The Modeling Process in Geography E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 600

Veröffentlichungsjahr: 2013

Beschreibung

This title focuses on the evolution of the modeling process and on new research perspectives in theoretical and applied geography, as well as spatial planning. In the last 50 years, the achievements of spatial analysis models opened the way to a new understanding of the relationship between society and geographical space. In this book, these models are confronted by the real conditions of territorial prospect, regional dynamism, cultural policy, HMO, and spatial segregation. This confrontation takes into account the instability of social behavior and the permanence of partial determinist trajectories.

Leseprobe

Table of Contents

Foreword

Preface

Acknowledgements

Chapter 1. The Place of Both the Model and Modeling in HSS

1.1. Models and modeling: definitions

1.2. The mathematical concept of a model

1.3. Is there a specificity of HSS?

1.4. Modeling: explain to understand?

1.5. Bibliography

Chapter 2. From Classic Models to Incremental Models

2.1. The geographic “object”

2.2. Lessons from the “classic models”

2.3. Introduction to dynamics and auto-organization

2.4. From auto-organization to complexity

2.5. Spatial agents

2.6. Incremental modeling

2.7. Bibliography

Chapter 3. The Formalization of Knowledge in a Reality Simplifying System

3.1. Formalizing a complex cultural system using a series of perspectives

3.2. Differentiation of the system of cities by culture: contribution of the spatial analysis for testing the “global cultural model”

3.3. Alternative formalizations

3.4. Conclusion

3.5. Bibliography

Chapter 4. Modeling and Territorial Forecasting: Issues at Stake in the Modeling of Réunion's Spatial System

4.1. Introduction

4.2. A few major theoretical breakthroughs for modeling spatial complexity

4.3. Modeling and territorial forecasting of the socio-spatial system of Réunion

4.4. Modeling of Réunion's socio-spatial system

4.5. Towards a modeling of the dynamics of Réunion's system

4.6. Conclusion

4.7. Bibliography

Chapter 5. One Model May Conceal Another: Models of Health Geographies

5.1. Modeling in order to surpass descriptions?

5.2. Mode of the models and models in vogue

5.3. Conclusion

5.4. Bibliography

Chapter 6. Operational Models in HMO

6.1. Buffer and barycenter to determine the location of cardiac defibrillation

6.2. Thiessen's accessibility formula

6.3. Accessibility: the direct added-value of the GIS

6.4. A regional database of road accessibility devoted to emergency

6.5. The reallocation projects and their consequences

6.6. Relocation of a medical clinic: simulation of a new accessibility

6.7. Bibliography

Chapter 7. Modeling Spatial Logics of Individual Behaviors: From Methodological Environmentalism to the Individual Resident Strategist

7.1. Reconsidering spatial determinism: modeling versus local development

7.2. Ecological methodology

7.3. Towards a post-industrialist behavior

7.4. From neighborhood effect to the theory of the citizen-resident-strategist

7.5. Bibliography

Chapter 8. Temporalities and Modeling of Regional Dynamics: The Case of the European Union

8.1. Integrating time and temporalities into spatial models

8.2. Introduction of complexity theory in the interpretation of regional inequalities in Europe

8.3. Conclusion

8.4. Bibliography

Chapter 9. Modeling the Watershed as a Complex Spatial System: A Review

9.1. Shape indices for measuring various forms of a watershed

9.2. Organization of the networks

9.3. Synthesis concerning the shape and organization indices

9.4. From morphometry to complex systems

9.5. Conclusion

9.6. Bibliography

Chapter 10. Understanding to Measure…or Measuring to Understand? HBDS: Towards a Conceptual Approach for the Geographic Modeling of the Real World

10.1. A forgotten face of the geographic approach

10.2. Formalizing a spatial reasoning in databases

10.3. Example of thematic application: the industrial risks at Notre-Dame-de-Gravenchon (lower Seine valley)

10.4. Back to the sources

10.5. Bibliography

Chapter 11. Complexity and Spatial Systems

11.1. The paradigm of complexity

11.2. The systemic paradigm: from the combinatorial to emergence

11.3. Moving towards a more formalized definition of the notion of a spatial system

11.4. Bibliography

Chapter 12. Cellular Automata for Modeling Spatial Systems

12.1. The concept of the automaton and its modeling

12.2. A little bit of history

12.3. The concept of the finite state automaton

12.4. The concept of the cellular automaton

12.5. CAs used for geographic modeling

12.6. Bibliography

12.7. Websites

Chapter 13. Multi-Agent Systems for Simulation in Geography: Moving Towards an Artificial Geography

13.1. Introduction

13.2. From global to local description of structures and spatial dynamics

13.3. Multi-agent systems

13.4. Artificial geography: simulations of structures and spatial dynamics

13.5. Conclusion

13.6. Bibliography

Conclusion

List of Authors

Index

First published in France in 2005 by Hermes Science/Lavoisier entitled: “Modélisations en géographie : déterminismes et complexités”

First published in Great Britain and the United States in 2008 by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Yves Guermond to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Modélisations en géographie. English.

  The modeling process in geography : from determinism to complexity / edited by Yves Guermond.

     p. cm.

 “First published in France in 2005 by Hermes Science/Lavoisier entitled: 'Modélisations en géographie : déterminismes et complexités'.”

  Includes bibliographical references and index.

  ISBN 978-1-84821-087-5

 1.  Regional planning. 2.  Human geography. 3.  Geographic information systems. I.  Guermond, Yves.

II. Title.

  HT391.M625513 2008

  307.1'2--dc22

2008035145

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN: 978-1-84821-087-5

Foreword

The Taste for Measuring and Modeling1

This book gives me the opportunity to reflect upon the reasons behind my complex relationship with mathematics, as well as the frustrations revealed by an insufficient deepening of the relationship between, on the one hand, the human and “interdisciplinary” geography that I practice, and, on the other hand, a question that remains fundamental: which models for which science?

The evidence of a taste…

Before analyzing the reasons that make me think that my use of the scientific practice referred to as “modeling” – of which I would have liked so much to be a part1 – has been insufficient, I must recall a few steps along my career that testify to this interest in quantification, that is, the concept of models and modeling.

