Models in geography? A sense to research (2022)

1We might have thought the topic thoroughly exhausted after the heated debates of 30 years ago. Why go back to it now? Perhaps because it is fashionable now to challenge models and perhaps because we might be able to talk about models differently.

2It is widely accepted that a major modelling period—readily qualified as "scientistic" by those who did not fully understand it—occurred in the 1960s and 1970s. This phase appears to have since been submerged or fossilised by the post-modernist wave. In fact, things may be a little more subtle. Every science has its rhythms and fluctuations, which are not unrelated to trends in society, even if they are more than a mere reflection of social trends. Talk of a "new geography", heavily staked on models, emerged at a time of economic and technological expansion, new scientific prospects, and structured (or petrified) ideologies. It also coincided with an affirmation of the supremacy of the United States and the power of calculation techniques, to the point that quantitative-theoretical geography and the related models were accused of being tricks of the capitalist demon and the computer his box of evils. In contrast, the period we are in now could be described as a submersion of research under mass education dispensed to worried students, a lack of reference points, "free" discourse, refuge in local beliefs in the name of what could be called "ethnodiversity"—in reference to no less venerated biodiversity—the return of the "singular" and especially the return of the "subject" of ecology, against a background of globalisation, arrogant transnational corporations and big money, i.e. a context of ‘having’, exacerbating the distressed individual quest for ‘being’.

3In short, everything seems to favour the idiographic over the nomothetic, to use two familiar categories from old geographical debates. Yet rarely has there been a period more productive of standards and regulations. In fields closely related to ours, school textbooks have enthusiastically embraced new sorts of models, and regional planners and politicians have shown a hearty appetite for models of the European area and models of territories. Things are indeed a little more complex than they seem, which is why I would like to put them in a triple perspective—historical, theoretical and practical. This will allow me to describe some new uses of modelling and some particular models. This is of special interest to me as a geographer, since my preference has been for regional geography, with a focus on difference—on the factors behind the singularity of places and regions—but with the aim of understanding and not just recording singularity. My goal is not just to say "it’s like that there", but to find out "why it’s like that there". Practice and theory teach us that we can only find out "why it’s like that" if we have models or references. In fact, thinking and experience tell us that we can only find out "that it’s like that" through models too.

4But first, what is a model? Geographers frequently refer to Peter Haggett’s classic 1965 definition: "a simplified version of reality, built in order to demonstrate certain of the properties of reality". Unfortunately, this formula is often translated into French as "simplified representation with a view to demonstration", a regrettable double shift in meaning. The word modèle was imported into French in the 15th century* from Italian modello, an alteration of Latin modulus meaning "mould". The model is thus a figure used to make reproductions. The root is med, found in words like "medicine" and "meditate", and denotes "measure". This idea of measuring gives the concept of model a sense of evaluation and adjustment. Alain Rey defines the model as a "system representing the essential structures of a reality". This is a long way from the idea of simplification, but not from that of essence, which has other requirements.

5Several concepts are close to these definitions, when we cannot, do not wish to, or do not know how to talk about models. The type has often been used instead of the model, and typologies have existed for a long time in geography. But type comes from Latin typus, meaning "image" or "model", and derives from Greek tupos, "matrix" or "mark", itself derived from Indo-European steu, "strike" (stamp, contusion, stupor, and even… study), i.e. "that which is marked by an identifier". However, the type differs from the model in that it suggests sorting and arrangement, while the model is a reference, a term of comparison. In short, the type presupposes the model. The case is frequently used for its exemplary value. However, this word has two meanings: we can "take" an example from among several to illustrate something; or we can "take something as" an example, "make" an example of something, i.e. seek the exemplarity in something. Yet the case and the example are in turn models. They are considered in their singularity, but with a view to deriving something of general scope from them. From their complex singularity, we extract data of general scope that are found in other individuals illustrated by the case. If I show this map of Yekaterinburg around 1890 (1), I am taking a case. If I emphasise its essential features, i.e. a) a grid plan, b) the foundry at the foot of the dam in the centre of the town, plus c) the barracks and d) the monastery, which form the base of a triangle, the apex of which is the factory, I am referring to a type—the classic Urals town. The type says a great deal about associations of power, through four linked elements that form a structure. This is clearly a model, which can be seen through the exact map of the city. I can choose to keep the map as it is with all its details and talk about it in that way. I can also extract these four representative elements from it and produce a transportable schema, which can be compared to the image of other towns. Either way, it will be a model.

