wilson. 2018. Generating vague neighbourhoods through data mining of passive web data. International Journal of Geographical Information Science, 32(3), 498–523. [101, 102] Brockman J, (Ed). 2013. This Explains Everything: Deep, Beautiful, and Elegant Theories of How the World Works. Harper Perennial. [246] Broome FR & DB Meixler. 1990. The TIGER data base structure. Cartography and Geographic Information Systems, 17(1), 39–47. [33] Bryan J & D Wood. 2015. Weaponizing Maps: Indigenous Peoples and Counterinsurgency in the Americas. Guilford Press. [116] Bryant LR. 2011. The Democracy of Objects. New Metaphysics. Open Humanities Press. [223] Bryant LR, N Srnicek & G Harman, (Eds). 2011. The Speculative Turn: Continental Materialism and Realism. Re.Press. [223] Buisseret D, (Ed). 1992. Monarchs, Ministers, and Maps: The Emergence of Cartography as a Tool of Government in Early Modern Europe. University of Chicago Press. [114]

262

REFERENCES

Bunge WW. 1962. Theoretical Geography. Gleerup. [22, 193] Bunge WW. 1971. Fitzgerald: Geography of a Revolution. Schenkman. [7, 154] Bunge WW. 1973. The Geography. The Professional Geographer, 25(4), 331–337. [1] Burks AW. 1970. Essays on Cellular Automata. University of Illinois. [231] Burrough PA. 1986. Principles of Geographical Information Systems for Land Resources Assessment. Clarendon Press. [7] Buttimer A. 1976. Grasping the dynamism of lifeworld. Annals of the Association of American Geographers, 66(2), 277–292. [84, 199, 204] Byrne D. 1998. Complexity Theory and the Social Sciences: An Introduction. Routledge. [227] Campelo CEC, B Bennett & V Dimitrova. 2011. Identifying geographical processes from time-stamped data. In C Claramunt, S Levashkin & M Bertolotto, (Eds). GeoSpatial Semantics. Lecture Notes in Computer Science 6631. Springer, 70–87. [189] Campelo CEC, B Bennett & V Dimitrova. 2012. From polygons and timestamps to dynamic geographic features: Grounding a spatio-temporal geo-ontology. In S Castano, P Vassiliadis, LV Lakshmanan & ML Lee, (Eds). Advances in Conceptual Modeling. Lecture Notes in Computer Science 7518. Springer, 251– 260. [189, 190] Capineri C. 2016. Kilburn High Road revisited. Urban Planning, 1(2), 128. [108] Caquard S & W Cartwright. 2014. Narrative cartography: From mapping stories to the narrative of maps and mapping. The Cartographic Journal, 51(2), 101– 106. [106, 107] Caquard S & S Dimitrovas. 2017. Story Maps & Co. The state of the art of online narrative cartography. Mappemonde. Revue trimestrielle sur l’image géographique et les formes du territoire, 121. [108] Caquard S, E Shaw & J Alavez. 2022. How distant is close enough? Exploring the toponymic distortions of life story geographies. GeoHumanities, 8(1), 102–121. [108] Carroll P. 2006. Science, Culture, and Modern State Formation. University of California Press. [114, 118] Casey ES. 1997a. Smooth spaces and rough-edged places: The hidden history of place. The Review of Metaphysics, 51(2), 267–296. [76, 84, 88] Casey ES. 1997b. The Fate of Place: A Philosophical History. University of California Press. [75] Catudal HM. 1974. Exclaves. Cahiers de géographie du Québec, 18(43), 107–136. [125]

REFERENCES

263

Chen G. 2018. The Humanist Spirit of Daoism. BRILL. [212] Cheshire J & O Uberti. 2014. London: The Information Capital: 100 Maps and Graphics That Will Change How You View the City. Penguin. [107] Cheung AKL, D O’Sullivan & G Brierley. 2015. Graph-assisted landscape monitoring. International Journal of Geographical Information Science, 29(4), 580– 605. [189] Chouinard V. 1989. Explaining local experiences of state formation: The case of cooperative housing in Toronto. Environment and Planning D: Society and Space, 7(1), 51–68. [90] Chrisman NR. 2006. Charting the Unknown: How Computer Mapping at Harvard Became GIS. ESRI Press. [vi, 3] Chrisman NR. 2017. Calculating on a round planet. International Journal of Geographical Information Science, 31(4), 637–657. [28] Christakis NA & JH Fowler. 2011. Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. Little, Brown. [147] Christaller W. 1966. Central Places in Southern Germany. Prentice-Hall. [220] Churchman CW. 1967. Guest editorial: Wicked problems. Management Science, 14(4), B141–B142. [216] Claramunt C. 2020. Ontologies for geospatial information: Progress and challenges ahead. Journal of Spatial Information Science, 20, 35–41. [41] Clarke KC. 2011. Getting Started with Geographic Information Systems. (5th edn). Pearson Education. [251] Clarke KC. 2017. Map projections and coordinate systems. In D Richardson, N Castree, MF Goodchild, A Kobayashi, W Liu & RA Marston, (Eds). International Encyclopedia of Geography: People, the Earth, Environment and Technology. Wiley. doi: 10.1002/9781118786352.wbieg0455. [23] Clauset A, MEJ Newman & C Moore. 2004. Finding community structure in very large networks. Physical Review E, 70(6), 1–6. [165] Clifford P & A Sudbury. 1973. A model for spatial conflict. Biometrika, 60(3), 581–588. [234] Codd EF. 1970. A relational model of data for large shared data banks. Communications of the ACM, 13(6), 377–387. [40] Cohn AG & J Renz. 2008. Qualitative spatial representation and reasoning. In B Porter, V Lifschitz & F Van Harmelen, (Eds). Handbook of Knowledge Representation. Elsevier, 551–596. [143] Connolly WE. 2011. A World of Becoming. Duke University Press. [227] Cook M. 2004. Universality in elementary cellular automata. Complex Systems, 15(1), 1–40. [234]

264

REFERENCES

Cooke DF & WF Maxfield. 1967. The development of a geographic base file and its uses for mapping. In Proceedings of the 5th Annual Conference of the Urban and Regional Information System Association, 207–218. [33] Cooper D & IN Gregory. 2011. Mapping the English Lake District: A literary GIS. Transactions of the Institute of British Geographers, 36(1), 89–108. [103] Cope M & S Elwood, (Eds). 2009. Qualitative GIS: A Mixed Methods Approach. Sage. [249] Couclelis H. 1988. Of mice and men: What rodent populations can teach us about complex spatial dynamics. Environment and Planning A, 20(1), 99–109. [232] Couclelis H. 1992. People manipulate objects (but cultivate fields): Beyond the raster-vector debate in GIS. In AU Frank, I Campari & U Formentini, (Eds). Theories and Methods of Spatio-Temporal Reasoning in Geographic Space. Lecture Notes in Computer Science 639. Springer, 65–77. [26, 59, 251] Couclelis H. 1997. From cellular automata to urban models: New principles for model development and implementation. Environment and Planning B: Planning and Design, 24(2), 165–174. [43, 231] Couclelis H, RG Golledge, N Gale & WR Tobler. 1987. Exploring the anchorpoint hypothesis of spatial cognition. Journal of Environmental Psychology, 7(2), 99–122. [85, 105] Coutin SB. 2010. Confined within: National territories as zones of confinement. Political Geography, 29(4), 200–208. [121] Cova TJ & MF Goodchild. 2002. Extending geographical representation to include fields of spatial objects. International Journal of Geographical Information Science, 16(6), 509–532. [39] Coveney P & R Highfield. 1995. Frontiers of Complexity: The Search for Order in a Complex World. Ballantine Books. [227] Cox KR. 2021. Human and physical geography and the question of space. Belgeo, 2021(4). [25, 225] Crampton J. 1994. Cartography’s defining moment: The Peters projection controversy, 1974–1990. Cartographica, 31(4), 16–32. [67] Crary J. 2014. 24/7: Late Capitalism and the Ends of Sleep. Verso. [186] Cresswell T. 1996. In Place/Out of Place: Geography, Ideology, and Transgression. University of Minnesota Press. [86, 87, 128] Cresswell T. 2006. On the Move: Mobility in the Modern Western World. Routledge. [127, 128] Cresswell T. 2011. Mobilities I: Catching up. Progress in Human Geography, 35(4), 550–558. [180, 205]

REFERENCES

265

Cresswell T. 2012. Mobilities II: Still. Progress in Human Geography, 36(5), 645– 653. [180] Cresswell T. 2014. Mobilities III: Moving on. Progress in Human Geography, 38(5), 712–721. [180] Crols T, R White, I Uljee, G Engelen, L Poelmans & F Canters. 2015. A travel time-based variable grid approach for an activity-based cellular automata model. International Journal of Geographical Information Science, 29(10), 1757– 1781. [238] Cromley EK & S McLafferty. 2012. GIS and Public Health. (2nd edn). Guilford Press. [15, 132] Curtis A, JW Curtis, LC Porter, E Jefferis & E Shook. 2016. Context and spatial nuance inside a neighborhood’s drug hotspot: Implications for the crime–health nexus. Annals of the American Association of Geographers, 106(4), 819–836. [103] Dacey MF. 1964. Two-dimensional random point patterns: A review and an interpretation. Papers in Regional Science, 13(1), 41–55. [220] Dalton CM & T Stallmann. 2018. Counter-mapping data science. The Canadian Geographer / Le Géographe canadien, 62(1), 93–101. [116] Dankel DJ, NS Vaage & JP van der Sluijs. 2017. Post-normal science in practice. Futures, 91, 1–4. [216] Davies C, I Holt, J Green, J Harding & L Diamond. 2009. User needs and implications for modelling vague named places. Spatial Cognition & Computation, 9(3), 174–194. [94] Davis M. 1990. City of Quartz: Excavating the Future in Los Angeles. Verso. [120] Davis S. 2011. The US military base network and contemporary colonialism: Power projection, resistance and the quest for operational unilateralism. Political Geography, 30(4), 215–224. [126] de Boer DH. 1992. Hierarchies and spatial scale in process geomorphology: A review. Geomorphology, 4(5), 303–318. [47] de la Torre AC & HO Mártin. 1997. A survey of cellular automata like the “game of life.” Physica A: Statistical Mechanics and Its Applications, 240(3), 560–570. [237] de Landa M. 1997. A Thousand Years of Non-Linear History. Swerve Editions. [227] de Landa M. 2002. Intensive Science and Virtual Philosophy. Transversals. Continuum. [225] de Landa M. [2006] 2019. A New Philosophy of Society: Assemblage Theory and Social Complexity. Bloomsbury Academic. [222, 224, 225, 227, 228, 242]

266

REFERENCES

Delaney D. 2005. Territory: A Short Introduction. Blackwell. [113] Deleuze G. 1994. Difference and Repetition. Athlone Press. [224] Deleuze G & F Guattari. 1987. A Thousand Plateaus: Capitalism and Schizophrenia. University of Minnesota Press. [223] Detroit Geographical Expedition and Institute. 1971. Field Notes 1. [154] Deutsche R. 1991. Boys town. Environment and Planning D: Society and Space, 9(1), 5–30. [91] de Voltaire M. [1738] 1967. The Elements of Sir Isaac Newton’s Philosophy. Frank Cass & Co. [20] Deza MM & E Deza. 2016. Encyclopedia of Distances. Springer. [32, 140, 221] Di Battista G, P Eades, R Tamassia & IG Tollis. 1999. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall. [176, 177] Dijkstra EW. 1959. A note on two problems in connexion with graphs. Numerische Mathematik, 1, 269–271. [160] Dijst M. 2009. Time geographic analysis. In R Kitchin & NJ Thrift, (Eds). International Encyclopedia of Human Geography. Elsevier, 266–278. [193] Dodge M & R Kitchin. 2001. Atlas of Cyberspace. Pearson Education. [78] Dodge S & TA Nelson. 2023. A framework for modern time geography: Emphasizing diverse constraints on accessibility. Journal of Geographical Systems, 25(3), 357–375. [205] Dodge S, R Weibel, SC Ahearn, M Buchin & JA Miller. 2016. Analysis of movement data. International Journal of Geographical Information Science, 30(5), 825– 834. [205] Doreian P. 2009. Positional analysis and blockmodeling. In RA Meyers, (Ed). Encyclopedia of Complexity and Systems Science. Springer, 6913–6927. [168] Douglas DH & TK Peucker. 1973. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. The Canadian Cartographer, 10(2), 112–122. [73] Downs RM & D Stea. 1973. Image and Environment: Cognitive Mapping and Spatial Behavior. Aldine Publishing. [84, 104] Drucker J. 2009. SpecLab: Digital Aesthetics and Projects in Speculative Computing. University of Chicago Press. [249] Duncan S & M Savage. 1989. Space, scale and locality. Antipode, 21(3), 179–206. [90] Duncan S & M Savage. 1991. Commentary: New perspectives on the locality debate. Environment and Planning A, 23(2), 155–164. [90]

REFERENCES

267

Dyck I. 1990. Space, time, and renegotiating motherhood: An exploration of the domestic workplace. Environment and Planning D: Society and Space, 8(4), 459– 483. [202] Eades GL. 2017. The Geography of Names: Indigenous to Post-Foundational. Routledge. [98] Edney MH. 1997. Mapping an Empire: The Geographical Construction of British India, 1765–1843. University of Chicago Press. [114, 118] Edwards G. 1993. The Voronoi model and cultural space: Applications to the social sciences and humanities. In AU Frank & I Campari, (Eds). Spatial Information Theory: A Theoretical Basis for GIS. Lecture Notes in Computer Science 716. Springer, 202–214. [38] Edwards PN. 2010. A Vast Machine: Computer Models, Climate Data, and the Politics of Global Warming. MIT Press. [231] Egenhofer MJ & RD Franzosa. 1991. Point-set topological spatial relations. International Journal of Geographical Information Systems, 5(2), 161–174. [123] Egenhofer MJ & DM Mark. 1995. Naive geography. In AU Frank & W Kuhn, (Eds). International Conference on Spatial Information Theory. Springer, 1–15. [7, 84, 143] Elden S. 2010. Land, terrain, territory. Progress in Human Geography, 34(6), 799– 817. [117] Elden S. 2013. The Birth of Territory. The University of Chicago Press. [22, 117, 118] Elwood S. 2006. Critical issues in participatory GIS: Deconstructions, reconstructions, and new research directions. Transactions in GIS, 10(5), 693–708. [116] Elwood S. 2008. Volunteered geographic information: Key questions, concepts and methods to guide emerging research and practice. GeoJournal, 72(3–4), 133–135. [102] Elwood S & MW Wilson. 2017. Critical GIS pedagogies beyond “Week 10: Ethics.” International Journal of Geographical Information Science, 31(10), 2098– 2116. [8] Entrikin JN. 1991. The Betweenness of Place: Towards a Geography of Modernity. Macmillan. [76, 88, 92, 93] Erdös P & A Rényi. 1959. On random graphs I. Publicationes Mathematicae (Debrecen), 6, 290–297. [173] Escobar A. 2007. The “ontological turn” in social theory. A Commentary on “Human geography without scale,” by Sallie Marston, John Paul Jones III and