First come the taste and need for measurements in order to identify facts and geographical processes, and to test the hypotheses used to understand them. Despite Hubert Béguin's reply of “But how do you measure it!”, when I enthusiastically told about the content of my talk for the VIIth European Colloquium on Theoretical and Quantitative Geography in September 1991 in Hasseludden (Sweden), from the beginning, and guided by Ernest Labrousse, I have known that one way or another “everything can be measured” and must be for an assertion to be credible. Measuring is also at the center of politics, as attested by the responsibility given by Napoleon to the two scientists Chaptal and Montalivet, for collating the agricultural statistics of France.

The Tableaux de l'agriculture française with its previously unpublished maps (1966, 1968), the attempt to measure the degrees of urbanization at the scale of the départements (1973), the arrondissements (1971) and of a sample of undefined districts between rural and urban (1974), are proof of the early use of mathematics in building clever indicators revealing the unequal spatial distribution of situations evaluated through the complex indicators of density, urban frame and the combined dynamics of the demographic components of rural districts. During those years, following what I had been taught by Ernest Labrousse and then Pierre Coutin (2001), the link between mathematics and politics became obvious as an ordinary experience of social sciences researchers. This is how, attempting to translate Pierre Coutin's prospective vision regarding the ways in which to modernize French agriculture while respecting the local and regional farming communities, Jean-Claude Bontron and myself have used standard deviation in order to theoretically calculate the “technically necessary agricultural population” in France, for each département, and to suggest to the Commissariat Général du Plan the objective of reducing the active agricultural population in equal proportion, calculated in relation to the level of overpopulation reached in each département.

You could say, as my colleague Denise Pumain did at the end of the 1970s, that I am “of the pioneer pre-quantitative generation”, because “it is not by using measurements, as cleverly as this may be done, that geography is theoretical and quantitative, but that it can rather be identified by what is defined by the term spatial analysis!”

Why was my way of using mathematics not theoretical? Was it because of an overly “applied” approach, as was said then? Yet, in my research on low-density areas, and still with the complicity of J.C. Bontron and Lucette Vélard, whose skills in statistical processing, multivariate analyses, and the ascending hierarchical classification method never ceased to grow, our aim was to test hypotheses concerning the functioning of these areas as a spatial system and to build a theory of the dynamics of the “reverse side” of urbanization processes! While these studies underlined measured spatial discontinuities2 (and were not ideological, as in La France du vide), at the same time as they highlighted (as pioneers, and going against the prevailing analysis techniques of the day) the fact that this level of organization and spatial structuring was not dependent on demographic evolution3, why was it that they not enter the canons of the theoretical and quantitative geography being built then.

Was it a matter of the cultural relationship with mathematics? Whatever the importance I granted to the dimension of data analysis in examining causes and effects hierarchically, it is true that I never used it exclusively. As was the case for the generation of which I was part, I had to distance myself with mathematical reasoning (the concept of modeling) and its top-down application to social and spatial facts. Above all, I had to confront what quantitative analysis proved in terms of what could be called the level of experiences, as suggested to me by P. Coutin, referring to Leplay, that is the experience of the complex object that are local monographs, field studies as models of a relationship system between populations and territories, between societies and living environments. This was probably the weakness in the eyes of Theoquant geographers looking for a science and purified spatial laws in the field.

Furthermore, in the 1980s, I sometimes used the concept of a model in a sense that diverted it from the mathematical or physical model. Among the various meanings of this term, I found it efficient and relevant to use the terms “prototype”, “object to imitate” or “exemplary”. Thus, the various situations of rural development politics at the local level that I had been observing from the 1970s until the end of the 1980s (rural planning schemes, national, then regional pays contracts), always complicated to analyze, appeared as being part of either one of two “models”, one based more on centrality and spatial equity, and the other “local”, i.e. giving free rein to the specific social dynamics of a territory. In this, it was both a model for analysis (for the researcher) and a model for action (for the politician). Once again, this multiple usage of the term and the incongruity of a quantified translation of this type of model led me away from the hard core of theoretical and quantitative geography.

Modeling as a necessity…

However, I was never discouraged, and the issue of method, the necessity of models and modeling to the study of complex objects has been a recurring motif of my research in the 1990s, when it took a clear turn towards environmental concerns. What was maybe only an “opinion”, or rather a “certainty”, then became the awareness of a necessity. The decision I made to research “complex objects” that “cannot be decomposed and made simple without being modified, and their nature transformed, by the reductions used” is a decision that necessarily entails interdisciplinarity. The social issue of the environment reactivates the paradigm of society/nature relationships and requires the modeling of interactions between social systems, natural systems and technico-political systems within the complex object that is an environmental problem. In this case, the modeling can only be local, which, translated into geographical language, means that the identification of the relationships of the complex system is only valuable in their strict co-localization. Thus, the two epistemological requirements of geography linked to environmental issues: the revival of what I have called “inner interdisciplinarity”, meaning 1) a work articulated between physical geography and human geography; 2) the modeling in situ of processes with distinct natures and times specific to this type of object. Hence also the importance of tools such as the geo-referencing with a constant grid and GIS, or the imperative, for all disciplines, to work on the same microsite.

From the Observatory for ecological, economic and social changes in Causse/Cévennes which Marcel Jollivet was in charge of and in which I was in charge of coordinating the teams for Causse Méjan, to the Méjan Observatory that followed that first PIREN program, and then during the PEVS program “Co-evolutions of the dynamics of the natural environment and the society of Méjan cattle breeders: the bush progression” coordinated by Marianne Cohen, I have never ceased to assert, as did the whole group of border crossers (we must keep in mind that Jean-Marie Legay was the leader of this group on the natural sciences side) the absolute necessity of using all the methods and tools of modeling and GIS to study these crossover issues between social and natural sciences, while advocating internal interdisciplinarity in geography, that is the re-articulation of the systemic knowledge possessed by physical geographers with that of spatial analysis geographers that was, at the time, more widely used in human geography. It was obvious and I was certain that, whatever method was used to build the models, be it a deductive method (a theory a model a situation) as used by mathematicians, physicists, biophysicists, or even chemists and some geographers, or an ascending method (a situation a model a theory) for which agronomists and physicians know the difficulties linked to the constraining hypotheses imposed by the situation, and which I preferred due to my attachment to the field, it was truly the back and forth movement between model and field, “this to-and-fro between model and experimentation”, which is the core of the method used to highlight the functioning of a complex geographic object at the boundary of physical and social systems.