6Better still: any definition of an object proposes a model. The definition of cuesta is a description of a model, which all cuestas resemble, although no two cuestas are identical. The definitions of volcano, island, laminar or turbulent flow, city, bocage or peripheral shopping centre with hypermarket all conjure up a general image and, immediately, a plethora of particular images, requiring predicates: rocky island, tropical island, sugar-cane-growing island, low-lying island soon to be submerged by the greenhouse effect, etc. Every time we define a category of objects, a type within the category, or an exemplary case to illustrate the type, we are using models and need to use models to understand and explain.

7Some of these models are iconic, i.e. they are in pictorial form. This is only one category of model, however. Philosophers, for example, seldom use iconic models, although they have produced a large quantity of models. Geographers frequently use iconic models, which some philosophers and historians would see as sign of weakness, as evidence of difficulty in attaining the level of pure thought. However, the hypothesis that this may be a strength or is inherent to the object of study itself is not completely excluded. Iconic models come in a wide variety of forms, including mathematical curves, hexagons (the ideal Thiessen polygon), grid plans and florid representations of the "modern metropolis" with legends of 40 or 50 symbols.

8Models are widely used in geomorphology, which is how I became acquainted with them. The elementary exercise of geomorphology consists in identifying forms and conjecturing their origin, by classing them according to precise definitions, with types and models, as in any "natural science". Human geography was for a long time much less advanced, with only a few typologies, which were much more formal than structural, more descriptive than explicative, and limited to villages and farms, with vague overtones of a certain French disdain for the Germanic mania for classifying.

9This is when the avalanche of models struck in the 1960s, triggered by a significant change of attitude (2). The ambition of mathematics, in its two aspects of measuring and forecasting, was fundamental to this. Old models, often derived from economics, which was quite advanced in this area, were transposed or rediscovered. Models that could make links between equations, curves and spatial forms were obviously the most promising. This marked the triumph of the four large families: von Thünen; Christaller revised by Lösch; Reilly and Thiessen; and, less congruously, Zipf. Diffusion models that involved the calculation of probabilities and games appeared. These were followed by simulation models that aimed to reproduce dynamic systems and thus anticipate the likelihood or the effects of a change. At the same time, models of spatial configurations, particularly networks, began to appear, and the use of flow charts to model systems began to develop.

10The only way to understand and explain something, as Borges wrote, is to compare it to something we know and therefore already understand. Fortunately, on a world scale and, in principle, on the scale of a scientific community, the sum of what is known and understood increases every instant—short of cases of regression and collective amnesia, a hypothesis that admittedly cannot be ruled out. In a geographical configuration, we can thus seek the manifestations (or absence of manifestation, which is no less interesting) of established models, such as zonal or meridian climatic dissymmetry, Fordism or metropolisation, i.e. models that are already understood. And if none of these models "works", then we need to imagine some other kind of model, prove its legitimacy and seek other manifestations of it, all of which is very exciting. Either way, we are working on interpretative comparisons, and not limiting ourselves to strictly formal comparisons of the old typologies, which put all street villages or all houses with inner courtyards in the same group as a matter of form.

11The conscious use of models has made a substantial contribution to geographical research, profoundly transforming it in the last third of the 20th century. It has also provoked criticisms, apparently of all kinds, but among which it is not too difficult to identify a few models (3). I shall attempt this exercise in half a dozen points.

121. Modelling is simplification, which means a loss of information. I have no intention of being ironic about detail-mad geographers who need every indentation in a shoreline and every meander of a river and are distressed by straight lines. I too am attached to tiny river bends, to place names and to the details of particular villages, and have initiated a number of meticulously detailed inventories, atlases and geographical dictionaries. But we need to distinguish between objectives and scales. We should not mistake noise for information, which is its exact opposite. Understanding and explaining the geography of a region or a country, like any object of knowledge, implies distinguishing between the fundamental and the secondary, which requires effort. This is what Husserl termed rather pompously as eidetic reduction, i.e. the art of going to the essential. Only a poor researcher or teacher would not do this. Some of those who reject modelling as "simplification" may well give excellent lectures by "simplifying" themselves.