268

REFERENCES

Keith Woodward. Transactions of the Institute of British Geographers, 32(1), 106– 111. [225] Estivill-Castro V & I Lee. 2002. Argument free clustering for large spatial point-data sets via boundary extraction from Delaunay diagram. Computers, Environment and Urban Systems, 26(4), 315–334. [37] Evans J. 2017. Polynesian Navigation and the Discovery of New Zealand. Libro International. [19] Evans KM. 2003. Larger than Life: Threshold-range scaling of Life’s coherent structures. Physica D: Nonlinear Phenomena, 183(1–2), 45–67. [237] Experian. 2015. Mosaic USA: The Consumer Classification Solution for Consistent Cross-Channel Marketing. Experian Information Solutions. [142] Farber S, MZ Morang & MJ Widener. 2014. Temporal variability in transitbased accessibility to supermarkets. Applied Geography, 53, 149–159. [152] Farber S, M O’Kelly, HJ Miller & T Neutens. 2015. Measuring segregation using patterns of daily travel behavior: A social interaction based model of exposure. Journal of Transport Geography, 49, 26–38. [205] Farmer CJQ & AS Fotheringham. 2011. Network-based functional regions. Environment and Planning A, 43(11), 2723–2741. [168] Farvacque-Vitkovic C, L Godin, H Leroux, R Chavez & F Verdet. 2005. Street Addressing and the Management of Cities. The World Bank. [78] Feng C-C & T Bittner. 2010. Ontology-based qualitative feature analysis: Bays as a case study. Transactions in GIS, 14(4), 547–568. [122] Filomena G, JA Verstegen & E Manley. 2019. A computational approach to “The Image of the City.” Cities, 89, 14–25. [105] Fischer MM. 2004. GIS and network analysis. In DA Hensher, KJ Button, KE Haynes & PR Stopher, (Eds). Handbook of Transport Geography and Spatial Systems. Elsevier, 391–408. [150] Fisher P. 1997. The pixel: A snare and a delusion. International Journal of Remote Sensing, 18(3), 679–685. [217] Fleischmann M, A Feliciotti, O Romice & S Porta. 2020. Morphological tessellation as a way of partitioning space: Improving consistency in urban morphology at the plot scale. Computers, Environment and Urban Systems, 80, 101441. [38] Floyd RW. 1962. Algorithm 97: Shortest path. Communications of the ACM, 5(6), 345. [160] Forer PC. 1978. A place for plastic space? Progress in Human Geography, 2(2), 230– 267. [24, 248]

REFERENCES

269

Forer PC & H Kivell. 1981. Space-time budgets, public transport, and spatial choice. Environment and Planning A, 13(4), 497–509. [202] Foresman TW, (Ed). 1997. The History of GIS: Perspectives from the Pioneers. Prentice Hall. [3] Forest B. 2004. Information sovereignty and GIS: The evolution of “communities of interest” in political redistricting. Political Geography, 23(4), 425–451. [137] Forsé M & M Parodi. 2010. Low levels of ethnic intolerance do not create large ghettos: A discussion about an interpretation of Schelling’s model. L’Année Sociologique, 60(2), 445–473. [241] Fortunato S. 2010. Community detection in graphs. Physics Reports, 486(3–5), 75–174. [164, 166] Fortunato S & D Hric. 2016. Community detection in networks: A user guide. Physics Reports, 659, 1–44. [164] Fossett M. 2006. Ethnic preferences, social distance dynamics, and residential segregation: Theoretical explorations using simulation analysis. Journal of Mathematical Sociology, 30(3–4), 185–273. [241] Fotheringham AS. 1997. Trends in quantitative methods I: Stressing the local. Progress in Human Geography, 21(1), 58–96. [221] Frank AU. 1998. Different types of "times" in GIS. In MJ Egenhofer & RG Golledge, (Eds). Spatial and Temporal Reasoning in Geographic Information Systems. Oxford University Press, 40–62. [185] Frank AU & MF Goodchild. 1990. Two Perspectives on Geographical Data Modelling. Technical Report 90-11. National Center for Geographical Information and Analysis. [10, 18] Fruchterman TMJ & EM Reingold. 1991. Graph drawing by force-directed placement. Software: Practice and Experience, 21(11), 1129–1164. [175, 176] Funtowicz SO & JR Ravetz. 1993. Science for the post-normal age. Futures, 25(7), 739–755. [216] Gahegan M. 2018. Our GIS is too small. The Canadian Geographer / Le Géographe canadien, 62(1), 15–26. [251] Gahegan M & W Pike. 2006. A situated knowledge representation of geographical information. Transactions in GIS, 10(5), 727–749. [41] Galton A. 2004. Fields and objects in space, time, and space-time. Spatial Cognition & Computation, 4(1), 39–68. [190, 191] Galton A. 2018. Processes as patterns of occurrence. In R Stout, (Ed). Process, Action, and Experience. Oxford University Press, 41–57. [211, 215, 220]

270

REFERENCES

Gardner M. 1970. Mathematical games: The fantastic combinations of John Conway’s new solitaire game “life.” Scientific American, 223(Oct), 120–123. [234] Gärling T & RG Golledge. 1989. Environmental perception and cognition. In EH Zube & GT Moore, (Eds). Advances in Environment, Behavior, and Design: Volume 2. Springer, 203–236. [58] Gatrell AC. 1983. Distance and Space: A Geographical Perspective. Oxford University Press. [24, 248] Gehlke CE & K Biehl. 1934. Certain effects of grouping upon the size of the correlation coefficient in census tract material. Journal of the American Statistical Association, 29(185), 169–170. [135] Gelernter DH. 1991. Mirror Worlds, or, the Day Software Puts the Universe in a Shoebox: How It Will Happen and What It Will Mean. Oxford University Press. [72] Gell A. 1992. The Anthropology of Time: Cultural Constructions of Temporal Maps and Images. Berg. [194, 199] Giddens A. 1985. Time, space and regionalisation. In D Gregory & J Urry, (Eds). Social Relations and Spatial Structures. Macmillan, 265–295. [199] Gilbert EN. 1959. Random graphs. The Annals of Mathematical Statistics, 30(4), 1141–1144. [173] Gilmore RW. 2007. Golden Gulag: Prisons, Surplus, Crisis, and Opposition in Globalizing California. University of California Press. [120, 127] Giraut F & M Houssay-Holzschuch, (Eds). 2022. The Politics of Place Naming: Naming the World. International Society for Technology in Education / Wiley. [98] Girvan M & MEJ Newman. 2002. Community structure in social and biological networks. Proceedings of the National Academy of Sciences, 99(12), 7821–7826. [165] Glacken CJ. 1967. Traces on the Rhodian Shore: Nature and Culture in Western Thought from Ancient Times to the End of the Eighteenth Century. University of California Press. [84] Gold CM. 1992. The meaning of “neighbour.” In AU Frank, I Campari & U Formentini, (Eds). Theories and Methods of Spatio-Temporal Reasoning in Geographic Space. Lecture Notes in Computer Science 639. Springer, 220–235. [37, 38] Golledge RG & RJ Stimson. 1997. Spatial Behavior: A Geographic Perspective. Guilford Press. [84] Good BH, Y-A de Montjoye & A Clauset. 2010. Performance of modularity maximization in practical contexts. Physical Review E, 81(4), 046106. [166]

REFERENCES

271

Goodchild MF. 1992. Geographical information science. International Journal of Geo-Information Systems, 6(1), 31–45. [8] Goodchild MF. 2006. GIScience ten years after Ground Truth. Transactions in GIS, 10(5), 687–692. [254] Goodchild MF. 2007. Citizens as sensors: The world of volunteered geography. GeoJournal, 69(4), 211–221. [102] Goodchild MF. 2011. Formalizing place in geographic information systems. In LM Burton, SA Matthews, M Leung, SP Kemp & DT Takeuchi, (Eds). Communities, Neighborhoods, and Health. Springer, 21–33. [93, 101] Goodchild MF. 2013. Prospects for a space–time GIS. Annals of the Association of American Geographers, 103(5), 1072–1077. [192] Goodchild MF. 2015. Four thoughts on the future of GIS. ArcWatch, (February). [vii] Goodchild MF. 2018. Reimagining the history of GIS. Annals of GIS, 24(1), 1–8. [8, 28] Goodchild MF, M Yuan & TJ Cova. 2007. Towards a general theory of geographic representation in GIS. International Journal of Geographical Information Science, 21(3), 239–260. [10, 18, 39, 122] Gould P. 1997. The structure of space(s). Geografiska Annaler: Series B, Human Geography, 79(3), 127–140. [146, 183] Gould P & R White. 1974. Mental Maps. Penguin. [84, 104] Graham DW. 2019. Heraclitus. In EN Zalta, (Ed). The Stanford Encyclopedia of Philosophy. Vol. Fall 2019. Metaphysics Research Lab, Stanford University. url: plato.stanford.edu/archives/fall2019/entries/heraclitus/. [212] Gregory D. 1985. Suspended animation: The stasis of diffusion theory. In D Gregory & J Urry, (Eds). Social Relations and Spatial Structures. Macmillan, 296–336. [200, 201] Gregory D & J Urry, (Eds). 1985. Social Relations and Spatial Structures. Macmillan. [200] Grimm V & SF Railsback. 2012. Pattern-oriented modelling: A “multi-scope” for predictive systems ecology. Philosophical Transactions of the Royal Society B: Biological Sciences, 367(1586), 298–310. [246] Grimm V, E Revilla, U Berger, F Jeltsch, WM Mooij, SF Railsback, H-H Thulke, J Weiner, T Wiegand & DL DeAngelis. 2005. Pattern-oriented modeling of agent-based complex systems: Lessons from ecology. Science, 310(5750), 987–991. [246] Gross T & B Blasius. 2008. Adaptive coevolutionary networks: A review. Journal of The Royal Society Interface, 5(20), 259–271. [238]

272

REFERENCES

Grubesic TH & TC Matisziw. 2006. On the use of ZIP codes and ZIP code tabulation areas (ZCTAs) for the spatial analysis of epidemiological data. International Journal of Health Geographics, 5(1), 58. [131] Grünbaum B & GC Shephard. 1987. Tilings and Patterns. W. H. Freeman. [219] Guimera R, S Mossa, A Turtschi & LAN Amaral. 2005. The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. Proceedings of the National Academy of Sciences, 102(22), 7794– 7799. [168] Hägerstrand T. 1968. Innovation Diffusion as a Spatial Process. University of Chicago Press. [193] Hägerstrand T. 1970. What about people in regional science? Papers in Regional Science, 24(1), 7–24. [12, 193, 194, 197, 199] Hägerstrand T. 1974. Impact of transport on the quality of life. In Transport in the 1980-1990 Decade. 5th International Symposium on Theory and Practice in Transport Economics, European Conference of Ministers of Transport, 1–51. [200] Hägerstrand T. 1982. Diorama, path and project. Tijdschrift Voor Economische En Sociale Geografie, 73(6), 323–339. [193, 199, 202, 203, 208] Haggett P & RJ Chorley. 1969. Network Analysis in Geography. Edward Arnold. [147, 173] Haigh T & PE Ceruzzi. 2021. A New History of Modern Computing. The MIT Press. Haklay M, D O’Sullivan, M Thurstain-Goodwin & T Schelhorn. 2001. “So go downtown”: Simulating pedestrian movement in town centres. Environment and Planning B: Planning and Design, 28(3), 343–359. [239] Hale RF. 1971. A Map of Vernacular Regions in America. PhD thesis. University of Minnesota. [102] Hammam Y, A Moore & P Whigham. 2007. The dynamic geometry of geographical vector agents. Computers, Environment and Urban Systems, 31(5), 502– 519. [240] Hamzei E, S Winter & M Tomko. 2020. Place facets: A systematic literature review. Spatial Cognition & Computation, 20(1), 33–81. [94, 108] Hannah MG. 2000. Governmentality and the Mastery of Territory in NineteenthCentury America. Cambridge University Press. [118] Hannah MG. 2009. Calculable territory and the West German census boycott movements of the 1980s. Political Geography, 28(1), 66–75. [129] Hanson S & P Hanson. 1980. Gender and urban activity patterns in Uppsala, Sweden. Geographical Review, 70(3), 291. [202]