Reasons for dissatisfaction and incompletion…

However, there then crept into my research practice, subtly but inevitably, a dissociation between what I was expecting others to do, in particular young researchers I oversee or those who are part of research collectives that I am a part of, and what I would do myself, thereby leading me further and further away from mathematical and modeling skills. In other words, while I am convinced that, in order to be heuristic, the geography that studies the urban environment, risk management, territory sustainability – be it sustainable cities or neighborhoods, or agricultural systems or rural and periurban territories – must be both model-dependent and multidisciplinary, I myself tend more and more to position myself as an observer of what is brought into environmental research by modeling without immersing myself in the new modeling tools that keep invading that field (fractals, MAS and cellular automata etc.). While I recommend this methodological orientation and support those who apply it (who can be found in C. Soulard and W. Hucy's work), while I even try through them to introduce with all its force the idea that spatial analysis methods are an aspect of “workshop site” programs that cannot be ignored and the aim of which is the cognitive and continuing observation of “eco-sociosystems”, I take a critical stance regarding some works in “spatial modeling” that, and I will come back to this, seem to me to be not only simplistic but antithetical to the complex objects they claim to be studying.

Out of respect for the way I am being welcomed, through this book, into the community of spatial analysis, I must decipher the undercurrents of this attitude bordering on schizophrenia. Thus I must first answer the question: is it a strictly personal issue, of a judgment cast on the way some people use modeling, or an awareness of the difficulties in “bringing together volunteers from all disciplines”, in particular those “good at math and modeling” in order to accomplish my own research ambitions?

Let us review these hypotheses one after the other. There is indeed, at the point of origin of this lack of enthusiasm in going from “pre-quantitative” to quantitative and model-based skills a matter of personal and theoretical perspective. Well trained in mathematics in high school, surrounded during my first research years by mathematicians and philosophers who reflected on the relationship between politics and sciences, mathematics and models4, I have come to think that mathematics does not consist of taking reality as a starting point, since mathematicians (whose intuitive gift for formalization is often detected in their early childhood) make discoveries in abstraction or rather in a realm of reasoning that do not go beyond mathematics as a discipline. Nurtured on many anecdotes about the career of Sophie Germain, Poincaré, etc. that all showed how mathematical discoveries are ill-adapted to life in academic society and would rather be fitted with social isolation, it seemed to me hard, even impossible, to reconcile my taste for the social and current aspects of the world in which I was living (which had made me choose to join the CNRS as a geographer rather than a historian) with a deepening sense of the heuristic virtues of mathematics applied to geography. More than that, whenever, led by a then poorly defined intuition of the importance of multidiciplinarity in solving complex issues, I tried to engage the attention of my mathematician and/or philosopher friends, I was immediately faced with a negative judgment of my attempt. The arguments used against it were quite similar: either the critique was aimed at the conceptual perversity of modeling that I have referred to before, or based on harsh judgments of my first attempts at applying mathematics to social sciences, considered as simplistic and, lacking conceptualization, as unconsciously serving the dominant ideology. If, I was told, quantum physics has made progress thanks to mathematics and has helped mathematics evolved, it is because the level of conceptualization was maximum. By choosing to apply mathematics to my research5, I was running the risk of weakening my theoretical capacity and my results through a mediocrity of mathematical foundation. In other words, it was better for me to deepen my hypotheses and build a system allowing a stronger conceptualization, rather than depend on already existing models and modelings (for instance regarding the processes of dissemination and polarization), which would modify my research goal, and maybe even put it under the influence of the then dominant ideology.

In short, from a personal perspective, doubt took hold: was I capable of being heavily involved, both in mathematics and geography, until I found the mathematical expression fitting each of my research objectives, which were oriented more and more towards the study of complex objects? This doubt was reinforced when I read Edgar Morin, who did not have to use mathematics in order to “introduce us to complex thought”, and this at the time when the “mathematics expert” Le Moigne joined him in his “theory of the general system” as a “theory of modeling”.

What can be said, then, about my relationship to others, geographers or those close to geography, who deliberately committed themselves to a path I was not willing to follow? A retrospective piece of internal enquiry has led me to distinguish three attitudes towards them that may be linked to the way I evaluate differences in the epistemological, even the ethical scope of these practices. It is true that generally I had a positive prejudice regarding all those who embarked on the adventure of models and modeling. Being curious about all the accomplishments, about progress in geography, I have always made a point of participating in the Dupont Géopoint group and in the European conferences on theoretical and quantitative geography. However, and this I admit is the first position that I took, I am somewhat wary of those who, compulsive and eager to be regarded as the most effective in spatial analysis, seem to forget the meaning of the research objects whose systemic functioning they claim to analyze. To try out a new method in se and per se is more important for them than the cognitive goal which seems to me to be the core, the ultimate value of research. I do not need to dwell on the texts that have led to my theoretical wariness of this usage of models and modeling. It may be enough to refer to my outrage when I read that the best example of urban growth following the fractal model was the town of Nouakchott! Nouakchott, the city of all poverties, but also of all the craftiness of informal economy, exploited in the quest for survival! How could anyone call this growth, what was no more than the extension of a spatial form emptied of its social and human content? How, when the research was supposed to be theoretical and fundamental, could anyone thus simplify the city to the variable of developed sites and to a demographic dynamic? Was the craving for a “mathematically expressed” result and a rigorous proof antagonistic to the effort to think complexly, to bring to light the intricacies of elements and processes that form urban spatial systems? Of course, this is an extreme example that does not represent all the attempts at modeling which are more concerned about the social dimension of geography, and also more concerned about the relationship between physical processes and natural processes than such a simulation model allows. Yet, it is representative of a tendency to use a method for its own sake without insisting upon the results yielded being repositioned within the broader conceptualization of the research field and the discipline.