132. Some models are so complicated that they are illegible. This is perfectly true: some flow charts and iconic models (particularly urban ones) are impossible to decipher and have therefore failed to achieve their objective. The people who produced them did not want not to "leave anything out". This does not condemn modelling as a whole, since these attempts at models are a negation of the idea of a model. When a model expresses the essential in a legible fashion, the way a summary expresses the contents of a book, it is always possible to change scale later and examine the details, the unexplained, opening the "black boxes" one after another.

143. The singularity of each place, of each geographical object, prohibits generalisation. This apparently fundamentalist affirmation is simply nonsense, because it can be said about anything, and no science or knowledge would have been possible if it had been followed. In Antiquity, the Greeks enjoyed the false debate between Herodotus, who supported this kind of foolishness, and Hecataeus of Miletus, whose intellectual requirements were somewhat different. But narrating unverified and unverifiable "histories" is not the same as thinking. In the context of scientific work, Hecataeus and the Eleatics were models, and Herodotus an antimodel. Any description needs models, without which it expresses nothing. The worst is that ordinary descriptions use and abuse clichés, which are nothing other than overused models. "Rustic", "hedgerows", "scenic", "pleasant", "many and varied"—one simply has to read the descriptions of landscapes in many guidebooks… and ordinary regional geographies.

154. The models used in geography come from elsewhere. This is partly true. So? Others may have worked better and earlier than we have. It is therefore intelligent and fruitful to take inspiration from their ideas when these contribute to our understanding of the production of geographical space. This is not a reason to forget that geographers have produced an abundance of their own models, which are no less useful: piedmont, huerta, estuary region, frontier, march, dead ground, distribution models of free ports and tax havens, and world megalopolises. Furthermore, some imports and analogies are worth being re-exported: in my view, the gravity model (the bigger and the closer, the more attractive) is infinitely easier to understand in geographical space than in cosmic space, simply because, in everyday life we clearly understand the reasons, i.e. the nature of the "energy" in question.

165. Modellers are dangerous, because their ambition is prediction and application and they want to force reality to fit their models. Apparently Christaller tried to persuade Hitler to "rectify" the network of Polish towns to coincide with his model. Even if true—and the anecdote needs to be verified—the undertaking did not succeed. At the same time, a plethora of territory-makers, neither geographers nor scientists, have attempted, sometimes successfully, to design or redesign spatial organisations to meet their requirements. This has nothing to do with the idea of models, except in the vulgar, prescriptive sense of the word. This argument is simply groundless accusation and is even comical in that it credits geographers with powers they have never had.

176. What is behind the model? It seems to me that the only serious criticism that can be made of some of the forms of modelling that appeared in this whole period is the one least mentioned: because of their strictly formal character, some models may neglect processes of society. The ambition to measure and calculate at all costs has produced an economistic tendency or a focus on calculation techniques for their own sake. Researchers sometimes seek purely mathematical adjustments, without thinking about the processes at work. Factor analysis is useful for highlighting strong correlations and facilitating typologies. But what happens when we turn the axes around? What is behind autocorrelation models or sector models of urban morphology? What is the significance of calculating a fractal measure? What is the purpose of concluding that all geographical forms are fractal simply because we can always make this measurement? When a researcher finds a complex mathematical model that fits a distribution, what does this model really describe and does it offer something more than a coincidence in the profound sense of the word? Since the organisation of geographical space is the work of human beings (performed in a particular environment filled with memories, people, issues and strategies), I only consider myself enlightened if the results resemble explanations, if we can perceive the reasons and means behind them, i.e. if they have a social legitimation, even if we have to allow for an element of "chance" in this "necessity". In my view, this criticism does not apply to modelling as a whole, but only to a purely technical approach to modelling, using the tool for its own sake, which has developed in the past 30 or so years.

18I believe we can draw three provisional conclusions from the above. The first is that almost all these efforts and a few of these debates have taught us a great deal. The second is an appeal in favour of memory and integration. In my view, science does not progress by successive negations, by fashions that replace fashions, but by accretion. At every instant, sometimes through fashion, science incorporates the best of new acquisitions. We should not forget these efforts and debates, but rather integrate the most resilient of their contributions. For example, to contest "quantitative" approaches, some geographers emphasised the role of firms and production relationships in spatial behaviour, and therefore in the production of geographical space, while others focused on the role of representations and myth. Both have benefited geographical knowledge in general. These contributions should be integrated into geography teaching alongside calculation and modelling methods, rather than replace them. The third conclusion is that, through these successive or simultaneous contributions, we should be seeking to base geographical modelling on logics of production of space, particularly by working on models that best express the organisation and differentiation of geographical space.