REFERENCES

273

Hanson S & P Hanson. 1981. The impact of married women’s employment on household travel patterns: A Swedish example. Transportation, 10(2), 165–183. [202] Haraway D. 1988. Situated knowledges: The science question in feminism and the privilege of partial perspective. Feminist Studies, 14(3), 575. [21, 93] Haraway D. 1991. Simians, Cyborgs, and Women: The Reinvention of Nature. Routledge. [223] Harley JB, D Woodward, GM Lewis, MH Edney, M Sponberg Pedley, RJP Kain & M Monmonier, (Eds). 1987-[2023]. The History of Cartography. University of Chicago Press. [vi] Harman G. 2018. Object-Oriented Ontology: A New Theory of Everything. Pelican Books. [223] Harris T & D Weiner. 1996. GIS and Society: The Social Implications of How People, Space, and Environment Are Represented in GIS: Scientific Report for the Initiative 19 Specialist Meeting. Technical Report 96-7. National Center for Geographical Information and Analysis. [7] Hart P, N Nilsson & B Raphael. 1968. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics, 4(2), 100–107. [160] Hartshorne R. 1939. The nature of geography: A critical survey of current thought in the light of the past. Annals of the Association of American, 39(3/4), 173–658. [182–184] Hartshorne R. 1955. “Exceptionalism in Geography”re-examined. Annals of the Association of American Geographers, 45(3), 205–244. [183] Harvey D. 1969. Explanation in Geography. Edward Arnold. [30] Harvey D. 1972. A commentary on the comments. Antipode, 4(2), 36–41. [207] Harvey D. 1973. Social Justice and the City. Edward Arnold. [20, 25, 26] Harvey D. 1989. The Condition of Postmodernity. Blackwell. [90, 91] Harvey D. 1996. Justice, Nature, and the Geography of Difference. Blackwell. [25, 217, 218, 221] Harvey D. 2006. Spaces of Global Capitalism: Towards a Theory of Uneven Geographical Development. Verso. [25, 26] Harvey DL & M Reed. 1996. Social science as the study of complex systems. In LD Kiel & EW Elliott, (Eds). Chaos Theory in the Social Sciences. University of Michigan Press, 295–324. [51] Harvey FJ & NR Chrisman. 2004. The imbrication of geography and technology: The social construction of geographic information systems. In

274

REFERENCES

SD Brunn, SL Cutter & JW Harrington, (Eds). Geography and Technology. Springer Netherlands, 65–80. [8] Havice E. 2018. Unsettled sovereignty and the sea: Mobilities and more-thanterritorial configurations of state power. Annals of the American Association of Geographers, 108(5), 1280–1297. [118] Hegselmann R. 2017. Thomas C. Schelling and James M. Sakoda: The intellectual, technical, and social history of a model. Journal of Artificial Societies and Social Simulation, 20(3). [240] Helmreich S. 1998. Silicon Second Nature: Culturing Artificial Life in a Digital World. University of California Press. [227] Hennig C. 2015. What are the true clusters? Pattern Recognition Letters, 64, 53– 62. [140] Hennig C, M Meila, F Murtagh & R Rocci, (Eds). 2016. Handbook of Cluster Analysis. CRC Press. [140] Heppenstall AJ, AT Crooks, M Batty & LM See, (Eds). 2012. Agent-Based Models of Geographical Systems. Springer. [242] Herod A. 1991. The production of scale in United States labour relations. Area, 23(1), 82–88. [53] Herod A. 2011. Scale. Routledge. [48] Hettner A. 1927. Die Geographie, Ihre Geschichte, Ihr Wesen Und Ihre Methoden. Ferdinand Hirt. [182] Hodgson DL & RA Schroeder. 2002. Dilemmas of counter-mapping community resources in Tanzania. Development and Change, 33(1), 79–100. [115] Holland JH. 1998. Emergence: From Chaos to Order. Perseus. [228] Hollenstein L & R Purves. 2010. Exploring place through user-generated content: Using Flickr to describe city cores. Journal of Spatial Information Science, 1, 21–48. [102] Holtzheimer PE. 1983. An introduction to the GBF/DIME: A primer. Computers, Environment and Urban Systems, 8(3), 133–173. [78] Horgan J. 1995. From complexity to perplexity: Can science achieve a unified theory of complex systems? Scientific American, 272(Jun), 104–109. [229] Hornsby K & MJ Egenhofer. 2000. Identity-based change: A foundation for spatio-temporal knowledge representation. International Journal of Geographical Information Science, 14(3), 207–224. [188] Huang Q, DC Parker, T Filatova & S Sun. 2014. A review of urban residential choice models using agent-based modeling. Environment and Planning B: Planning and Design, 41(4), 661–689. [242]

REFERENCES

275

Itami RM. 1994. Simulating spatial dynamics: Cellular automata theory. Landscape and Urban Planning, 30(1-2), 27–47. [237] Ittelson WH. 1973. Environment perception and contemporary perceptual theory. In WH Ittelson, (Ed). Environment and Cognition. Seminar Press, 141–154. [58] Jiang J & MF Worboys. 2009. Event-based topology for dynamic planar areal objects. International Journal of Geographical Information Science, 23(1), 33–60. [189] Johnston RJ, R Harris, K Jones, D Manley, CE Sabel & WW Wang. 2014. Mutual misunderstanding and avoidance, misrepresentations and disciplinary politics: Spatial science and quantitative analysis in (United Kingdom) geographical curricula. Dialogues in Human Geography, 4(1), 3–25. [221] Jones CB, RS Purves, PD Clough & H Joho. 2008. Modelling vague places with knowledge from the Web. International Journal of Geographical Information Science, 22(10), 1045–1065. [102] Jones GR. 2015. Human friendly coordinates. Geoinformatics, 18(Jul/Aug), 10– 13. [80] Jones III JP, H Leitner, SA Marston & ES Sheppard. 2017. Neil Smith’s scale. Antipode, 49(S1), 138–152. [51, 52] Jünger M & P Mutzel, (Eds). 2004. Graph Drawing Software. Springer. [176] Kamada I & S Kawai. 1989. An algorithm for drawing general undirected graphs. Information Processing Letters, 31(1), 9. [175] Kansky K. 1963. Structure of Transportation Networks: Relationships Between Network Geometry and Regional Characteristics. PhD thesis. University of Chicago. [147] Karrer B & MEJ Newman. 2011. Stochastic blockmodels and community structure in networks. Physical Review E, 83(1), 016107. [171] Kauffman SA. 1993. The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press. [227] Kauffman SA. 1995. At Home in the Universe: The Search for Laws of Complexity. Penguin. [246] Kimura M. 1953. “Stepping Stone” Model of Population. Annual Report. National Institute of Genetics of Japan. [234] Kirsch S. 2013. Cultural geography I: Materialist turns. Progress in Human Geography, 37(3), 433–441. [223] Kirsch S & D Mitchell. 2004. The nature of things: Dead labor, nonhuman actors, and the persistence of Marxism. Antipode, 36(4), 687–705. [222]

276

REFERENCES

Kitchin R & M Dodge. 2007. Rethinking maps. Progress in Human Geography, 31(3), 331–344. [14, 44, 185, 250] Knowles AK, L Westerveld & L Strom. 2015. Inductive visualization: A humanistic alternative to GIS. GeoHumanities, 1(2), 233–265. [108] Kobayashi A. 2014. Neoclassical urban theory and the study of racism in geography. Urban Geography, 35(5), 645–656. [220] Krieger N, P Waterman, JT Chen, M-J Soobader, SV Subramanian & R Carson. 2002. ZIP code caveat: Bias due to spatiotemporal mismatches between ZIP codes and US census–defined geographic areas—the public health disparities geocoding project. American Journal of Public Health, 92(7), 1100–1102. [131] Krygier J & D Wood. 2009. Ce n’est pas le monde (this is not the world). In R Kitchin, M Dodge & C Perkins, (Eds). Rethinking Maps: New Frontiers in Cartographic Theory. Routledge, 189–219. [14, 250] Kukutai T, J Whitehead & H Kani. 2022. Tracing Opuatia: Repatriating and repurposing colonial land data. New Zealand Geographer, 78(2), 134–146. [129] Kulpa Z. 1997. Diagrammatic representation of interval space in proving theorems about interval relations. Reliable Computing, 3, 209–217. [187] Kwan M-P. 1998. Space-time and integral measures of individual accessibility: A comparative analysis using a point-based framework. Geographical Analysis, 30(3), 191–216. [203] Kwan M-P. 1999a. Gender and individual access to urban opportunities: A study using space-time measures. The Professional Geographer, 51(2), 210–227. [203] Kwan M-P. 1999b. Gender, the home-work link, and space-time patterns of nonemployment activities. Economic Geography, 75(4), 370–394. [203] Kwan M-P. 2000. Interactive geovisualization of activity-travel patterns using three-dimensional geographical information systems: A methodological exploration with a large data set. Transportation Research Part C: Emerging Technologies, 8(1–6), 185–203. [203] Kwan M-P. 2002. Feminist visualization: Re-envisioning GIS as a method in feminist geographic research. Annals of the Association of American Geographers, 92(4), 645–661. [203] Kwan M-P. 2012. The uncertain geographic context problem. Annals of the Association of American Geographers, 102(5), 958–968. [100] Kwan M-P. 2013. Beyond space (as we knew it): Toward temporally integrated geographies of segregation, health, and accessibility. Annals of the Association of American Geographers, 103(5), 1078–1086. [205] Kwan M-P & T Schwanen. 2009. Quantitative revolution 2: The critical (re)turn. The Professional Geographer, 61(3), 283–291. [203]

REFERENCES

277

L’Hostis A & F Abdou. 2021. What is the shape of geographical time-space? A three-dimensional model made of curves and cones. ISPRS International Journal of Geo-Information, 10(5), 340. [23] Ladyman J, J Lambert & K Wiesner. 2013. What is a complex system? European Journal for Philosophy of Science, 3(1), 33–67. [227] Ladyman J & D Ross. 2007. Every Thing Must Go: Metaphysics Naturalized. In collab. with D Spurrett & JG Collier. Oxford University Press. [146] Lally N. 2022. Sculpting, cutting, expanding, and contracting the map. Cartographica, 57(1), 1–10. [254] Lam NS-N. 2019. Resolution. Geographic Information Science & Technology Body of Knowledge, 2019(Q2). [70] Lam NS-N & DA Quattrochi. 1992. On the issues of scale, resolution, and fractal analysis in the mapping sciences. The Professional Geographer, 44(1), 88–98. [70] Lane SN. 2017. Slow science, the geographical expedition, and Critical Physical Geography. The Canadian Geographer / Le Géographe canadien, 61(1), 84–101. [v, 216] Langran G. 1989a. A review of temporal database research and its use in GIS applications. International Journal of Geographical Information Systems, 3(3), 215– 232. [190] Langran G. 1989b. Time in Geographic Information Systems. PhD thesis. University of Washington. [185, 190] Langran G. 1992. Time in Geographic Information Systems. Taylor & Francis. [190] Latham A. 2003. Research, performance, and doing human geography: Some reflections on the diary-photograph, diary-interview method. Environment and Planning A, 35(11), 1993–2017. [204] Latham A & PRH Wood. 2015. Inhabiting infrastructure: Exploring the interactional spaces of urban cycling. Environment and Planning A, 47(2), 300–319. [204] Latour B. 1987. Science in Action: How to Follow Scientists and Engineers Through Society. Harvard University Press. [155] Latour B. 1993. We Have Never Been Modern. Trans. C Porter. Harvard University Press. [222] Latour B. 1999. On recalling ANT. In J Law & J Hassard, (Eds). Actor Network Theory and After. Blackwell, Sociological Review, 15–25. [155] Latour B. 2004. Why has critique run out of steam? From matters of fact to matters of concern. Critical Inquiry, 30(2), 225–248. [216] Laube P. 2014. Computational Movement Analysis. Springer. [206]

278

REFERENCES

Lave R, MW Wilson, ES Barron, C Biermann, MA Carey, CS Duvall, L Johnson, KM Lane, N McClintock, D Munroe, R Pain, J Proctor, BL Rhoads, MM Robertson, J Rossi, NF Sayre, G Simon, M Tadaki & C Van Dyke. 2014. Intervention: Critical physical geography. The Canadian Geographer / Le Géographe canadien, 58(1), 1–10. [v] Law J. 1999. After ANT: Complexity, naming and topology. In J Law & J Hassard, (Eds). Blackwell, Sociological Review, 1–14. [155] Law J & J Hassard, (Eds). 1999. Actor Network Theory and After. Blackwell, Sociological Review. [155] Law J & K Hetherington. 2000. Materialities, spatialities, globalities. In J Bryson, P Daniels, N Henry & J Pollard, (Eds). Knowledge, Space, Economy. Routledge, 33–49. [15] Law J & P Lodge. 1984. Science for Social Scientists. Macmillan Press. [155] Law R. 1999. Beyond “women and transport”: Towards new geographies of gender and daily mobility. Progress in Human Geography, 23(4), 567–588. [204] Leathwick JR, FJ Morgan, G Wilson, D Rutledge, M McLeod & K Johnston. 2002. Land Environments of New Zealand - Nga Taiao o Aotearoa: A Technical Guide. Ministry for the Environment & Manaaki Whenua Landcare Research. [142] Lee J-Y & H-Y Kim. 2006. A geocoding method implemented for hierarchical areal addressing system in Korea. Journal of Korea Spatial Information Society, 14(4), 403–419. [78] Lefebvre H. 1991. The Production of Space. Trans. D Nicholson-Smith. Blackwell. [75, 85, 88] Lefebvre H. 2005. Critique of Everyday Life. Trans. J Moore. Verso. [85] Leszczynski A. 2009. Quantitative limits to qualitative engagements: GIS, its critics, and the philosophical divide. The Professional Geographer, 61(3), 350– 365. [v] Levin SA. 1998. Ecosystems and the biosphere as complex adaptive systems. Ecosystems, 1(5), 431–436. [228] Levinson M. 2006. The Box: How the Shipping Container Made the World Smaller and the World Economy Bigger. Princeton University Press. [56] Li Vigni F. 2022. Hayek at the Santa Fe Institute: Origins, models, and organization of the cradle of complexity sciences. Centaurus, 64(2), 443–481. [227] Ligozat G. 2013. Qualitative Spatial and Temporal Reasoning. International Society for Technology in Education. [85]