Although they are in a very different position from those mentioned above, certain well-used studies in the scientific milieu concerned with the environment and more specifically on the management of renewable resources also make me circumspect. Here is the second reason inhibiting my personal involvement in the use of modeling tools. From reading the journal Natures Sciences Sociétés, I cannot help but notice the current craze for “modeling as an accompanying tool” corollary to the valorization of “action research” (or “development research”), corollary also to praising the virtues of spatial modeling as a decision-making aid. New computer tools such as GIS, MAS, cellular automata, etc. that is to say artificial intelligence applied to localized (geographical, territorialized) complex situations, are at the core of this type of modeling. This research trend is being used more and more in the big applied research institutions such as INRA6, CIRAD7 or CEMAGREF8 and suggests models with joint “resource/exploitation” dynamics, between field and theory, that are supposed to both produce knowledge about complex systems and facilitate the dialog between users and the learning of collective decision making concerning the management of ecosystems and renewable resources. We may wonder if in this shift from systemic analysis to systemic modeling, and then the building of expert systems using computing modeling tools, there might be some confusion between what is called a mathematical model, which is supposed to be extremely reliable in its own realm of application, and mathematico-computing models that are supposed to simulate various dynamic behaviors (some of which cannot be expressed mathematically) in scripts that impact the spatial system. However, this is not really the issue since, as I have already mentioned, the conceptual clarification that comes from going back and forth between a situation (or an experience of reality) and the model built to explain it is in itself positive. What raises questions is the risk taken by these researchers, even when they do try to follow deontological principles of respect for participants who do not have scientific expertise, of missing out on certain scientific knowledge without which the “decisions” made by the actors can in no way be understood. Who are the “actors”? What does it mean to make a decision? What is the meaning of territory in the simulation? What do “landscape dynamics” mean to the researcher in the simulation model and in the mind of the people to whom it is presented, and from whom a decision, or even a consensus is expected? In other words, once again, the risk of simplifying complexity to the point of misrepresenting the object regarding which a decision must be made, is important. Is obtaining a consensus with the use of scripts simulating consequences not a way of making use, as being blind, of those who are supposed to make decisions and about whom very little is being said? Once again, skills are considered as most important and weaken the awareness of being in a position of power. How could I not choose to be careful when confronting experiments already considered as models to help make decisions, and which I think are premature and insufficiently thought out in relation to the social stake they raise?

Thus, it is a matter of science partners and trust in a collective of researchers intent on studying a complex object even if, as is the case for the sustainable city, the study of the object depends on “social demand”, or even the well-being desired by its inhabitants. Here is the third reason for my relative neglect of spatial analysis and modeling. In order to overcome the criticism I just referred to, the only tenable position, on the theoretical and practical levels, is to be certain I am part of a multidisciplinary team aware of the skills of everyone, and its complementarities. As I have written earlier, interdisciplinarity is a practice in which, step-by-step, a conceptual approach and a multidisciplinary research plan is built around a complex object, the study of which is of equal interest to all scientific partners. For us geographers, it is often an issue involving interactions between natural systems and social systems (for instance, flooding risks due to erosive run-off, or the management of biodiversity in an urban environment, etc.). This type of complex issue requires a broadened multidisciplinarity, at least between physical geographers and human geographers, which is still an exceptional occurrence. Modeling no doubt has a place, but not exclusively, as must be the case for all disciplines involved, and above all, under the condition that it is introduced when the problem is very clearly expressed and the need to model is clearly identified, and also when, as mentioned before, there is a to-and-fro between the model (modeling) and the experience (field work), the latter being defined as “any organized way of acquiring information that includes, in the perspective of an expressed goal, a confrontation of reality”.

However this internal interdisciplinarity in geography aiming to build a common approach to spatial analysis, social geography and physical geography, is still a utopia. Not that I underestimate the results obtained in the Causse Méjean Observatory! Not that I deny the forward strides of the MTG group, in particular around Daniel Delahaye, in articulating physical issues and social dimension! But the interdisciplinary practice in geography, as I have tried to define it, is still a minority, and its results are still too meager. Each research group tries to innovate within its own activity, with its scientific capital, without trying to move in terra incognita, or beyond its recognized horizons. As I did when I was part of MTG and tried in vain to build a research program bringing together Patrice Langlois and Marianne Cohen, I still regret that a more vigorous work is not being implemented between our two laboratories in order to think together about the place of modeling in the advances of our research.

The acceptance of a conceptual modeling based on the statement of an interaction system

While at the onset of this reflection I pointed to the incongruity of my being one of the authors of this book, I find myself able to conclude a conciliating approach that would reinvigorate the dialog between the “modeling and graphic processing” and “social dynamics and recomposition of space” laboratories, precisely on the subject of modeling in geography . My suggestion is a mutual recognition of the importance of conceptualizing the issue to be studied before using models and modeling. Indeed, I think that in the research school to which I belong, the enunciating of hypotheses regarding the interaction between elements whose mutual connection is not obvious, in particular interactions between social and spatial practices and natural elements, should be taken into account. This logical statement of the relationships between natural systems and social systems relies on the identification and the construction of concepts that can open mediation in these relationships (for instance, the practice/representation duo, or the concept of mode of inhabitance). The logical statement also has a temporal value and must articulate the various temporalities of nature and society. These properties are found in the “heuristic research model on sustainable development” suggested by Monique Barrué-Pastor: examining all the terms of the relationship; discussing notions down to the definition of useful concepts; building a hierarchy of concepts and relationships, etc. Enunciating a relationship system seems to me to be a scientific result, but that is not really recognized by the specialists of spatial analysis and modeling because it is a conceptual approach that cannot be immediately translated into measuring methods that do not immediately call for a certain already tested model. Would it not be a worthy intellectual adventure to bring together means of thought that, in the end, leaves a large place to the conceptualization of a complex system?