19This discussion of models naturally raises questions about research practice in geography. In this regard, we have all learned, created and acquired a great deal over the period under review. The parascientific (or antiscientific) phase that some groups of geographers appear to be going through may make us lose some of what has been acquired. Perhaps it will also enrich our scientific culture, if there is a move from egology to ontology, i.e. from the navel to the brain. Augustin Berque has made some suggestions in this direction (4). My feeling is that we are about to enter a new phase of construction, where thinking on and knowledge of systems, models and even some Grundrisse will be reinterpreted and better employed, in a world where even shareholders in pension funds will realise that the maximisation of their profit depends on some regulation and where scientific work will offer more than researchers’ self-contemplation in re-enchanted nature.

20This type of concern has inspired most of my own research and led me to develop a certain idea about geography, models and the meeting of the two. In 1965, my thesis on the Toulouse countryside proposed replacing the conventional determinist model—which sought to explain the slightest development through a kind of climatic fatalism—with a model based on the development of the social system of the production and distribution of wealth. At the same time, my complementary thesis on discontinuities in geography, partly developed from my initial research in geomorphology and hydrology, was based on the examination of a whole series of threshold models in system dynamics. I then conducted research on "rural districts", the first analyses of spatial structures and geographical situations illustrated by structural and dynamic iconic models. In the 1970s, I worked on social science practices in general, the Soviet system in particular and models of alienation—particularly spatial alienation—in the USSR; and the processes of modelling particular geographical objects (e.g. the towns of the Massif Central in France, the Champagne region, and the structures and dynamics of the territory of France). I then sought to formulate a coherent representation of geography as a place and a system of knowledge, which I drafted in 1985 and which provided the introduction to the Géographie Universelle in 1990. The concept of the choreme and related representations, which spread at first slowly, then even surprisingly broadly (at less in France), led me to expand certain aspects more than others. The influences on my work are fairly obvious: a basic Marxian culture; training in reasoning from geomorphology; the thinking on systems, structures and cybernetics of the 1960s; some of the "radical" criticisms of the 1970s; the efforts of so-called quantitative-theoretical geography; my association with other social sciences; "applied" work with architects, planners and ministerial managers; and numerous regular informal meetings through L’Espace géographique, the Géographie Universelle, the Groupe Dupont, GIP RECLUS, etc.

21Some of the "sense" of this research, to which the sub-heading of this paper refers, can be found in ten related hypotheses, which together form a "model" of the representation of geographical knowledge. Naturally, there can be others. It is sufficient (but necessary) for this model to be coherent. This is what I have presented elsewhere as the "hard core" of a so-called "soft" science, like all human sciences. These proposals could be considered as axioms. I prefer to call them hypotheses, because they can be demonstrated or refuted. Although summarising them misrepresents them, it is worth making an attempt.

  • Every society, through its very existence, produces space and even territory, or territories. In the long list of things that societies produce, geographical space is the geographer’s priority object of study.

  • The production of space is the translation (expression) of certain social activities. It responds to a few simple needs of societies (shelter, food, protection, trade, and even leisure, worship, etc.) and, for this purpose, follows some principles tested by experience (praxis).

  • These actions are unevenly deployed by agents (individuals or groups) with distinct—and possibly even contrary—interests, resources and representations, which leads to an awareness of relationships of power and social divisions.

  • Actions and tensions are reflected in a territory by spatial forms (or geographical figures) that reveal these choices, actions, tensions and differences.

  • These geographical figures result from the interplay of several laws, sometimes in combination, sometimes in opposition, whose expression stems from social practice and which only have meaning in the relationship between space and society. To enumerate without analysing them, these laws include appropriation, spatial division of labour, confinement, entrenchment, exchange, and two kinds of gravitation.

  • Through social practice, these laws and figures appear in an environment that already exists, which contains earlier work, legacies of nature and neighbouring systems. These memories have their own inertias, logics and processes and have different reactions to the actions performed, which creates a double filter: that which is imprinted with past actions is also a matrix for future actions; any produced space is also an environment space, a milieu.