REFERENCES

279

Little J, L Peake & P Richardson, (Eds). 1988. Women in Cities: Gender and the Urban Environment. Macmillan Education. [202] Livingstone DN. 1993. The Geographical Tradition: Episodes in the History of a Contested Enterprise. Blackwell. [2] Lloyd CD. 2014. Exploring Spatial Scale in Geography. Wiley Blackwell. [74] Lloyd CD, IG Shuttleworth & DWS Wong, (Eds). 2015. Social-Spatial Segregation: Concepts, Processes and Outcomes. Policy Press. [130] Longley PA. 2000. The academic success of GIS in geography: Problems and prospects. Journal of Geographical Systems, 2(1), 37–42. [2] Longley PA. 2005. Geographical information systems: A renaissance of geodemographics for public service delivery. Progress in Human Geography, 29(1), 57–63. [142] Lu Y, S Laffan, C Pettit & M Cao. 2019. Land use change simulation and analysis using a vector cellular automata (CA) model: A case study of Ipswich City, Queensland, Australia. Environment and Planning B: Urban Analytics and City Science, 47(9), 1605–1621. [238] Lucchesi AH. 2022. Mapping violence against Indigenous women and girls: Beyond colonizing data and mapping practices. ACME: An International Journal for Critical Geographies, 21(4), 389–398. [8] Lynch K. 1960. The Image of the City. MIT Press. [84, 85, 104, 105] MacEachren AM. 1995. How Maps Work: Representation, Visualization and Design. Guilford Press. [251] MacGill SM. 1984. Cluster analysis and Q-Analysis. International Journal of ManMachine Studies, 20(6), 595–604. [147] Mackenzie K, J Pirker & F Reitsma. 2020. Towards a spatiotemporal data model for traditional ecological knowledge/indigenous knowledge. Cartographica, 55(1), 29–41. [186] MacKinnon D. 2011. Reconstructing scale: Towards a new scalar politics. Progress in Human Geography, 35(1), 21–36. [56] Madden DJ. 2014. Neighborhood as spatial project: Making the urban order on the Downtown Brooklyn waterfront. International Journal of Urban and Regional Research, 38(2), 471–497. [83] Madden DJ. 2018. Pushed off the map: Toponymy and the politics of place in New York City. Urban Studies, 55(8), 1599–1614. [98] Maggi E & E Vallino. 2016. Understanding urban mobility and the impact of public policies: The role of the agent-based models. Research in Transportation Economics, 55, 50–59. [242]

280

REFERENCES

Mahoney MS. 2005. The histories of computing(s). Interdisciplinary Science Reviews, 30(2), 119–135. [1] Malpas J. 1999. Place and Experience: A Philosophical Topography. Cambridge University Press. [86] Malpas J. 2012. Putting space in place: Philosophical topography and relational geography. Environment and Planning D: Society and Space, 30(2), 226–242. [24] Mamadouh V, A Meijer, JD Sidaway & H van der Wusten. 2015. Toward an urban geography of diplomacy: Lessons from The Hague. The Professional Geographer, 67(4), 564–574. [126] Manolescu M. 2018. Cartographies of New York and Other Postwar American Cities: Art, Literature and Urban Spaces. Palgrave Macmillan. [36] Manson SM. 2008. Does scale exist? An epistemological scale continuum for complex human–environment systems. Geoforum, 39(2), 776–788. [57] Mark DM, SM Freundschuh, AU Frank, MJ Egenhofer, MR White & M McGranahan. 1989. Languages of Spatial Relationships. Technical Report 89-2. National Center for Geographic Information and Analysis. [59] Marston SA. 2000. The social construction of scale. Progress in Human Geography, 24(2), 219–242. [54, 203] Marston SA, JP Jones III & K Woodward. 2005. Human geography without scale. Transactions of the Institute of British Geographers, 30(4), 416–432. [54– 56] Marston SA & N Smith. 2001. States, scales and households: Limits to scale thinking? A response to Brenner. Progress in Human Geography, 25(4), 615– 619. [54] Martin D. 1998. Optimizing census geography: The separation of collection and output geographies. International Journal of Geographical Information Science, 12(7), 673–685. [138] Martin GJ. 1989. The nature of geography and the Schaefer-Hartshorne debate. In JN Entrikin & SD Brunn, (Eds). Reflections on Richard Hartshorne’s “The Nature of Geography.” Occasional Papers of the Association of American Geographers. AAG, 69–88. [183] Martin S, WM Brown, R Klavans & KW Boyack. 2011. OpenOrd: An opensource toolbox for large graph layout. In SPIE Proceedings Volume 7868 Visualization and Data Analysis. [175] Massey D. 1991a. A global sense of place. Marxism Today, (June), 24–29. [89, 92, 101, 208]

REFERENCES

281

Massey D. 1991b. Flexible sexism. Environment and Planning D: Society and Space, 9(1), 31–57. [91] Massey D. 1991c. The political place of locality studies. Environment and Planning A, 23(2), 267–281. [90, 91] Massey D. 1995. Spatial Divisions of Labor: Social Structures and the Geography of Production. (2nd ed.). Routledge. [53, 90] Massey D. 1999. Space-time, “science” and the relationship between physical geography and human geography. Transactions of the Institute of British Geographers, 24(3), 261–276. [v] Massey D. 2001. Talking of space-time. Transactions of the Institute of British Geographers, 26(2), 257–261. [v] Massey D. 2005. For Space. SAGE. [14, 75, 76, 86, 90–92, 109, 200] Matthews RB, NG Gilbert, A Roach, JG Polhill & NM Gotts. 2007. Agent-based land-use models: A review of applications. Landscape Ecology, 22(10), 1447– 1459. [242] Mavoa S, N Bagheri, MJ Koohsari, AT Kaczynski, KE Lamb, K Oka, D O’Sullivan & K Witten. 2019. How do neighbourhood definitions influence the associations between built environment and physical activity? International Journal of Environmental Reseach and Public Health, 16, 1501. [100] Mavoa S, K Lamb, D O’Sullivan, K Witten & M Smith. 2018. Are disadvantaged children more likely to be excluded from analysis when applying global positioning systems inclusion criteria? BMC Research Notes, 11, 578. [101] McDowall C & T Denee. 2019. We Are Here: An Atlas of Aotearoa. Massey University Press. [99, 107] McElroy E. 2022. Digital cartographies of displacement: Data as property and property as data. ACME: An International Journal for Critical Geographies, 21(4), 357–371. [8] McKenzie G & B Adams. 2017. Juxtaposing thematic regions derived from spatial and platial user-generated content. In E Clementini, M Donnelly, M Yuan, C Kray, P Fogliaroni & A Ballatore, (Eds). 13th International Conference on Spatial Information Theory, L’Aquila, Italy. Schloss Dagstuhl, 20:1–20:14. [103] McLafferty SL. 2002. Mapping women’s worlds: Knowledge, power and the bounds of GIS. Gender, Place and Culture: A Journal of Feminist Geography, 9(3), 263–269. [254] Mennis J, DJ Peuquet & L Qian. 2000. A conceptual framework for incorporating cognitive principles into geographical database representation. International Journal of Geographical Information Science, 14(6), 501–520. [187]

282

REFERENCES

Merrifield A. 2017. The Amateur: The Pleasures of Doing What You Love. Verso. [7] Merriman P. 2012. Human geography without time-space. Transactions of the Institute of British Geographers, 37(1), 13–27. [205] Mesle CR. 2008. Process-Relational Philosophy: An Introduction to Alfred North Whitehead. Templeton Foundation Press. [214, 215] Miller HJ & EA Wentz. 2003. Representation and spatial analysis in geographic information systems. Annals of the Association of American Geographers, 93(3), 574–594. [248, 249] Miller R. 1982. Household activity patterns in nineteenth-century suburbs: A time-geographic exploration. Annals of the Association of American Geographers, 72(3), 355–371. [202] Miller R. 1983. The Hoover® in the garden: Middle-class women and suburbanization, 1850–1920. Environment and Planning D: Society and Space, 1(1), 73–87. [202] Mitchell D. 2003. The Right to the City: Social Justice and the Fight for Public Space. Guilford Press. [87] Mitchell M. 2008. Complexity: A Guided Tour. Oxford University Press. [227] Mocnik F-B. 2022. Putting geographical information science in place – towards theories of platial information and platial information systems. Progress in Human Geography, 46(3), 798–828. [77, 94, 106] Mocnik F-B & D Fairbairn. 2018. Maps telling stories? The Cartographic Journal, 55(1), 36–57. [106] Molotch H. 1979. Capital and neighborhood in the United States: Some conceptual links. Urban Affairs Quarterly, 14(3), 289–312. [83] Monk J & S Hanson. 1982. On not excluding half of the human in human geography. The Professional Geographer, 34(1), 11–23. [54, 202] Monmonier MS. 2001. Bushmanders & Bullwinkles: How Politicians Manipulate Electronic Maps and Census Data to Win Elections. University of Chicago Press. [136] Montello DR. 1993. Scale and multiple psychologies of space. In AU Frank & I Campari, (Eds). Spatial Information Theory: A Theoretical Basis for GIS. Lecture Notes in Computer Science 716. Springer, 312–321. [57–59] Moore A, M Nowostawski, C Frantz & C Hulbe. 2018. Comic strip narratives in time geography. ISPRS International Journal of Geo-Information, 7(7), 245. [204] Moretti F. 2007. Graphs, Maps, Trees: Abstract Models for Literary History. Verso. [107]

REFERENCES

283

Morrill RL. 1987. Redistricting, region and representation. Political Geography Quarterly, 6(3), 241–260. [137] Morrill RL. 2005. Hägerstrand and the “quantitative revolution”: A personal appreciation. Progress in Human Geography, 29(3), 333–336. [193] Morrone JJ. 2018. The spectre of biogeographical regionalization. Journal of Biogeography, 45(2), 282–288. [48] Morton GM. 1966. A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing. Technical Report. IBM. [80] Moudon AV & M Hubner, (Eds). 2000. Monitoring Land Supply with Geographic Information Systems: Theory, Practice, and Parcel-Based Approaches. Wiley. [128, 185] Mountz A. 2010. Seeking Asylum: Human Smuggling and Bureaucracy at the Border. University of Minnesota Press. [121, 127] Mountz A. 2013. Political geography I: Reconfiguring geographies of sovereignty. Progress in Human Geography, 37(6), 829–841. [119, 126] Mountz A. 2015. Political geography II: Islands and archipelagos. Progress in Human Geography, 39(5), 636–646. [120] Mountz A. 2018. Political geography III: Bodies. Progress in Human Geography, 42(5), 759–769. [121] Mukherjee F. 2015. Public participatory GIS. Geography Compass, 9(7), 384–394. [115] Muniesa F. 2015. Actor-network theory. In JD Wright, (Ed). International Encyclopedia of the Social & Behavioral Sciences. (2nd edn). Elsevier, 80–84. [155, 156] Mustafa A, A Heppenstall, H Omrani, I Saadi, M Cools & J Teller. 2018. Modelling built-up expansion and densification with multinomial logistic regression, cellular automata and genetic algorithm. Computers, Environment and Urban Systems, 67, 147–156. [238] Nathan R, WM Getz, E Revilla, M Holyoak, R Kadmon, D Saltz & PE Smouse. 2008. A movement ecology paradigm for unifying organismal movement research. Proceedings of the National Academy of Sciences, 105(49), 19052– 19059. [182, 205] Nelson GD & A Rae. 2016. An economic geography of the United States: From commutes to megaregions. PLOS ONE, 11(11), e0166083. [166] Neutens T, N Van de Weghe, F Witlox & P De Maeyer. 2008. A threedimensional network-based space–time prism. Journal of Geographical Systems, 10(1), 89–107. [198]

284

REFERENCES

Neveling P. 2020. The political economy of special economic zones: Pasts, presents, futures. In A Oqubay & JY Lin, (Eds). The Oxford Handbook of Industrial Hubs and Economic Development. Oxford University Press, 189–205. [120] New Zealand Post. 2018. Postcode Network File Overview. Technical Report. New Zealand Post Group. [81] Newman MEJ. 2004. Fast algorithm for detecting community structure in networks. Physical Review E, 69(6), 066133. [165] Newman MEJ. 2018. Networks. (2nd edn). Oxford University Press. [147, 156, 164, 171] Newman MEJ & M Girvan. 2004. Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113. [165] Newman MEJ & TP Peixoto. 2015. Generalized communities in networks. Physical Review Letters, 115(8), 088701. [171] Nunes J. 1991. Geographic space as a set of concrete geographical entities. In DM Mark & AU Frank, (Eds). Cognitive and Linguistic Aspects of Geographic Space. Springer Netherlands, 9–33. [17] O’Sullivan D. 2001. Graph cellular automata: A generalised discrete urban and regional model. Environment and Planning B: Planning and Design, 28(5), 687– 705. [43, 238] O’Sullivan D. 2002. Toward micro-scale spatial modeling of gentrification. Journal of Geographical Systems, 4(3), 251–274. [238] O’Sullivan D. 2004. Complexity science and human geography. Transactions of the Institute of British Geographers, 29(3), 282–295. [4, 227] O’Sullivan D. 2005. Geographical information science: Time changes everything. Progress in Human Geography, 29(6), 749–756. [5, 192] O’Sullivan D. 2006. Geographical information science: Critical GIS. Progress in Human Geography, 30(6), 783–791. [5, 7] O’Sullivan D. 2008. Geographical information science: Agent-based models. Progress in Human Geography, 32(4), 541–550. [5] O’Sullivan D. 2009. Changing neighborhoods–neighborhoods changing: A framework for spatially explicit agent-based models of social systems. Sociological Methods Research, 37(4), 498–530. [238] O’Sullivan D. 2018. Big data ... why (oh why?) this computational social science? In JE Thatcher, J Eckert & A Shears, (Eds). Thinking Big Data in Geography: New Regimes, New Research. University of Nebraska Press, 21–38. [230] O’Sullivan D & M Haklay. 2000. Agent-based models and individualism: Is the world agent-based? Environment and Planning A, 32(8), 1409–1425. [243]