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[MAT 92] MATHIEU N., 1992, “Un outil d'observation de l'interaction entre systèmes naturels et systèmes sociaux: l'observatoire du Méjan en Lozère”, in Trente communications au 27è Congrès International de Géographie, Washington, INTERGEO/AFDG.

[MAT 92] MATHIEU N., 1992, “Géographie et interdisciplinarité, rapport naturel ou rapport interdit ?” in Sciences de la nature, sciences de la société, les passeurs de frontiers, M. JOLLIVET (ed.), Paris, CNRS Editions, pp. 129–154.

[MAT 97] MATHIEU N., 1997, “French geography status in interdisciplinary research” in Modeling Space and Networks, Progress in Theoretical and Quantitative Geography, Einar HOLM (ed.), Gerum Kulturgeography, Umea Universitet, pp. 325–342.

[MAT 97] MATHIEU N., 1997, “Interdisciplinarité interne, interdisciplinarité externe, quel intérêt heuristique pour la géographie: Réflexion à partir d'une confrontation de pratiques”, Actes du Colloque Géographie Interface, Représentation Interdisciplinarité, Institut Universitaire Kurt BÖSCH, Sion (Switzerland).

[MAT 99] MATHIEU N., “L'expérience et le modèle, un discours sur la méthode, compte rendu de l'ouvrage de Jean Marie LEGAY”, Economie rurale, 251, May–June 1999, p.61–62.

[MAT 01] MATHIEU N., “Pierre Coutin et la formation des élites. Une certaine idée du rôle des sciences socials”, Les Etudes Sociales, 134, 2001, pp. 23–34.

[MAT 71] MATHIEU N., BONTRON J.C., 1971, Les zones à faible densité de peuplement, Note created for Intergroupe CNAT/Espace rural, 4 p. mimeo + 1 map: Types d'espaces ruraux selon la densité de population et l'encadrement urbain par arrondissement.

[MAT 73] MATHIEU N., BONTRON J.C., 1973, “Les transformations de l'espace rural. Problèmes de méthode”, Études rurales, no. 58–59, January–June, pp. 137–159.

[MAT 96] MATHIEU N., COHEN M., FRIEDBERG C., LARDON S., OSTY P.L., 1996, “Approches pour la modélisation des interactions entre dynamiques de la végétation, dynamiques sociales et techniques: confrontation des énoncés logiques et des méthodes: l'embroussaillement sur trois sites du Causse Méjan”, in Tendances nouvelles en modélisation pour l'environnement, Paris, CNRS, Actes des journées du Programme Environnement, Vie et Sociétés, session A, pp. 37–42.

[MAT 96] MATHIEU N., COHEN M., 1996, “Approches pour la modélisation des interactions entre dynamiques de systèmes naturels et de systèmes sociaux: l'embroussaillement du Causse Méjan (France)”, 28th International Geographical Congress, Abstract Book, The Hague, p. 289.

[MAT 85] MATHIEU N., DUBOSCQ P., 1985, Voyage en France par les pays de faible densité, Toulouse, CNRS Editions, 179 p.

[MAT 85] MATHIEU N. and Équipe Analyse des Espaces Ruraux, 1985, “Un nouveau modèle d'analyse des transformations en cours: la diversification/spécialisation de l'espace rural français”, Économie Rurale, no. 166, pp. 38–44 (abstract in English).

[MAT 86] MATHIEU N., MENGIN J. DALLA ROSA G. and AVENTUR D., 1986, “Nature et signification de la diversité des modèles de développement rural”, Min. de la Recherche et de la Technologie .

[MAT 86] MATHIEU N., MENGIN J., 1986, La diversité des modèles de développement rural: histoire, nature et signification. Paris, FORS, Ministère de la Recherche et de la Technologie, p. 49.

[MAT 88] MATHIEU N., MENGIN J., 1988. “Les politiques de développement rural: unité ou diversité”, in JOLLIVET M., (ed.), Pour une agriculture diversifiée, Paris, Ed. L'Harmattan, 335 p., pp. 268–282.

[MOR 01] MORIN, E., 1977–2001, La Méthode, Paris, Le Seuil.

[ROB 82] ROBIC M.–C., MATHIEU N. (en collaboration), 1982, “Accident climatique et fonctionnement de la société agricole, la sécheresse de 1976 chez les éleveurs d'un canton de la Nièvre”, Espace géographique, 2, pp. 111–123.

[ROB 01] ROBIC M.–C., MATHIEU N., “Géographie et durabilité: redéployer une expérience et mobiliser de nouveaux savoir-faire”, in Le développement durable, de l'utopie au concept: de nouveaux chantiers pour la recherche, Marcel Jollivet, Editeur scientifique Paris; Amsterdam; New York: Elsevier, 2001, pp. 167–19.

1 Written by Nicole MATHIEU, Emeritus Research Director, CNRS, Paris.

1 In particular when Alain Pavé started, at the beginning of the 1990s, a special program in the Programme Environment of the CNRS, “Method Models, Theories”, whose results (along with others) led to a conference in 1996 Tendances nouvelles en modélisation pour l'environnement, Paris, CNRS, Actes des journées du Programme Environnement, Vie et Sociétés.

2 See Map “Zones des faibles densités et écarts de densité avec les régions voisines” in Bontron, J.C., Mathieu, N., 1977. La France des Faibles Densités, Délimitation Problèmes Typologies, Paris, ACEAR/Segesa, p. 32.

3 Hence the notice taken, as early as 1975, of the reversal of the century-old tendency to exodus and depopulation in rural districts, as well as highlighting the importance of non-agricultural activities and jobs, and of the new living practices.

4 I am simply referring to my acquaintance in the 1960s–1970s with Louis Althusser and Alain Badiou at the École Normale Supérieure, they themselves being friends with Maurice Mathieu who was then a mathematician at the Collège de France in Perrin's team. I am also referring to conversations with the mathematicians at the ENS, including Adrien Douady who was connected to the Bourbaki school (formalist, metamathematician, structuralist), but also Benzécri and Françoise Badiou.