  • While there are laws governing the production of space, i.e. the behaviour of societies on the surface of the Earth, there are no "laws of space" independent from human action and human projects. "Friction of distance", for example, only occurs in relation to an action or a project, to the resources devoted to it, etc. Of course there are laws and phenomena of nature, but, apart from a few obvious facts (gravity, the rotation and inclination of the Earth, biosynthesis), these are always perceived through human activity in geographical space.

  • The local composition of these actions, laws and figures is singular. This is what makes the diversity of the world and the singularity of its places. This singularity can be understood and appreciated all the better if its components are identified and its trajectory is evaluated.

  • The interpretations of the structure and dynamics of a geographical object must reveal the interplay of actions, laws and figures that are determinant today, that were probable yesterday and that will be possible tomorrow.

  • The structure and dynamics of any geographical object can be analysed through the composition of general models. In other words, we can model the structure and dynamics of a singular geographical object ("regional" geography), which in turn enhances and re-evaluates the stock of known models ("general" geography).

22Guided by these fundaments, we can reconsider modelling as an heuristic instrument in geography. This sets several conditions, or at least gives us several aspects to think about.

231. Identity and identification.—To define a geographical object, place, country, field or distribution, is to describe its singularity or, in other words, its identity. But how do we describe an identity and what does this word mean? Identity comes from idem, the same. We define an identity by observing a similarity. This is an interesting paradox, and a logical one: we can only define something in reference to known models. Tall, strong, blond, blue eyes, red skin, turned-up nose and round face are elements of identification which, in sufficient number, will describe a singular person. This description is based on a selection from among general, common, inventoried, understood features. The singular is described through the universal. It is the list of models used that is unique. This is why it makes no sense to consider the singular in opposition to the universal, since the singular can only be perceived through readily understood, universal categories. And this is why, whether we like it or not, we cannot do without models.

242. Meaning.—To advance, these models must have meaning. Recognising forms implies that we understand where they come from and what produces them. The subject is also complicated by phenomena of convergence: identical forms can have different origins, and vice versa. The geographer must at least make a conscious effort to recognise and interpret spatial forms. This is the difference between science and esoterism. The geomancer, astrologer or augur who "reads" coffee grinds, a palm or a chicken’s innards observes forms whose origin bears no relation to the question asked. They are the only ones to "see" (or imagine), but they claim to have the gift of trance and divine inspiration. Geographers, usually devoid of both, use known forms, for which they have learned the logic of production (whether of social or natural origin), even if they sometimes have to discover new forms. If I observe an exceptional concentration of people, wealth, towns and production along a curved axis that runs from England to Lombardy via the Rhine, anyone can verify it and try to understand it, by using what is already known about isthmuses, megalopolises and the history of European trade. And anyone can see that this form does not summarise the whole of Europe: it is simply one of its spatial structures.

253. Models and residues.—Modelling does not only consist in inferring models with a generalist ambition from reality. This is necessary, but highly insufficient. We need to strive to use models to interpret unique objects and consider that the understanding of structures and dynamics of unique objects is not only a legitimate objective, but sufficient and exciting. When we are dealing with complex phenomena or objects—and all our regions, towns and distributions are complex—we need to strive to model these singularities to understand and represent their structure, organisation and system. In its initial, major phase, modelling was mainly aimed at revealing and justifying general models. This was indispensable. But today we should only be moderately satisfied when we confirm locally that a model "works", e.g. when we arrive at the conclusion of a core-periphery dissymmetry. It is highly likely that effective models will work. Therefore it is often more interesting to look for what escapes the models, or their contradictions. There is a need to cultivate the residue, but in two opposite and complementary directions. In the Husserlian and chemical sense, the residue is what remains after secondary matter has been removed by "reduction", in other words, the residue is the essence, or precipitate. In the mathematical sense, the residue is what the model does not explain, what deviates from the adjustment curve. There can be no valid research without this effort of reduction, which makes it possible to delimit the essential and identify the deviations—and thus to stimulate and refocus the investigation.