REFERENCES

285

O’Sullivan D, A Morrison & J Shearer. 2000. Using desktop GIS for the investigation of accessibility by public transport: An isochrone approach. International Journal of Geographical Information Science, 14(1), 85–104. [198] O’Sullivan D & GLW Perry. 2013. Spatial Simulation: Exploring Pattern and Process. Wiley. [207, 231, 237, 241] O’Sullivan D & A Turner. 2001. Visibility graphs and landscape visibility analysis. International Journal of Geographical Information Science, 15(3), 221– 237. O’Sullivan D & DJ Unwin. 2010. Geographic Information Analysis. (2nd edn). Wiley. [31, 219, 220] O’Sullivan D, T Evans, S Manson, S Metcalf, A Ligmann-Zielinska & C Bone. 2016. Strategic directions for agent-based modeling: Avoiding the YAAWN syndrome. Journal of Land Use Science, 11(2), 177–187. [242] Odell J. 2019. How to Do Nothing: Resisting the Attention Economy. Melville House. [13] Okabe A, B Boots, K Sugihara & SN Chiu. 2000. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. (2nd edn). Wiley. [37] Okabe A & K Sugihara. 2012. Spatial Analysis Along Networks: Statistical and Computational Methods. Wiley. [179] Okubo A. 1986. Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds. Advances in Biophysics, 22, 1–94. [241] Okuyama T. 2009. Local interactions between predators and prey call into question commonly used functional responses. Ecological Modelling, 220(9–10), 1182–1188. [239] Olsson G. 1969. Inference problems in locational analysis. In KR Cox & RG Golledge, (Eds). Behavioral Models in Geography: A Symposium. Northwestern University Press, 14–24. [221] Olsson G. 1980. Birds in Egg: Eggs in Bird. (2nd edn). Pion. [13] Openshaw S. 1977. A geographical solution to scale and aggregation problems in region-building, partitioning and spatial modelling. Transactions of the Institute of British Geographers, 2(4), 459. [137] Openshaw S. 1983. The Modifiable Areal Unit Problem. CATMOG 38. Geo Abstracts. [137] Openshaw S & L Rao. 1995. Algorithms for reengineering 1991 census geography. Environment and Planning A, 27(3), 425–446. [137] Openshaw S & PJ Taylor. 1979. A million or so correlation coefficients: Three experiments on the modifiable areal unit problem. In N Wrigley, (Ed). Statistical Applications in the Spatial Sciences. Pion, 127–144. [134, 135]

286

REFERENCES

Parkes DN & NJ Thrift. 1975. Timing space and spacing time. Environment and Planning A, 7(6), 651–670. [199] Parkes DN & NJ Thrift, (Eds). 1980. Times, Spaces, and Places: A Chronogeographic Perspective. Wiley. [199] Pavlovskaya M. 2006. Theorizing with GIS: A tool for critical geographies? Environment and Planning A, 38(11), 2003–2020. [249] Pavlovskaya M. 2009. Feminist Visualization. In RM Kitchin & NJ Thrift, (Eds). International Encylopedia of Human Geography. Elsevier, 157–164. [203] Payne WB. 2017. Welcome to the polygon: Contested digital neighborhoods and spatialized segregation on Nextdoor. Computational Culture, 6. [101] Pearce MW & MJ Hermann. 2010. Mapping Champlain’s travels: Restorative techniques for historical cartography. Cartographica, 45(1), 32–46. [106] Peixoto TP. 2014. Hierarchical block structures and high-resolution model selection in large networks. Physical Review X, 4(1), 1–18. [171] Pelekis N, B Theodoulidis, I Kopanakis & Y Theodoridis. 2004. Literature review of spatio-temporal database models. The Knowledge Engineering Review, 19(3), 235–274. [192] Peluso NL. 1995. Whose woods are these? Counter-mapping forest territories in Kalimantan, Indonesia. Antipode, 27(4), 383–406. [115] Peña E & H Sayama. 2021. Life worth mentioning: Complexity in life-like cellular automata. Artificial Life, 27(2), 105–112. [237] Pereyra PJ. 2016. Revisiting the use of the invasive species concept: An empirical approach. Austral Ecology, 41(5), 519–528. [88] Peucker TK & N Chrisman. 1975. Cartographic data structures. The American Cartographer, 2(1), 55–69. [33, 35] Peuquet DJ. 1984. A conceptual framework and comparison of spatial data models. Cartographica, 21(4), 66–113. [26] Peuquet DJ. 1994. It’s about time: A conceptual framework for the representation of temporal dynamics in geographic information systems. Annals of the Association of American Geographers, 84(3), 441–461. [184, 191] Peuquet DJ. 2003. Representations of Space and Time. Guilford Press. [184, 191] Phillips JD. 1999. Divergence, convergence, and self-organization in landscapes. Annals of the Association of American Geographers, 89(3), 466–488. [227] Phillips JD. 2016. Vanishing point: Scale independence in geomorphological hierarchies. Geomorphology, 266, 66–74. [48] Phillips JD, W Schwanghart & T Heckmann. 2015. Graph theory in the geosciences. Earth-Science Reviews, 143, 147–160. [156] Piaget J & B Inhelder. 1967. The Child’s Conception of Space. Norton. [84]

REFERENCES

287

Pickles J, (Ed). 1995. Ground Truth: The Social Implications of Geographic Information Systems. Guilford Press. [4, 14, 250] Pickles J. 1997. Tool or science? GIS, technoscience and the theoretical turn. Annals of the Association of American Geographers, 87(2), 363–372. [253] Pickles J. 2004. A History of Spaces: Cartographic Reason, Mapping and the Geo-coded World. Routledge. [3, 17, 21, 114] Pickles J. 2006. Ground Truth 1995–2005. Transactions in GIS, 10(5), 763–772. [253] Pike D. 2018. The History of Navigation. Pen & Sword Maritime. [19] Plummer P & ES Sheppard. 2001. Must emancipatory economic geography be qualitative? Antipode, 33(2), 194–199. [249] Poiker T. 1995. Preface to special issue. Cartography and Geographic Information Systems, 22(1), 3–4. [7] Poorthuis A. 2018. How to draw a neighborhood? The potential of big data, regionalization, and community detection for understanding the heterogeneous nature of urban neighborhoods. Geographical Analysis, 50(2), 182–203. [138] Portugali J. 2000. Self-Organization and the City. Springer-Verlag. [227] Pred A. 1981. Social reproduction and the time-geography of everyday life. Geografiska Annaler. Series B, Human Geography, 63(1), 5–22. [199] Pred A. 1983. From here and now to there and then: Some notes on diffusions, defusions and disillusions. In M Billinge, D Gregory & R Martin, (Eds). Recollections of a Revolution: Geography as Spatial Science. Macmillan Education, 86– 103. [5] Pred A. 1984. Place as historically contingent process: Structuration and the time-geography of becoming places. Annals of the Association of American Geographers, 74(2), 279–297. [89, 199] Prigogine I & I Stengers. 1984. Order Out of Chaos: Man’s New Dialogue with Nature. Bantam Books. [216] Prytherch DL. 2007. Urban geography with scale: Rethinking scale via Wal-mart’s “geography of big things.” Urban Geography, 28(5), 456–482. [56] Prytherch DL. 2008. It’s not about big or small, it’s how you play the game: A rejoinder to Woodward, Jones, and Marston. Urban Geography, 29(1), 85–86. [57] Purves RS & C Derungs. 2015. From space to place: Place-based explorations of text. International Journal of Humanities and Arts Computing, 9(1), 74–94. [94, 101, 102]

288

REFERENCES

Qiang Y, M Delafontaine, M Versichele, P De Maeyer & N Van de Weghe. 2012. Interactive analysis of time intervals in a two-dimensional space. Information Visualization, 11(4), 255–272. [187] Randell DA, Z Cui & AG Cohn. 1992. A spatial logic based on regions and connection. In B Nebel, C Rich & W Swartout, (Eds). Principles of Knowledge Representation and Reasoning. 3rd International Conference KR’92. Morgan Kaufmann, 165–196. [189] Rankin W. 2016. After the Map: Cartography, Navigation, and the Transformation of Territory in the Twentieth Century. University of Chicago Press. [19, 23] Raper J & D Livingstone. 2001. Let’s get real: Spatio-temporal identity and geographic entities. Transactions of the Institute of British Geographers, 26(2), 237– 242. [v] Raposo P. 2017. Scale and generalization. Geographic Information Science & Technology Body of Knowledge, 2017(Q4). [72] Reid G & R Sieber. 2020. Do geospatial ontologies perpetuate Indigenous assimilation? Progress in Human Geography, 44(2), 216–234. [213] Reid G, R Sieber & S Blackned. 2020. Visions of time in geospatial ontologies from Indigenous peoples: A case study with the Eastern Cree in Northern Quebec. International Journal of Geographical Information Science, 34(12), 2335– 2360. [186, 213] Reutzel DR. 1985. Story maps improve comprehension. The Reading Teacher, 38(4), 400–404. [107] Reynolds CW. 1987. Flocks, herds, and schools: A distributed behavioral model. Computer Graphics (SIGGRAPH ’87 Conference Proceedings), 21(4), 25–34. [241] Rickard H. 2020. Crowdsourcing Neighbourhood Delineations in Wellington City, New Zealand. MSc. Victoria University of Wellington. [82] Ripley BD. 1981. Spatial Statistics. Wiley. [31] Rittel HWJ & MM Webber. 1973. Dilemmas in a general theory of planning. Policy Sciences, 4(2), 155–169. [216] Robinson GWS. 1959. Exclaves. Annals of the Association of American Geographers, 49(3), 283–295. [125] Robinson I, J Webber & E Eifrem. 2015. Graph Databases. (2nd edn). O’Reilly. [41] Robinson K. 2005. Towards a metaphysics of complexity. Interchange, 36(1–2), 159–177. [227] Robinson WS. 1950. Ecological correlations and the behavior of individuals. American Sociological Review, 15(3), 351–357. [135]

REFERENCES

289

Rose G. 1993. Feminism and Geography: The Limits of Geographical Knowledge. Polity Press. [202, 203] Rose-Redwood RS. 2006. Governmentality, geography, and the geo-coded world. Progress in Human Geography, 30(4), 469–486. [78] Rose-Redwood RS. 2012. With numbers in place: Security, territory, and the production of calculable space. Annals of the Association of American Geographers, 102(2), 295–319. [78] Roth RE, CA Brewer & MS Stryker. 2011. A typology of operators for maintaining legible map designs at multiple scales. Cartographic Perspectives, 68, 29–64. [73] Sack RD. 1986. Human Territoriality: Its Theory and History. Cambridge University Press. [117] Sack RD. 1997. Homo Geographicus: A Framework for Action, Awareness and Moral Concern. John Hopkins University Press. [108] Sadler RC. 2019. Misalignment between ZIP codes and municipal boundaries: A problem for public health. Cityscape, 21(3), 335–340. [130] Sahr K, D White & AJ Kimerling. 2003. Geodesic discrete global grid systems. Cartography and Geographic Information Science, 30(2), 121–134. [80] Sakoda JM. 1971. The checkerboard model of social interaction. Journal of Mathematical Sociology, 1(1), 119–132. [240] Samet H. 1990. The Design and Analysis of Spatial Data Structures. AddisonWesley. [34, 62] Sampson RJ. 2012. Great American City: Chicago and the Enduring Neighborhood Effect. University of Chicago Press. [141] Sampson RJ, JD Morenoff & G-R Thomas. 2002. Assessing “neighborhood effects”: Social processes and new directions in research. Annual Review of Sociology, 28, 443–478. [100] Santos M. [2002] 2021. The Nature of Space. Trans. BC Baletti. Duke University Press. [44] Sayer A. 1985. The difference that space makes. In D Gregory & J Urry, (Eds). Social Relations and Spatial Structures. Macmillan, 49–66. [25] Sayer A. 1989. The “new” regional geography and problems of narrative. Environment and Planning D: Society and Space, 7(3), 253–276. [92] Sayer A. 1992. Method in Social Science: A Realist Approach. Routledge. [201] Sayre NF. 2005. Ecological and geographical scale: Parallels and potential for integration. Progress in Human Geography, 29(3), 276–290. [54]

290

REFERENCES

Schaefer FK. 1953. Exceptionalism in geography: A methodological examination. Annals of the Association of American Geographers, 43(3), 226. [183] Scheider S & K Janowicz. 2014. Place reference systems: A constructive activity model of reference to places. Applied Ontology, 9(2), 97–127. [103] Schellinck J & T White. 2011. A review of attraction and repulsion models of aggregation: Methods, findings and a discussion of model validation. Ecological Modelling, 222(11), 1897–1911. [242] Schelling TC. 1969. Models of segregation. American Economic Review, 59(2), 488–493. [240] Schelling TC. 1971. Dynamic models of segregation. Journal of Mathematical Sociology, 1(2), 143–186. [240] Schelling TC. 1978. Micromotives and Macrobehavior. Norton. [241] Schulze J, B Müller, J Groeneveld & V Grimm. 2017. Agent-based modelling of social-ecological systems: Achievements, challenges, and a way forward. Journal of Artificial Societies and Social Simulation, 20(2). [242] Schuurman N. 1999. Critical GIS: Theorizing an emerging science. Cartographica, 36(4), 1–107. [7, 14, 250] Schuurman N & G Pratt. 2002. Care of the subject: Feminism and critiques of GIS. Gender, Place & Culture, 9(3), 291–299. [vi] Schwanen T. 2007. Matter(s) of interest: Artefacts, spacing and timing. Geografiska Annaler: Series B, Human Geography, 89(1), 9–22. [201] Schwanen T & M-P Kwan. 2009. “Doing” critical geographies with numbers. The Professional Geographer, 61(4), 459–464. [203] Scott JC. 1998. Seeing Like a State: How Certain Schemes to Improve the Human Condition Have Failed. Yale University Press. [118] Seibt J. 2018. Process philosophy. In EN Zalta, (Ed). The Stanford Encyclopedia of Philosophy. (Winter 2018). Metaphysics Research Lab, Stanford University. url: plato . stanford . edu / archives / win2018 / entries / process - philosophy/. [212, 214] Semboloni F. 2000. The growth of an urban cluster into a dynamic selfmodifying spatial pattern. Environment and Planning B: Planning and Design, 27(4), 549–564. [238] Shatford S. 1986. Analyzing the subject of a picture: A theoretical approach. Cataloging & Classification Quarterly, 6(3), 39–62. [102] Shaviro S. 2009. Without Criteria: Kant, Whitehead, Deleuze, and Aesthetics. MIT Press. [227]