5 I wanted to try and build a typology of farms in which I could integrate temporal processes (dynamics of the family and the reproduction of the farm) and spatial processes (layout of crop parcels, proximity and contiguity, etc.) See MATHIEU N., 1972, “Typologie dynamique d'exploitations agricoles des plateaux de Haute-Saône”, in Approche géographique des exploitations agricoles, Cahier no.1, Paris, April, pp. 9–24 (Équipe rurale du LA de Géographie Humaine).

6 Institut National de Recherche Agronomique: National Institute for Agronomical Research.

7 Centre de coopération Internationale en Recherche Agronomique: Center for International Cooperation in Agronomical Research.

8 Institut de recherche pour l'ingénierie de l'agriculture et de l'environnement: public agricultural and environmental research institute.

Preface

In a book published in 2007, Lena Sanders [SAN 07] revealed the great variety of choices made by geographers in the field of spatial analysis modeling. Our aim is not to produce a new inventory, but to propose general reflections about the realizations and perspectives of modeling research, both in the field of theoretical geography and in the field of applied geography in town and country planning. The tools are widely available, and are continuously improving, for spatial analysis as well as for geographic information systems. The MTG research group (models and graphic processing in geography) was created in 1986, with the ambitious target of keeping “close control of the new technical tools, with a permanent link to social demand, and to discover all the opportunities of interface between science and technology”. These 20 years of collective research have now given us an opportunity to propose this “reflection”. The chapters below are the work of researchers currently working in the laboratory, as well as former members of the initial team, who are now working in other universities.

The first two chapters situate our research program: what does a modeling process mean, and what is the specificity of this process in the field of human and social sciences? The path covered since the early realizations of spatial analysis is a basis from which new research has developed, mainly in terms of simulation techniques, thanks to recent computing developments.

In Chapters 3 to 8, we see how these models are confronted with the reality of what geographers are being asked to do in the field of land planning and management: cultural policy, territorial forecasting, socio-spatial segregation, inequity of regional dynamics, polarization, enclosing. Geography is, by definition, engaged in a process of understanding the relationship between society and space, but these confrontations with material work must not occlude the importance of a permanent evolving theory.

Towards that aim, the final chapters make it clear that some distance is necessary in responding to social demand, to enhance a new reflection on the fundamental concepts structuring the discipline, as well as the weaving of new links with the present level of science and technology. This distance is the only means of progressing towards the new horizons of a theoretical geography allowing numerical experimentation, or, in other words, an “artificial geography”. However, this research is only valuable if it prevents a retreat into previously tested methods. By keeping a concern for a constant reference to socially suitable themes, this reflection must allow methodological transfers towards the social agents. This to-and-fro gives its value to theoretical geography and prevents the interpretation models of the social life from staying set.

Bibliography

[SAN 07] SANDERS L., Models in Spatial Analysis, ISTE, 2007.

Acknowledgements

I wish to thank the members of the “translation team” who helped me in finalizing the English version: Sandrine Baudry, Lyla Bradley, Lee Campbell, Bobby Hiltz, Shivani Khosla, Donnacha O'Ceallaigh, Aruna Popuri, Philana Rustin, James Taylor and Pierrick Tranouez.

Chapter 1

The Place of Both the Model and Modeling in HSS1

The aim of this chapter is to present a few points of view on the concept of the model or on the modeling process. In Human and Social Sciences (HSS), modeling can cause some specific problems because of the immersion of the human researcher in his object of study, which is equally human. Our goal is to show the specificity of modeling in HSS, and the conditions of its utilization. The rigor with which the modeler will demonstrate the conditions of use of his own tool will allow the precision of the field of its utility in HSS.

It is helpful to specify the definition of the model and modeling utilization because of the different assertions in common sense, but also in HSS. The same definition in the same discipline can hide paradigms, methodologies and different issues, diverging or contradictory. The same theoretical posture in two different disciplines can lead to the use of two different words.

We will thus start from the definition that common sense gives to the word “model”. This is the object from the beginning. Modeling being used most often to mathematically formalize a reality, we will explore the notion of a model in mathematics. Modeling's different utilities and issues in social sciences will thus be examined before putting them in perspective with mathematical language.

1.1. Models and modeling: definitions

The term “modeling” means both the activity required to produce a model as well as the result of this activity. From this distinction, the concept of modeling is larger than that of the model as it corresponds to the human activity producing a finished model, while the model is an object (concrete or abstract), voluntarily drawn from the activity. The model does not appear all of a sudden at the end of the modeling activity, it is progressively formed like a vase from the hands of a potter. It establishes itself in an activity, without identifying itself with it, it existed before (during the conception phase), it exists during the utilization phase, it exists even after its rejection, or in the will to create a better model, one which surpasses the first.

First we discuss definitions of the word “model”.

Among the many definitions in the Encyclopedia Britannica, we will retain two:

1. on the one hand, a “model” is a “formalized structure to realize a set of phenomena, which between them possess certain links”. In the mathematical model, this is the case defined as a mathematical representation of a physical, economical and human phenomenon…;

2. on the other hand, a model is a “schematic representation of a process, of a sound approach”.

These two definitions are on different levels; however they still possess certain connections.

The first definition is associated with the relation in the middle of a structure. It implies two notions: that of totality and that of interdependence between elements which is not the result of accidental accumulations. Thus, in this definition, the use of models would consist of “taking the totalizing attitude in any case”, as with what Sartre says about structuralism [SAR 60]. The catchphrase would be: “We don't know if what we say is true, but we know that it makes sense.” This definition also returns to the system's notion addressed in Chapter 11. In this category (the structure-model) a mathematical sense is given to the term “model”.