264. The form of models.—Since forms of communication are not infinitely varied, despite the evident profusion, wealth and complexity of research using models, we can see that there are still three major categories of models. There are rhetorical models, expressed by a text, a discourse. There are mathematical models, expressed by formulas—between image and text. And there are iconic models (6), expressed by pictures, in the form of curves, outlines or spatial configurations. These are distinct things, but they stem from the same concern, the same attitude. They are mutually supportive and are sometimes only different expressions of the same phenomenon. The gravity model can be expressed by a formula, by a curve on two axes of coordinates, by a spatial scheme (the map of its effects on the area) or by a text—its literal definition. These three forms are equally valid and constructive, equally necessary. There is no need to establish a hierarchy of values. All three have the same objective: not only to describe, but to attempt to understand and explain by identifying (or conjecturing) the processes and forms that appear to be determinant.

275. The model-map.—It is also true that, because of the very nature of things, i.e. the nature of the object of knowledge specific to geographers, the drawing of forms in space is of particular interest. "We liked to create images, which we called models […] to grasp a fragment of the mosaic of the world" (Ernst Jünger, On the Marble Cliffs). The iconic model offers a panoptic—or synchronous—vision; it shows places in relation to one another; it sets them in a context. A drawing makes it possible to understand effects of the interference of forms, the reciprocal deformation of the models. We see clearly that the European megalopolis is an arc, which steps lightly over the Alps. Why? When we construct a model of the peri-Brussels orbit, which includes all the second-tier Belgian towns, and of the ecological organisation of the Belgian territory, we see clearly how it is deformed into an ellipse (elongated from an O into an E). The drawing is optional, but we have to admit it is practical, and even productive. Far from excluding quantification or mathematisation, it encourages them, as a check. The drawing must meet two requirements: it must be faithful and legible.

286. Modelling is not simplifying.—It is a serious error to equate modelling with simplification, particularly in geography where simplification is equated no less often with the "generalisation" of contours in the cartographic sense. Simplification redraws and eliminates "accidents", which may be fundamental. It is often blind because it is without principles, except for that of economy, which is irrelevant here. There is no point in transforming the image of the contours of a country into a regular polygon or shapeless potatoid. Modelling is based on hypotheses, which are a function of the nature and context of the geographical object under study. It relates these hypotheses to each other and pushes them to their limit. It constructs, deconstructs and reconstructs. It goes through a series of iterations between deduction and induction. The first drawings, if there are drawings, are abstract. Little by little, they come closer to the complexity of reality, which is never simplified. Little by little, they track down the residues, in the sense of deviations. The only strategic decision is when to stop the process, at which point that which will be considered as secondary is left in the shadows. But this is common to all intellectual activity and follows logistic law.

297. Four fields in geography.—Modelling in geography is used in at least four areas, to differing degrees. The study of networks and flows has probably benefited the most. The work of engineers and economists has contributed a great deal to this, assisted by the many forms of graph theories. A second area is delimited, named geographical objects: towns, countries and States. Towns have been explored for a long time, and "regional" groupings more recently, but sometimes abundantly. A third area is fields, which has not been studied much except through diffusion analyses. It is nevertheless fascinating to explore the margins, borders and fluctuations of fields, to recognise their poles and axes, their relays and recesses. A fourth area is the spatial distribution of particular phenomena. Any thematic map can and deserves to be a medium and an object of modelling and, thus, a source of fertile interdisciplinary research. Just think of the information that can be drawn from epidemiological, criminological, electoral and demographic maps. Geographers have been commenting on these for a long time. Rigorous methods of analysis using proven models may well have made a contribution (7).

308. Modelling as a research process.—In relation to my ideas and practices as a geographer, modelling involves seeking which composition of model takes best account of a regional or local organisation, of a configuration of a field or network, or of a spatial distribution. It also involves, if necessary, proposing a new model to be added to the stock of information we already have, i.e. to fill in an apparent gap in this existing knowledge. Because these models have a defined and known meaning, and represent a process, or a social response to spatial problems, they clarify the issues that are or have been at stake. This is the central gamble. It is an heuristic gamble. Modelling is a research procedure. As such it requires exacting standards and rules of usage. Modelling in geography begins with two inevitable and related questions: "where are we?" and "what is likely to be at stake?". Guided by these questions, we try a few keys, i.e. models to be adjusted to configurations of reality. The process is iterative and follows logistic law: we end it when the marginal gain becomes too low. Each attempt must involve a clear interpretation of the process in question: no form deserves to be used for its own sake, unless its meaning—and in this case, its social logic—has been understood. In this way, we define a set of determinations, translated by interlaced spatial forms. These pieces or keys can be refuted. Of course, there is always an element of chance in the selection or sequence of determinations, but the hypothesis of chance can be a possible conclusion, not a necessary introduction. Without this, all research would be pointless and all science impossible.