REFERENCES

291

Shaw S-L & D Sui, (Eds). 2018. Human Dynamics Research in Smart and Connected Communities. Human Dynamics in Smart Cities. Springer. [205, 206] Sheller M & J Urry. 2006. The new mobilities paradigm. Environment and Planning A, 38(2), 207–226. [180, 205] Shelton T. 2018. Rethinking the RECAP: Mapping the relational geographies of concentrated poverty and affluence in Lexington, Kentucky. Urban Geography, 39(7), 1070–1091. [154] Shep S, M Frean, R Owen, R Pope, P Reihana & V Chan. 2021. Indigenous frameworks for data-intensive humanities: Recalibrating the past through knowledge engineering and generative modelling. Journal of Data Mining & Digital Humanities, Histoinformatics, 6095. [129] Sheppard ES. 1995. GIS and society: Towards a research agenda. Cartography and Geographic Information Systems, 22(1), 5–16. [8] Sheppard ES. 2001. Quantitative geography: Representations, practices, and possibilities. Environment and Planning D: Society and Space, 19(5), 535–554. [248, 249] Sheppard ES. 2002. The spaces and times of globalization: Place, scale, networks, and positionality. Economic Geography, 78(3), 307–330. [23] Sheppard ES. 2006. David Harvey and dialectical space-time. In N Castree & D Gregory, (Eds). David Harvey. Blackwell Publishing Ltd, 121–141. [91] Sheppard ES & RB McMaster, (Eds). 2004. Scale and Geographic Inquiry: Nature, Society, and Method. Blackwell Pub. [45] Shewly HJ. 2013. Abandoned spaces and bare life in the enclaves of the India–Bangladesh border. Political Geography, 32, 23–31. [126] Siabato W, C Claramunt, S Ilarri & MA Manso-Callejo. 2018. A survey of modelling trends in temporal GIS. ACM Computing Surveys, 51(2), 1–41. [184, 192] Sibson R. 1981. A brief description of natural neighbour interpolation. In V Barnett, (Ed). Interpreting Multivariate Data. Wiley, 21–36. [38] Sieber R. 2004. Rewiring for a GIS/2. Cartographica, 39(1), 25–39. [249] Simes JT. 2021. Punishing Places: The Geography of Mass Imprisonment. University of California Press. [120] Simon D. 2002–2008. The Wire. [92] Simon HA. 1962. The architecture of complexity. Proceedings of the American Philosophical Society, 106(6), 467–482. [49, 229] Simon HA. 1973. The organization of complex systems. In HH Pattee, (Ed). Hierarchy Theory: The Challenge of Complex Systems. George Braziller, 1–27. [50]

292

REFERENCES

Simons PM. 1987. Parts: A Study in Ontology. Clarendon Press. [143] Singleton AD & PA Longley. 2009. Creating open source geodemographics: Refining a national classification of census output areas for applications in higher education. Papers in Regional Science, 88(3), 643–666. [142] Singleton AD & SE Spielman. 2013. The past, present, and future of geodemographic research in the United States and United Kingdom. The Professional Geographer, 66(4), 558–567. [141] Smith B. 1994. Fiat objects. In N Guarino, L Vieu & S Pribbenow, (Eds). Parts and Wholes: Conceptual Part-Whole Relations and Formal Mereology, 11th European Conference on Artificial Intelligence. European Coordinating Committee for Artificial Intelligence, 15–22. [121] Smith B. 1995. On drawing lines on a map. In AU Frank & W Kuhn, (Eds). Spatial Information Theory: A Theoretical Basis for GIS. Lecture Notes in Computer Science 988. Springer, 475–484. [121, 122] Smith B. 2001. Fiat objects. Topoi, 20(2), 131–148. [121–123, 143] Smith B & DM Mark. 2003. Do mountains exist? Towards an ontology of landforms. Environment and Planning B: Planning and Design, 30(3), 411–427. [96, 102, 122] Smith B & AC Varzi. 1997. Fiat and bona fide boundaries: Towards an ontology of spatially extended objects. In SC Hirtle & AU Frank, (Eds). Spatial Information Theory: A Theoretical Basis for GIS. Lecture Notes in Computer Science 1329. Springer, 103–119. [121] Smith B & AC Varzi. 2000. Fiat and bona fide boundaries. Philosophy and Phenomenological Research, 60(2), 401. [121] Smith CW. 2000. Straying beyond the boundaries of belief: M¯aori epistemologies inside the curriculum. Educational Philosophy and Theory, 32(1), 43–51. [213] Smith N. 1982. Gentrification and uneven development. Economic Geography, 58(2), 139–155. [51, 52] Smith N. 1984. Uneven Development: Nature, Capital, and the Production of Space. Blackwell. [51] Smith N. 1989. Geography as museum: Conservative idealism in “The Nature of Geography.” In JN Entrikin & SD Brunn, (Eds). Reflections on Richard Hartshorne’s “The Nature of Geography.” Occasional Papers of the Association of American Geographers. AAG, 89–120. [183] Smith N. 1992. Contours of a spatialized politics: Homeless vehicles and the production of geographical scale. Social Text, 33, 54–81. [51, 53]

REFERENCES

293

Smith N. 2005. Neo-critical geography, or, the flat pluralist world of business class. Antipode, 37(5), 887–899. [224] Smith N & W Dennis. 1987. The restructuring of geographical scale: Coalescence and fragmentation of the northern core region. Economic Geography, 63(2), 160–182. [52] Smith T. 2000. Ng¯a tini a¯ huatanga o whakapapa korero. Educational Philosophy ¯ and Theory, 32(1), 53–60. [213] Snyder JP. 1987. Map Projections: A Working Manual. U.S. Government Printing Office. [65] Sobel D. 2007. Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time. Bloomsbury. [19] Soja EW. 1971. The Political Organization of Space. Association of American Geographers, Commission on College Geography. [117] Spielman SE, D Folch & N Nagle. 2014. Patterns and causes of uncertainty in the American Community Survey. Applied Geography, 46, 147–157. [72] Staeheli LA & D Mitchell. 2008. The People’s Property? Power, Politics, and the Public. Routledge. [88] Stein LD. 2008. Bioinformatics: Alive and kicking. Genome Biology, 9(12), 114. [2] Steinberg PE. 2009. Sovereignty, territory, and the mapping of mobility: A view from the outside. Annals of the Association of American Geographers, 99(3), 467– 495. [118] Stell JG. 2017. Mereotopology and computational representations of the body. Computational Culture, 6. [144] Stellman SD. 1973. A spherical chicken. Science, 182(4119), 1296. [229] Stengers I. 2008. A constructivist reading of Process and Reality. Theory, Culture & Society, 25(4), 91–110. [218] Stengers I. 2011. Thinking with Whitehead: A Free and Wild Creation of Concepts. Trans. M Chase. Harvard University Press. [214] Stengers I. 2018. Another Science Is Possible: A Manifesto for Slow Science. Trans. S Muecke. Polity. [216] Stevens D & S Dragićević. 2007. A GIS-based irregular cellular automata model of land-use change. Environment and Planning B: Planning and Design, 34(4), 708–724. [238] Stewart GT. 2020. M¯aori Philosophy: Indigenous Thinking from Aotearoa. Bloomsbury Academic. [212, 223] Stoneham AKM. 1977. The small-world problem in a spatial context. Environment and Planning A, 9(2), 185–195. [173]

294

REFERENCES

Storey D. 2012. Territories: Nations, States, and the Claiming of Space. (2nd edn). Routledge. [117] Stoyan D. 2006. Fundamentals of point process statistics. In A Baddeley, P Gregori, J Mateu, R Stoica & D Stoyan, (Eds). Case Studies in Spatial Point Process Modeling. Springer, 3–22. [31] Stuesse A & M Coleman. 2014. Automobility, immobility, altermobility: Surviving and resisting the intensification of immigrant policing. City & Society, 26(1), 51–72. [121] Sugiura K. 2014. Experiments in “Time Distance Map.” Kajima Publishing. [177] Sui D. 2012. Looking through Hägerstrand’s dual vistas: Towards a unifying framework for time geography. Journal of Transport Geography, 23, 5–16. [207, 208] Sundberg J. 2014. Decolonizing posthumanist geographies. cultural geographies, 21(1), 33–47. [212, 213] Swyngedouw E. 1997. Neither global nor local: “Glocalisation” and the politics of scale. In KR Cox, (Ed). Spaces of Globalisation: Reasserting the Power of the Local. Guilford Press, 137–166. [53] Takeyama M. 1997. Building spatial models within GIS through geo-algebra. Transactions in GIS, 2(3), 245–256. [43] Takeyama M & H Couclelis. 1997. Map dynamics: Integrating cellular automata and GIS through geo-algebra. International Journal of Geographical Information Science, 11(1), 73–91. [43, 231] Tamassia R, (Ed). 2014. Handbook of Graph Drawing and Visualization. CRC Press. [177] Taylor PJ. 1981. Geographical scales within the world-economy approach. Review (Fernand Braudel Center), 5(1), 3–11. [52] Taylor PJ. 1982. A materialist framework for political geography. Transactions of the Institute of British Geographers, 7(1), 15–34. [52] Taylor PJ. 1999. Places, spaces and Macy’s: Place–space tensions in the political geography of modernities. Progress in Human Geography, 23(1), 7–26. [53] Taylor PJ, G Catalano & DRF Walker. 2002. Measurement of the world city network. Urban Studies, 39(13), 2367–2376. [161, 162] Thatcher JE, LR Bergmann & D O’Sullivan. 2016. Searching for common ground (again). In JA Miller, D O’Sullivan & N Wiegand, (Eds). International Conference on GIScience Short Paper Proceedings. GIScience 2016, 304–307. [247]

REFERENCES

295

Thatcher JE, R Burns & TP Lauriault. 2020. Digital Geographies. In A Kobayashi, (Ed). International Encyclopedia of Human Geography. Elsevier Science. url: search.credoreference.com/articles/Qm9va0FydGljbGU6NTg0NDE=. [8] Thompson DW. [1942] 1992. On Growth and Form. (2nd edn). Dover. [246] Thrift NJ. 1977a. An Introduction to Time-Geography. CATMOG 13. Geo Abstracts. [193, 200] Thrift NJ. 1977b. Time and theory in human geography. Part I. Progress in Human Geography, 1(1), 65–101. [199] Thrift NJ. 1977c. Time and theory in human geography. Part II. Progress in Human Geography, 1(3), 413–457. [199] Thrift NJ. 1983. On the determination of social action in space and time. Environment and Planning D: Society and Space, 1(1), 23–57. [200] Thrift NJ. 1999. The place of complexity. Theory, Culture & Society, 16(3), 31–69. [226, 230] Thrift NJ. 2005. Torsten Hägerstrand and social theory. Progress in Human Geography, 29(3), 337–340. [201] Thrift NJ & A Pred. 1981. Time-geography: A new beginning. Progress in Geography, 5(2), 277–286. [200] Timander L & SL McLafferty. 1998. Breast cancer in West Islip, NY: A spatial clustering analysis with covariates. Social Science and Medicine, 46(12), 1623– 1635. [254] Tivers J. 1988. Women with young children: Constraints on activities in the urban environment. In J Little, L Peake & P Richardson, (Eds). Women in Cities. Macmillan Education, 84–97. [202] Tobler WR. 1961. Map Transformations of Geographic Space. PhD thesis. University of Washington. [22, 248] Tobler WR. 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography, 46(Supp. 1), 234–240. [50, 146, 251] Tobler WR. 2000. The development of analytical cartography: A personal note. Cartography and Geographic Information Science, 27(3), 189–194. [177] Tobler WR & Z-T Chen. 1986. A quadtree for global information storage. Geographical Analysis, 18(4), 360–371. [67, 68] Tomlin CD. 1994. Map algebra: One perspective. Landscape and Urban Planning, 30(1-2), 3–12. [27] Torrens PM. 2012. Moving agent pedestrians through space and time. Annals of the Association of American Geographers, 102(1), 35–66. [242]

296

REFERENCES

Torrens PM. 2022. Data science for pedestrian and high street retailing as a framework for advancing urban informatics to individual scales. Urban Informatics, 1(1), 9. [204] Tracy M, M Cerdá & KM Keyes. 2018. Agent-based modeling in public health: Current applications and future directions. Annual Review of Public Health, 39(1), 77–94. [242] Tuan Y-F. 1977. Space and Place: The Perspective of Experience. University of Minnesota Press. [84–86, 101] Turner A, M Doxa, D O’Sullivan & A Penn. 2001. From isovists to visibility graphs: A methodology for the analysis of architectural space. Environment and Planning B: Planning and Design, 28(1), 103–121. [39] Tutte WT. 1963. How to draw a graph. Proceedings of the London Mathematical Society, s3-13(1), 743–767. [176] U.S. Bureau of the Census. 1968. DIME underwent lots of testing too. Census Bulletin, XVIII(18), 1. [78] U.S. Bureau of the Census. 1970. Census Use Study: The DIME Geocoding System. Technical Report 4. U.S. Bureau of the Census. [78] Unwin DJ. 2005. Fiddling on a different planet? Geoforum, 36(6), 681–684. [7] Urry J. 2000. Sociology Beyond Societies: Mobilities for the Twenty-First Century. Routledge. [204] Urry J. 2007. Mobilities. Polity Press. [180, 182, 205] Varsanyi MW. 2008. Rescaling the “alien,” rescaling personhood: Neoliberalism, immigration, and the state. Annals of the Association of American Geographers, 98(4), 877–896. [121] Vickers D & P Rees. 2007. Creating the UK National Statistics 2001 output area classification. Journal of the Royal Statistical Society: Series A (Statistics in Society), 170(2), 379–403. [142] Vinokurov E. 2007. A Theory of Enclaves. Lexington Books. [126] Vliet J van, R White & S Dragićević. 2009. Modeling urban growth using a variable grid cellular automaton. Computers, Environment and Urban Systems, 33(1), 35–43. [238] von Bertalanffy L. 1950. An outline of general system theory. The British Journal for the Philosophy of Science, 1(2), 134–165. [226] von Neumann J. 1966. Theory of Self-Reproducing Automata. University of Illinois. [231] Wachowicz M. 1999. Object-Oriented Design for Temporal GIS. Taylor & Francis. [191]