In the second definition, we can use the example of the geographical map. This is also the case for a Conceptual Data Model (CDM) in the framework of the elaboration of a database. However, we must acknowledge that the schematic-model is not a long way from the first definition, in as much that “a schematic representation” can very well be a graphical representation of the formalized structure returning back to the first definition. Frequently we associate a verbal formalization (like in mathematics, physics, chemistry, geography, etc.); a graphical formalization (like a picture associated with a graph; a diagram of phases associated with a differential system; a molecular schema of a chemical formula; and a map associated with the values of a structure-model). The schematic-model is thus a representation of the structure-model. In summary, it is a model of a model. It is possible that a schematic-model is not associated with a more formalized structure, like the water cycle schema or a “choreme” [BRU 86]. It then corresponds to a more empirical measure, which can be a stage in the modeling activity becoming (emerging towards) a formalized model.

Is the forming of verified but not yet explained observations already a model? The catchphrase for this radical empiricism would be “we don't know if what we are saying makes sense, but we know it's true”.

We think that there is a gradation in the models and that it is impossible to fix absolute criteria of “modelicity”. In fact, a model is always preceded and followed by a complex scientific procedure, since the reflection on the choice of data, and after on the tools (physical, institutional or methodological) allowing the collection, the observation, the organization, the structure, the digitizing capability, until the final formatting of the model's data. Also with respect to the downstream of the modeling, we must define some forms of selection and observation from the model's results. We must translate the results in the framework of theoretical interpretation. All of these stages also contain modeling forms. The execution of a map necessitates different sources of data: a census report on the population that gives databases, the remote sensing that gives images after complex processes of satellite pictures are already forms of abstraction of reality, which we can qualify as models. The map which results is in itself a model resulting from the former. This map, numerically structured under a GIS form, can lead to a mathematical model, which can then generate several results. These results will themselves be formatted to be interpreted in the frame of a theoretical corpus, this translation phase is also a form of modeling, as the same results of a model can produce very different theoretical interpretations. Thus, we can see that the model does not have to be extracted from the general scientific approach.

Even though it is not our goal to bring a general and unifying semantic clarification, it would seem useful in the pursuit of our study to formulate four positions concerning modeling:

– establishing the norm, stating the pros and cons. We are not concerned herein with “modeling morale”;

– explanatory, which consists of finding a general law outside of the object;

– comprehensive, which consists of understanding motivations that have a meaning for each person;

– interpretative, which is the will to give a significance by putting a field of representation (signified) in relation with another (signifying).

Let us note here that the explanatory and comprehensive procedures are complementary, but the modeling in a comprehensive perspective seems much more delicate.

In a contemporary economic dictionary (Mokhtar Lakehal, Dictionary of Contemporary Economy, Ed. Wuibert, November 2002), five pages are dedicated to the word “model”. In fact, it has very little to do with presenting a definition of the concept, while this seems obvious. For the economic dictionary, it has to do with presenting different models, with which their authors sometimes associated their names (Walras' equilibrium model, the Keynesian model, the Marxist model, Makowitz' model, etc.). This is evidence of the importance of the modeling practice in this discipline, which has for that matter won many Nobel prizes awarded for the development of these models.

After having noted the Italian origin of the word model (figure destined to be reproduced), the Robert Dictionary of Sociology, in a chapter written by Pierre Ansart [ANS 99] distinguishes two assertions on the concept of the word “model”. The first one, relative to social practices, would be a “reality that we force ourselves to reproduce” (here again?). The second one, relating to methodology, would be a “constructed representation, more or less abstract, of a social reality”. One is the reality as an object of reproduction; the other is a representation of reality.

The first sense thus returns to reproduction, but the model is the reality, it is the object of reproduction. It could consist, in the common sense, of the artist's model. Meanwhile even Miro, who is not even known for the figurative character in his work, used models, which he did not even reproduce. “In my paintings, each form, each color is taken from a fragment of reality.” In this sense, a reproduction practice would not be associated with the use of models, but they would be a source of inspiration. Miro added that a moving object, like a jack-in-the-box surprisingly springing from its box, could serve as a model for him. Thus, the painter's model would not be an object of reproduction. It would only be supporting the imagination, maybe even a suggestion of dynamics.

In the second definition given by the Robert Dictionary of Sociology, the model “doesn't reproduce reality, it simulates it”. We notice that if the modeling is an instrument, a technique “that enables us to think and interpret reality”, we can apply a technical definition to “simulation” which is none other than a “method…. that consists of replacing a phenomenon… by a more simple model, but which has an analogous behavior”. In this definition, the model is a simulation, always approximate, of reality. In this case, the model sets its heart on coming closer to it, to the best of its ability, without pretending to return all of its complexity. The choice of the components of reality, integrated into the model, results in the construction of the research agenda, of its theoretical frame. The components thus selected are seen as fundamental for the purpose of the study. Therefore, the model can pretend to return all of the components, but not the wholeness of reality. The parts of reality that are beyond the object of study are voluntarily excluded from these components. The aspects of reality that are not linked between themselves by relations leave the scope of the parameters of the model, even if these aspects of reality are a part of the object of study. A provisional use is not more stated for simulation than for modeling.

After having defined various forms of the model's concept, we will study precisely the model in mathematics before putting in perspective its use in human sciences.

1.2. The mathematical concept of a model

There are at least two mathematical definitions of the term model: the first one is situated in the framework of model theory, and the second one in the interface between mathematics and the other sciences.

1.2.1. The semantic conception

In the framework of model theory, the notion of a model is used in a rather particular manner, since the term is used as something that allows us to give a “meaning” to a theoretical discussion by end-to-end correspondence between the model and the formal theory. A model is thus a sort of reference example, of the fulfillment of the theory, allowing the justification of the theory by an external significance. However, this also gives the model a theoretical framework, allowing us to rigorously formalize it. Moreover, the same theory possibly having various models in different contexts, their comprehension reinforces them mutually and they can be studied in the framework of a formalized theory with a great economy of thought, in so far as the same (theoretical) thinking scheme is used in different contexts. If likewise, all of the model's elements and properties correspond to the theory's symbols and formulae, the model, in this theory, is then known as complete. We then see the convergence interest between syntactic and semantic aspects and the importance of the theorems of completeness or of incompleteness. Thus, Gödel enunciated the incompleteness of arithmetic by proving that there exists at least one property of arithmetic that cannot be demonstrated nor refuted starting from the axioms. This result ruined Hilbert's plan to constitute a totally formalized and coherent foundation of mathematics, and disproved the Vienna Circle's formalist theses.

