The Modeling Process in Geography

From Determinism to Complexity

Yves Guermond, Yves Guermond

• Editorial: Wiley-ISTE
• Año: 2013
• ISBN:
  9781118622575
• Edición: 1
• Categoría: Naturwissenschaften
• Categoría: Geographie

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.

Chapter 1

The Place of Both the Model and Modeling in HSS ¹

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 no...

Índice

• Cover
• Title Page
• Copyright
• Foreword
• Preface
• Acknowledgements
• Chapter 1: The Place of Both the Model and Modeling in HSS
• Chapter 2: From Classic Models to Incremental Models
• Chapter 3: The Formalization of Knowledge in a Reality Simplifying System
• Chapter 4: Modeling and Territorial Forecasting: Issues at Stake in the Modeling of Réunion's Spatial System
• Chapter 5: One Model May Conceal Another: Models of Health Geographies
• Chapter 6: Operational Models in HMO
• Chapter 7: Modeling Spatial Logics of Individual Behaviors: From Methodological Environmentalism to the Individual Resident Strategist
• Chapter 8: Temporalities and Modeling of Regional Dynamics: The Case of the European Union
• Chapter 9: Modeling the Watershed as a Complex Spatial System: A Review
• Chapter 10: Understanding to Measure...or Measuring to Understand? HBDS: Towards a Conceptual Approach for the Geographic Modeling of the Real World
• Chapter 11: Complexity and Spatial Systems
• Chapter 12: Cellular Automata for Modeling Spatial Systems
• Chapter 13: Multi-Agent Systems for Simulation in Geography: Moving Towards an Artificial Geography
• Conclusion
• List of Authors
• Index