REFERENCES

297

Warren GC, C Katz & N Heynen. 2019. Myths, cults, memories, and revisions in radical geographic history. In TJ Barnes & ES Sheppard, (Eds). Spatial Histories of Radical Geography. Wiley, 59–85. [254] Warshall S. 1962. A theorem on boolean matrices. Journal of the ACM, 9(1), 11– 12. [160] Wassermann S & K Faust. 1994. Social Network Analysis: Methods and Applications. Cambridge University Press. [156] Waters J. 2013. Mobilities. In R Lee, N Castree, R Kitchin, V Lawson, A Paasi, C Philo, S Radcliffe, SM Roberts & CWJ Withers, (Eds). The SAGE Handbook of Progress in Human Geography. SAGE, 22–44. [182] Watson JW. 1955. Geography—A discipline in distance. Scottish Geographical Magazine, 71(1), 1–13. [30] Watt MS, DJ Palmer, MO Kimberley, BK Höck, TW Payn & DJ Lowe. 2010. Development of models to predict Pinus radiata productivity throughout New Zealand. Canadian Journal of Forest Research, 40(3), 488–499. [142] Watts DJ. 2003. Six Degrees: The Science of a Connected Age. Norton. [147] Watts DJ & SH Strogatz. 1998. Collective dynamics of “small-world” networks. Nature, 393(6684), 440–442. [157, 172] Weaver W. 1948. Science and complexity. American Scientist, 36(4), 536–544. [226] Weidlich W. 1971. The statistical description of polarization phenomena in society. British Journal of Mathematical and Statistical Psychology, 24(2), 251–266. [234] Weisberg M. 2013. Simulation and Similarity: Using Models to Understand the World. Oxford University Press. [231] Werritty A. 2010. D’Arcy Thompson’s “On Growth and Form” and the rediscovery of geometry within the geographic tradition. Scottish Geographical Journal, 126(4), 231–257. [246] Wesselung CG, D-J Karssenberg, PA Burrough & WPA Van Deursen. 1996. Integrating dynamic environmental models in GIS: The development of a dynamic modelling language. Transactions in GIS, 1(1), 40–48. [237] Westerveld L & AK Knowles. 2021. Loosening the grid: Topology as the basis for a more inclusive GIS. International Journal of Geographical Information Science, 35(10), 2108–2127. [108] Whatmore S. 2006. Materialist returns: Practising cultural geography in and for a more-than-human world. cultural geographies, 13(4), 600–609. [201]

298

REFERENCES

White R & G Engelen. 1997. Cellular automata as the basis of integrated dynamic regional modelling. Environment and Planning B: Planning and Design, 24(2), 235–246. [237] Whitehead AN. 1920. The Concept of Nature: Tarner Lectures. Cambridge University Press. [218, 219, 245, 246] Whitehead AN. [1925] 1967. Science and the Modern World: Lowell Lectures, 1925. The Free Press. [10, 18, 19, 215–217, 219, 222, 246] Whitehead AN. [1927] 1978. Process and Reality. The Free Press. [19, 24, 213, 214, 216, 219, 222, 224, 228] Whittlesey D. 1954. The regional concept and the regional method. In PE James & CF Jones, (Eds). American Geography: Inventory and Prospect. AAG - Syracuse University Press, 19–68. [17] Whyte BR. 2002. Waiting for the Esquimo: An Historical and Documentary Study of the Cooch Behar Enclaves of India and Bangladesh. Research Papers 8. School of Anthropology, Geography and Environmental Studies, University of Melbourne. [125, 127] Wiener N. 1948. Cybernetics: Or, Control and Communication in the Animal and the Machine. MIT Press. [226] Wiens JA. 1989. Spatial scaling in ecology. Functional Ecology, 3(4), 385–397. [70] Williams L. 2011. Modeling, Building, Writing: A History of Nonlinear Dynamics and Complex Systems. PhD thesis. Harvard University. [227] Wilmott C, C Perkins, S Lammes, S Hind, A Gekker, E Fraser & D Evans. 2016. Playful Mapping in the Digital Age. Institute of Network Cultures. [254] Wilson MW. 2017. New Lines: Critical GIS and the Trouble of the Map. University of Minnesota Press. [vi, 3, 14, 253] Wilson MW & BS Poore. 2009. Theory, practice, and history in critical GIS: Reports on an AAG panel session. Cartographica, 44(1), 5–16. [5] Wilson RJ. 1996. Introduction to Graph Theory. Longman. [149] Winichakul T. 1994. Siam Mapped: A History of the Geo-Body of a Nation. University of Hawaii Press. [114] Winsberg E. 2010. Science in the Age of Computer Simulation. University Of Chicago Press. [231] Winter S & C Freksa. 2012. Approaching the notion of place by contrast. Journal of Spatial Information Science, 5(5), 31–50. [94] Winter S, M Tomko, B Elias & M Sester. 2008. Landmark hierarchies in context. Environment and Planning B: Planning and Design, 35(3), 381–398. [105]

REFERENCES

299

Wolfram S. 1983. Statistical mechanics of cellular automata. Review of Modern Physics, 55(3), 601–643. [231–233] Wood D. 1992. The Power of Maps. Guilford Press. [14, 112] Wood D. 2010a. Everything Sings: Maps for a Narrative Atlas. In collab. with I Glass. Siglio. [107] Wood D. 2010b. Rethinking the Power of Maps. In collab. with J Fels & J Krygier. Guilford Press. [14, 112–114, 117, 121, 129, 133, 250] Woodward K, JP Jones III & SA Marston. 2008. Downsizing Wal-mart: A reply to Prytherch. Urban Geography, 29(1), 78–84. [56, 57] Woodward K, JP Jones III & SA Marston. 2010. Of eagles and flies: Orientations toward the site. Area, 42(3), 271–280. [56] Wooldridge M. 2002. An Introduction to MultiAgent Systems. Wiley. [239] Worboys MF & M Duckham. 2018. GIS: A Computing Perspective. (3rd edn). CRC Press. [35] Worboys MF & M Duckham. 2021. Qualitative-geometric “surrounds” relations between disjoint regions. International Journal of Geographical Information Science, 35(5), 1032–1063. [143] Worboys MF & K Hornsby. 2004. From objects to events: GEM, the geospatial event model. In MJ Egenhofer, C Freksa & HJ Miller, (Eds). Geographic Information Science. Lecture Notes in Computer Science 3234. Springer, 327–343. [189] Wright DJ, MF Goodchild & JD Proctor. 1997a. Demystifying the persistent ambiguity of GIS as “tool” versus “science.” Annals of the Association of American Geographers, 87(2), 346–362. [253] Wright DJ, MF Goodchild & JD Proctor. 1997b. Reply: Still hoping to turn that theoretical corner. Annals of the Association of American Geographers, 87(2), 373– 373. [253] Yuan J, Y Zheng, X Xie & G Sun. 2011. Driving with knowledge from the physical world. In Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD ’11. ACM Press, 316. [206] Yuan J, Y Zheng, C Zhang, W Xie, X Xie, G Sun & Y Huang. 2010. T-drive: Driving directions based on taxi trajectories. In Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems GIS ’10. ACM Press, 99. [206] Yuan M. 1999. Representing geographic information to enhance GIS support for complex spatiotemporal queries. Transactions in GIS, 3(2), 137–160. [184] Yuan M. 2018. Human dynamics in space and time: A brief history and a view forward. Transactions in GIS, 22(4), 900–912. [205]

300

REFERENCES

Yuan M. 2022. From representation to geocomputation: Some theoretical accounts of geographic information science. In B Li, X Shi, A-X Zhu, C Wang & H Lin, (Eds). New Thinking in GIScience. Springer Nature, 1–8. [39] Zelinsky W. 1980. North America’s vernacular regions. Annals of the Association of American Geographers, 70(1), 1–16. [102, 139] Zhou L, X Dang, Q Sun & S Wang. 2020. Multi-scenario simulation of urban land change in Shanghai by random forest and CA-Markov model. Sustainable Cities and Society, 55, 102045. [238] Ziman JM. 2000. Real Science: What It Is, and What It Means. Cambridge University Press. [216] Zukin S. 1982. Loft Living: Culture and Capital in Urban Change. Johns Hopkins University Press. [83]

Index Note. f following a page number indicates a figure. Author names are indexed in the References. A Absolute space. See also Space overview, 19, 20–22, 21f relational space and, 25 relative space and, 23–24 space in giscience, 26–31, 28f, 29f Abstractions, 215–216 Actor-network theory (ANT), 155–156, 223 Actual occasions, 214, 226–227. See also Process philosophies Adaptivity, 228 Addressing, 78–83, 79f, 82f Adjacency, 33–36, 34f, 35f, 153 Administrative boundaries, 122. See also Boundaries Affordances, 103 Agent-based models (ABM), 192, 238–245, 240f

Agglomerative methods, 140 Aggregation generalization and, 72–73, 73f modifiable areal unit problem (MAUP) and, 134–137, 135f Airports, 120–121 ArcGIS Desktop, 17 Areas, 11, 111–112, 131–142, 133f, 134f, 135f, 136f, 138f, 141f, 143–144. See also Boundaries Assemblage complexity theory and, 226–227 flat ontologies and, 222–223, 224–225 scale and, 56 Attribute values, 187–189 Authority constraints, 193–194 Automated cartography, 2, 27–28, 184–185

301

302

INDEX

Automating zoning procedure (AZP), 137–138. See also Zoning effect B Betweenness centrality, 163–164. See also Centrality Biogeography, 15–16, 47–48 Bipartite graph, 169 Black geography, 15–16 Blockmodels, 168–171, 169f, 170f Boids model of flocking behavior, 241–242, 207f Bona fide boundaries and objects, 112, 121–125, 123f. See also Boundaries Borders, 120–121, 127–128, 128f Boundaries arbitrariness of, 131–142, 133f, 134f, 135f, 136f, 138f, 141f lines and, 112 overview, 11, 16 place and, 88 between polygons, 35–36 statistical aggregations and, 129–131, 131f territory and, 121–125, 123f C Cadastral data, 34, 114, 128–129 Capability constraints, 193–194, 197–198, 197f Capitalism, 51–54, 91 Cartography. See also Automated cartography generalization and, 72–73, 73f map projection and, 68–69 representation as a process and, 251

scale and web maps and, 45–46, 60–62, 61f space in giscience and, 27–28, 28f, 29f, 30–31 time and, 184–190, 188f Cell states, 232–234, 233f, 234f, 237–238. See also Cellular automata (CA) Cellular automata (CA) as geographical process models, 243–245 overview, 192 simulation models and, 231–238, 233f, 234f, 235f, 236f spatial models and, 43 Census, 71–72, 129–131, 131f, 187–189. See also Polygons Centrality, 160–164, 162f, 163f Change over time. See also Time geography imperfectibility of representations and, 13 overview, 181–182, 185–186 snapshot approach and, 190–192 Closeness centrality, 163. See also Centrality Clusters clustering coefficient, 157–158, 158f connection, disconnection, and communities and, 168 network science and, 147n overview, 139–140 regionalizing space and, 140 Cognitive maps, 84, 104–105, 104f Communities, 115–116, 164–168, 167f Complex adaptive system, 228

INDEX

Complex assemblages, 56 Complexity theory. See also Process agent-based models (ABM) and, 238–245, 240f cellular automata (CA) and, 231–238, 233f, 234f, 235f, 236f, 243–245 overview, 211–212, 226–230, 245–246 Computational representations, 250–251. See also Representations Conference on Spatial Information Theory (COSIT), 57–58 Connection, 159–160, 159f, 164–168, 167f Constraints, 195–200, 195f, 196f, 197f, 198f Countermapping. See also Maps and mapping fiat/bona fide boundary distinction and, 124–125 new lines and, 114–116 representation as a process and, 252 Coupling constraints, 193–194, 197–198, 197f Critical GIS, 7–9, 250–251, 255. See also Geographic information systems (GIS) Cylindrical projections, 65–68, 66f, 68f D Data collection, 74, 251 Data layers, 70, 71f, 72–73 Data structures data storage and processing, 74

303

data tables, 148, 179 space in giscience and, 44 that include adjacency, 33–36, 34f, 35f time and, 185–186 from time to dynamic processes, 208–209 Deformation grid output, 29f, 30 Diffusion models, 193 Digital geographies, 8–9 Digital humanities, 102 Digital twins, 72 Diorama, 199 Directed edges, 150n, 153–154. See also Edges Directed graphs, 150, 151f. See also Graphs Disconnection, 164–168, 167f Discrete global grid (DGG) systems, 79f, 80 Drawing lines, 112–116. See also Lines Drawings, graph, 174–177, 175f, 176f, 178f. See also Graphs Duality, 127–128, 128f Dynamics, 13, 181–182, 208–209 E Ecological correlation, 135 Edge list approaches, 152–153 Edges centrality and, 160–164, 162f, 163f connection, disconnection, and communities, 164–168, 167f functional roles and blockmodels, 168–171, 169f, 170f graph drawings as projections and, 174–177, 175f, 176f, 178f

304

INDEX

mathematical graphs and, 149–153, 151f representation as a process and, 252 small world effects, 171–173, 173f, 174f Enclaves, 125–126, 127f, 128–129 Entity–attribute model, 40–41, 215 Environmental classification of scale, 58–59, 59f. See also Scale Euclidean geometry, 20, 23, 28, 139–140 Events, 192, 215, 220 Exaggeration, 72–73, 73f Exclaves, 125–126, 127f Extent, 69–70 F Feminist geography, 15–16, 201–204, 253 Fiat boundaries and objects, 112, 121–125, 123f. See also Boundaries Figural classification of scale, 58–59, 59f. See also Scale First-order effects, 220 Flat ontology perspectives, 54–57, 222–225 Flocking behavior, 241–242, 244, 207f Flows, 11, 145–147, 177–180 Free speech, 88 Functional roles, 168–171, 169f, 170f G Game of life, 234, 235f, 237–238. See also Cellular automata (CA)

Gazetteers, 94–99, 96f, 97f, 99f Generalization, 69–73, 71f, 73f Geodemographic analysis, 140–141, 140f Geographic information systems (GIS) absolute space and, 22 author’s history with, 3–9 “doing” differently, 253–254 overview, vi, vii, 1–3, 17, 247–250, 255 space in giscience, 26–32, 28f, 29f, 32f Geographical classification of scale, 58–59, 59f. See also Scale Geographical context, 100–101, 247–250, 255 Geographical theory, v–vi, 46–57, 48f, 50f Geohashing, 79–80, 79f Geometric duality, 127–128, 128f Geometry, Euclidean, 20, 23, 28, 139–140 Geomorphology, 47–48, 53 Georeferencing, 30–31 Geospatial event model, 189 Geotag, 103 Gerrymandering effect, 136–137, 136f Giscience author’s history with, 3–9 overview, v–vi, vii, 2, 14–15, 17, 44, 247–250, 255 place in, 92–105, 96f, 97f, 99f, 104f relative/relational space and, 33–43, 34f, 35f, 37f, 38f, 42f