1.2.2. The empirical concept

The second aspect of the mathematical model's concept, which we could call empirical, or simply a mathematical model, is much more widespread, as it largely overlaps the frame of pure mathematics and is seen in all sciences. A mathematical model is a representation by a formulation or a mathematical formalization of a portion of reality (whether static or dynamic).

The thinking scheme is contrary to the preceding one, in so far as in the first case, the model is a fulfillment which gives significance to a theory, whereas in this case, it is an operation of abstraction that allows us, by simplifying it, to give an explanation of reality… Furthermore, the link between the model's mathematical formulation and the reality to which it refers itself, is not mathematically formalized as before, from where its denomination of empirical stems. We can tell that the meaning of empirical conception used here is very large, whereas the notion of simulation is much stronger, as it holds a will to reproduce reality, to imitate it in certain dynamics, consequently in time. Thus, the model's notion cannot be confused with that of simulation, especially when it is applied to human behaviors.

We are necessarily in an interdisciplinary situation here, where we correspond a certain mathematical formulation to a concrete reality. What we call concrete reality is quite relative, this only means that we are referring to a non-mathematical area, such as actual objects or phenomena, but this can be non-material, such as information (ideas, texts, images, observations, measures, etc.) and this can even be a part of the psychic universe, such as mental representations, fantasies, desires, etc. as could be used in psychology, psychoanalysis or sociology. Let us think about the considerable development of cognitive sciences that have produced models for multiple applications like neuronal networks, self-adapting systems, etc. Another example, in the very different context of lacanian psychoanalysis, is the torus as a topological surface modeling the neurosis; the subject's desire and pleasure are modeled by the projective plan, illustrated by the Cross-Cap (a figure obtained by the suture of a hemisphere and a Moebius strip). By contrast, in social sciences, only the observable externalized concrete realities can be studied.

Similarly, what we call mathematical formulation, may also be very diversified, going from the simple number (the number of sheep in the flock) to the statistical chart (a population census), then to formulae and equations (Newton's law of gravity), or a mathematical structure having certain properties (vector space of the representation of variables from a statistical table, in an principal components analysis), and then going all the way to the formalized theory's enunciations (the quantum theory of fields).

1.2.3. Links between the mathematical model and its object

The link between concrete reality and mathematical formulation cannot be in itself mathematized because the so-called “concrete reality” should also be a mathematical formalization. We would then fall back on the former semantic conception. The link is then built up empirically. The shepherd who brings back his sheep every night decides to model his herd using an integer. Putting the correspondence between the herd and the mathematical object “integer” depends only on its observational capacities, bringing his counting technique into play. He would then use mathematics to compare both this evening's and last night's numbers; the results give him indications that he should interpret in terms of reality, by using all of his experience as a shepherd: if the two numbers are equal, he can interpret this by saying that there has been no change in his herd. But he can also wonder if this result does not hide an equal number of losses and births, making him reflect upon the appropriateness of his model, relatively to the knowledge and the mastering that he seeks of his herd… He will perhaps consider the set theory, or develop a much more complex specific theory, to better model his herd. His science progresses this way, as does science in general … by confronting theory with reality, going back to it and making it evolve.

Thus we must consider the two arrows of correspondence: the one that makes it possible to pass from concrete to abstract, which is the activity of modeling, then of observation-measure and information of the model, and the other, from the abstract to the concrete, which corresponds to the activities of interpretation of the results and validation of the model. These activities include almost the entire scientific procedure and it would be vain to give it a definition here. We often call it the modeling context. Nonetheless, this makes it obvious that the existence of a mathematical model is not a guarantee of scientificity, “truth”, or of the control of reality that this entails, since all of that depends on the quality of the modeling context. Stated in a caricatured manner, a solely mathematical formula has no significance if we do not give the components of this formula the precise correspondence that it symbolizes together with reality. When this demand is carried out, it can then obtain the status of model.

1.3. Is there a specificity of HSS?

As we have just stated, mathematics cannot take the place of scientific truth independently of the problems to which they are supposed to answer and which are firstly the result of human activity and social constructs. Thus, they impose perpetually, not a doubt, which is a posture of retreat, but the critical verification, the explanation of the procedure, and the reinforcement of the coherence. This procedure addresses not the purely mathematical aspect, which by its essence is the most verifiable, but the empirical aspect that links the purely mathematical discussion to the reality that it is supposed to describe or explain. It addresses the translation of hypotheses in mathematical terms and some conclusions in terms relative to the disciplinary problem and the interpretation that results from it. Thus, the risk is either to caricaturize these problems by an overly simple mathematical formalization or to delegate to “specialists” who are not in the field of HSS, resulting in an incomprehensible formalization. On the other hand, because of the plural character of the different models available to the researcher, their choice cannot escape the ideological, political and economic challenges and the theoretical postures that run throughout the social sciences.

The HSS phenomena are “multi-determined”. The instability, inherent to the complex systems, offers, at certain times, degrees of freedom between these determinisms with the possibility for mankind not only to change its behavior but also to influence these determinisms. A phenomenon in HSS is thus defined as “a succession of choices to make in situations of tension balance joined by portions of determinist trajectories”.

Already, the phenomenon of the living individual (that also produces social issues as much as it is produced by them) bears the unique capacity of auto-reproduction, not identical reproduction but with the possibility of mutation, which is generating a Darwinist evolution, by growing complexity. This goes against the rest of the physical world, ruled by the second law of thermodynamics, which stipulates that the universe, globally, always tends towards more disorder. Thus, life seems to be the bearer of a “project”, that of self-perpetuation. For that, it must be able to adapt to environmental changes. The chance of mutation plays a constructive role in as far as it permits only the choice of those forms of life capable of surviving, therefore producing an evolution towards forms of life that are more and more complex. However, the cultural dimension of mankind cannot be solely explained by biology.