INDEX

representation as a process and, 250–252 scale in, 45–46, 57–73, 59f, 61f, 63f, 71f, 73f space in, 26–32, 28f, 29f, 32f, 44 time and, 184–190, 188f from time to dynamic processes, 208–209 Global perspective, 91, 108–109 Global Positioning System (GPS), 19 Governance, 118–119, 129–131, 131f Graffiti, 86–87 Grain, 69–70 Graph databases, 40–41, 93n, 153 Graphs centrality and, 160–164, 162f, 163f connection, disconnection, and communities, 164–168, 167f drawings as projections and, 174–177, 175f, 176f, 178f functional roles and blockmodels, 168–171, 169f, 170f local properties and, 157–158, 158f network distance and path lengths, 159–160, 159f overview, 149–154, 151f small world effects, 171–173, 173f, 174f H Hägerstrand’s time geography. See Time geography Hexagonal grid schemes, 79f, 80 Hierarchy complexity theory and, 226–227, 228–229 flat alternative to, 54–57

305

hierarchy theory, 49–50 scale as, 47–51, 48f, 50f Hilbert curve, 79f, 80 Historical geography, 181. See also Time geography Homelessness, 88 Human dynamics, 204–208, 206f, 207f Humanistic geography, 15–16, 45–46, 86 I Immigration, 120–121 Imperfectibility of representations, 12–14. See also Representations Indigenous geography, 15–16, 223 Interactive web maps, 74. See also Web maps Islands, 120 Isovists, 39 K Kantian space-time-entity perspective, 183–184 L Land Environments of New Zealand (LENZ) classification, 142 Land ownership, 88, 113, 128–129 Latitude–longitude (𝜙, 𝜆 ) coordinates, 63–65, 64f Lattice, 231 Life CA. See Cellular automata (CA); Game of life Lines. See also Boundaries; Polygons countermapping and, 114–116 drawing, 112–116

306

INDEX

overview, 11, 111–112, 143–144 territory and, 116–125, 123f Local properties, 90, 157–158, 158f, 221 Location, 9–10, 17–18, 94–99, 96f, 97f, 99f M Map lines. See Lines Map projection, 62–69, 63f, 64f, 65f, 66f, 68f. See also Projections Map tiles map projection and, 62–69, 63f, 64f, 65f, 66f, 68f scale and, 60–62, 61f Map-centered (x, y) coordinates, 63–64, 65 Maps and mapping. See also Projections absolute space and, 22 arbitrariness of boundaries and, 131–142, 133f, 134f, 135f, 136f, 138f, 141f countermapping and, 114–116 drawing lines and, 112–116 overview, 116–125, 123f relative space and, 22–24 representation as a process and, 251 space in giscience and, 27–28, 28f, 29f territory and, 125–131, 127f, 128f, 131f, 143 Marxist geography, 15–16, 85, 253 Materialisms, 223 Mathematical graphs, 149–153, 151f. See also Graphs

Meaning, 10–11, 12–13, 75–77, 101–103. See also Place Measurement scales, 71. See also Scale Mercator projection, 65–68, 66f, 68f Mereology, 143 Mereotopology, 143 Migration, 88, 120–121 Military applications, 2 Mobilities, 180, 204–208, 206f, 207f Modifiable areal unit problem (MAUP) overview, 10–11, 133–138, 134f, 135f, 136f, 138f regionalizing space and, 138–142, 141f scale and, 73 Modularity, 165 Morton curve, 79f, 80 Movement, 16, 127–128, 128f Multidimensional data use of a space-time GIS, 192 Multidimensional scaling (MDS) methods, 105 Multiple datasets, 72–73 Multipolygon, 40 Municipal boundaries, 130. See also Boundaries N Narrative approach, 92–93, 106–108, 204 National boundaries, 122. See also Boundaries Nearest-neighbor distances, 31–32, 32f Neighborhoods addressing and, 78–83, 79f, 82f

INDEX

cellular automaton (CA) and, 231–232 local properties and, 157–158, 158f Nested hierarchies, 228–229 Network science centrality, 160–164, 162f, 163f connection, disconnection, and communities, 164–168, 167f functional roles and blockmodels, 168–171, 169f, 170f local properties, 157–158, 158f network distance and path lengths, 159–160, 159f overview, 156–157 small world effects, 171–173, 173f, 174f Networks, 11–12, 145–147, 149–153, 151f, 159–160, 159f, 177–180. See also Network science Newtonian physics, 20–21, 182 O Object-oriented ontologies, 39, 212, 223 Ownership. See Cadastral data, Land ownership, Property P Participatory GIS, 115–116 Path dependency, 228 Path lengths, 159–160, 159f Pattern complexity theory and, 226–230 overview, 12, 222–226, 245–246 pattern-oriented modeling (POM), 246 patterns and, 225–226

307

process philosophies and, 216–221 simulation models and, 230–245, 233f, 234f, 235f, 236f, 240t Permanences, 229–230 Philosophies, process. See Process philosophies Physical geography, 15–16, 25, 229–230 Place cognitive maps and, 104–105, 104f as geographical context, 100–101 in giscience, 92–105, 96f, 97f, 99f, 104f maps and, 112–113 meaning and, 101–103 overview, 10, 16, 75–77, 83–86, 106–109 place dependency, 228 process philosophies and, 216–221 relations and, 88–92, 147–156, 151f, 154f space and, 43, 77–92, 79f, 82f as vague location, 94–99, 96f, 99f Planar graphs, 158n Point patterns, 220, 32f. See also Pattern Point processes, 220 Polygons. See also Lines addressing and, 79–80, 79f change over time and, 187, 188f data structures that include adjacency and, 33–36, 34f, 35f fiat/bona fide boundary distinction and, 123–125, 123f modifiable areal unit problem (MAUP) and, 133–138, 134f, 135f, 136f, 138f

308

INDEX

overview, 112 resolution and, 71–72 spatial weights applied to, 41–43, 42f Voronoi model of space, 37–39, 37f, 38f Positive feedbacks, 228 Poststructuralism, 91 Potential path area, 197–198 Power relationships, 113–114, 224 Prisons, 119–120 Probability, 168, 171, 238 Process agent-based models (ABM) and, 243–245 cellular automaton (CA) and, 243–245 complexity theory and, 226–230 flat ontologies and, 222–225 imperfectibility of representations and, 12–13 overview, 12, 211–212, 216–221, 222–226, 245–246 patterns and, 225–226 relational space and, 24 representation as, 250–252 simulation models and, 230–245, 233f, 234f, 235f, 236f, 240f Process philosophies, 24, 211, 212–226. See also Process Projections. See also Map projection; Scale graph drawings as, 174–177, 175f, 176f, 178f overview, 10, 45–46 space in giscience and, 27–28, 29f, 30 Projects, 199–200

Property, 88, 113, 128–129 Protest, 88 Proximal space, 43 Proximity polygons. See Polygons; Voronoi model of space Public policy, 215–216 Q Q-analysis, 147n Qualitative spatial reasoning, 143–144 Quantitative geography, 31–32, 32f Queer geography, 15–16 R Random graph, 173. See also Graphs Range of scales, 46–47, 69 Raster data. See also Resolution overview, 70, 71f relations and, 148 space-time GIS and, 192 Raster surfaces, 187 Raster-vector debate, 26–27, 251n Redrawings of graphs, 174–177, 175f, 176f, 178f Regionalizing space, 11, 138–142, 141f Regulatory factors, 120 Relational database management systems (RDBMS), 40–41 Relational space. See also Relations; Space giscience and, 33–43, 34f, 35f, 37f, 38f, 42f overview, 19, 24–26, 43–44, 147–148, 248–249 place in, 88–92 Relations, 11, 145–156, 151f, 154f, 179–180. See also Networks

INDEX

Relative space. See also Space giscience and, 33–43, 34f, 35f, 37f, 38f, 42f overview, 19, 22–24, 43–44 relational space and, 25 space in giscience, 31–32, 32f Representations CA and ABMs and, 244–245 imperfectibility of, 13–14 maps and, 113 as a process, 250–252 representative fraction, 60 Rescaling, 52–53. See also Scale Resolution, 69–73, 71f, 73f Resource Description Framework (RDF), 41 Road networks, 179. See also Networks S Scale. See also Projections complexity theory and, 226–227 flat alternative to, 54–57 in geographical theory, 46–57, 48f, 50f in giscience, 57–73, 59f, 61f, 63f, 64f, 65f, 66f, 68f, 71f, 73f as hierarchy, 47–51, 48f, 50f map projection and, 62–69, 63f, 64f, 65f, 66f, 68f overview, 10, 16, 45–46 resolution and generalization and, 69–73, 71f, 73f salience of, 74 as scope, 46–47 as size, 46–47 as socially constructed, 51–54

309

space in giscience and, 27–28, 28f, 29f web maps and, 60–62, 61f Scale effect, 135–136 Schelling-Sakoda model, 240–241, 240f Scientific knowledge, 215–216 Scope, 46–47 Second-order effects, 220 Selection, 72–73, 73f Self-organization, 227 Semantic mapping, 107n Setting, 189–190 Simple features, 33 Simple graphs, 150, 151f. See also Graphs Simple location, 18, 216–218. See also Space Simplification, 72–73, 73f Simulation models agent-based models (ABM) and, 238–245, 240f cellular automaton (CA) and, 231–238, 233f, 234f, 235f, 236f, 243–245 complexity theory and, 230 overview, 212, 230–246, 233f, 234f, 235f, 236f, 240f Site, 56 Six degrees of separation, 172 Size, 46–47 Small world effects, 171–173, 173f, 174f Snapshot approach, 190–192 Social complexity. See Complexity theory Social construction, 51–54 Sovereignty, 119–121

310

INDEX

Space. See also Absolute space, Relative space, Relational space addressing and, 78–83, 79f, 82f in giscience, 26–32, 28f, 29f, 32f, 44 nature of, 18–26, 21f overview, 9–10, 16, 17–18, 43–44, 75–77 process philosophies and, 216–221 regionalizing, 138–142, 141f relations and, 147–156, 151f, 154f from space to place, 77–92, 79f, 82f space–place binary, 75–77 time and, 182–192, 188f Space-time diagram or aquarium, 193, 195–200, 195f, 196f, 197f, 198f Space-time paths and constraints, 193, 195–200, 195f, 196f, 197f, 198f Space-time perspective, 25 Space-time prism, 197f, 198 Spatial analysis overview, 41–43, 42f patterns and, 216–221 regionalizing space and, 140 from time to dynamic processes, 208–209 Voronoi model of space and, 37–39, 37f, 38f Spatial bias, 76–77, 220 Spatial elements, 148 Spatial models, 41–43, 42f Spatial scales, 71. See also Scale Spatial weights matrices, 41–43, 42f Spatio-temporal data, 190–192, 221. See also Time Spatiotemporal GIS (STGIS), 192

State, 112–114, 117–118 Statistical aggregations, 129–131, 131f Stochastic blockmodel, 168–169. See also Blockmodels Story mapping, 107–108 Street addressing systems, 78–83, 79f, 82f Street art, 86–87 Substance philosophies, 212 Symmetries, 219, 232 T Technology, 186, 254 Temporal factors, 71, 192. See also Change over time; Scale; Time Terrestrial measurements, 22 Territory arbitrariness of boundaries and, 131–142, 133f, 134f, 135f, 136f, 138f, 141f countermapping and, 114–116 maps and, 113–114, 125–131, 127f, 128f, 131f overview, 11, 116–125, 123f, 143 Thiessen polygons. See Polygons; Voronoi model of space Tile-based web maps, 60–62, 61f. See also Web maps Time. See also Time geography mobilities and human dynamics and, 204–208, 206f, 207f overview, 181–182, 185–186 process philosophies and, 213 relational space and, 24 space and, 182–192, 188f from time to dynamic processes, 208–209

INDEX

Time geography. See also Change over time; Time limits to, 200–204 mobilities and human dynamics and, 204–208, 206f, 207f overview, 12, 181–182, 193–200, 195f, 196f, 197f, 198f, 209 relational space and, 25 Time stamps, 186–187 Topological approach to polygon data fiat/bona fide boundary distinction and, 123–125, 123f Voronoi model of space, 37–39, 37f, 38f Toponyms, 94–99, 96f, 97f, 99f. See also Place Tracking use of a space-time GIS, 192 Transactions use of a space-time GIS, 192 Transition rules, 232 U Uncertain geographical context problem (UGCoP), 100–101 Universal Coordinated Time (UTC), 186 V Vague location, 94–99, 96f, 97f, 99f. See also Location Vector-based models, 148, 192 Vertices centrality and, 160–164, 162f, 163f connection, disconnection, and communities, 164–168, 167f functional roles and blockmodels, 168–171, 169f, 170f

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graph drawings as projections and, 174–177, 175f, 176f, 178f local properties and, 157–158, 158f mathematical graphs and, 149–153, 151f network distance and path lengths, 159–160, 159f small world effects, 171–173, 173f, 174f Vista classification of scale, 58–59, 59f. See also Scale Visualizations, 74 Volunteered geographic information (VGI), 102 Voronoi model of space, 37–39, 37f, 38f Voter models, 136–137, 136f, 234, 236f, 237. See also Cellular automata (CA) W Web maps map projection and, 62–69, 63f, 64f, 65f, 66f, 68f scale and, 60–62, 61f, 74 Web crawler agents, 239 Weighted graphs, 150, 151f. See also Graphs What3words, 80–81 Z Zoning effect modifiable areal unit problem (MAUP) and, 134f, 135–138, 136f, 138f regionalizing space and, 138–142, 141f z-order curve, 79f, 80

About the Author David O’Sullivan, PhD, is an independent scholar who has held positions at Te Herenga Waka — Victoria University of Wellington, Berkeley, Auckland, and Penn State. He has published extensively on novel approaches to the simulation of change in urban and ecological systems, and the implications of different representations in giscience in relation to wider currents in geographical thought. He is author of Geographic Information Analysis (with David Unwin) and Spatial Simulation: Exploring Pattern and Process (with George Perry). David lives in Aotearoa New Zealand and enjoys shouting at the radio, boardgames, origami, and following cricket in his spare time.

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