319. Communication.—Modelling also has undeniable advantages for the communication of results. When this is done properly, the reaction is not unlike the "I should have known all along!" when a mystery crime is solved, to the point that modelling seems easy, simple and purpose-designed for communicating. We almost forget the considerable amount of work involved. Peter Haggett even made this mistake himself in his definition. However, the use of models for understanding is first a pour-soi: it is no less fertile without the intention of communicating; after all, we do not always wish to communicate our discoveries. Geographic modelling procedures have nevertheless been extremely popular with consumers of geography, be they teachers or planners, particularly in the past 10 or 15 years—strategists have long been aware of the value of models as communication tools. As to how much of this popularity can be attributed to the quality of the theoretical background, to the novelty of the conclusions, to the effectiveness of the demonstration or to the appeal of the image is a complex question, which is worth investigating. I do not think that any one of these four factors is sufficient. I would even go so far as to say that the absence of one of them would compromise the whole.

32In Les Mots de la géographie, I defined the model as a "formal, refined representation of reality or of a system of relationships", without adding a particular purpose. There is no question of idealisation and even less of simplification, nor of being limited to communication. I maintain this position. To be even more concise, I could write "formalised representation of a phenomenon". "Phenomenon" covers our entire field, while "formalised" implies exacting standards. For those who must know what modelling is for and want a purpose to be indicated, I could add "for purposes of interpretation". Of course, this representation passes through several filters, which all have their traps: the perception of the phenomenon; its representation; the construction of a model; the interpretation of the sense of this model; the ability of the model to take account of the phenomenon. But who ever said research was meant to be easy?

33I am aware that the construction I have just presented is itself a sort of model. Do not misinterpret me. My paper is not and does not propose the model, but rather a model, which expresses a "formalised representation" of a personal theory and practice of geographical research. As in any particular object, we find elements of several proven models, which are shared and practised to varying degrees: some of you will identify partly or fully with this. It remains to be known whether the resulting arrangement has an interpersonal value. Naturally, I hope it does.

34Lastly, I would like to conclude with a quotation from the Belgian poet, Émile Verhaeren:

"Le menuisier du vieux savoir
Fait des cercles et des carrés
Tenacement pour démontrer
Comment l’âme doit concevoir
Les lois indubitables et profondes

Qui sont la règle et la clarté du monde."
(The carpenter of old knowledge
Makes circles and squares
Tenaciously to demonstrate
How the soul should perceive
The indubitable and profound laws
That are the rule and clarity of the world.
I am learning to become a carpenter of old knowledge.)

35(1) See Section on Russia and its neighbours, p. 331, Volume 10 of Géographie Universelle, Belin-Reclus.

36(2) Basic references: Bunge 1962, Theoretical Geography, Lund Studies in Geography; Haggett 1965, Locational Analysis in Human Geography, London: E. Arnold; Chorley and Haggett 1967, Models in Geography, London: Methuen; D. Harvey 1969, Explanation in Geography, London: E. Arnold; Abler, Adams and Gould 1971, Spatial Organization, London: Prentice-Hall; Haggett 1972, Geography: A Modern Synthesis, London: Harper & Row. First publications in French by J.-B. Racine: with H. French, "La Nécessité d’un dialogue" in Quantitative and Qualitative Geography, Univ. d’Ottawa 1971; with H. Reymond in L’analyse qualitative en géographie, Paris: PUF, 1973. In related fields, spatial models have been used for a long time. Apart from the spatial models of von Thünen and Christaller, we should at least remember Köppen’s image of the "ideal continent" to take account of the effects of zoning and climatic and biogeographic dissymmetry. There have been debates on this topic in French, at a session of the Association de géographes français in 1973 (Bulletin de l’AGF janv.-fév. 1974, including a contribution by F. Durand-Dastès, who also wrote a summary of the subject in the Encyclopédie de géographie by Bailly, Ferras, Pumain (Paris: Economica, 1992); and at a symposium in Lausanne directed by J.-B. Racine in 1978 (Les modèles comme source d’inspiration dans la géographie contemporaine). In my own publications, there are models in: Les Discontinuités en géographie (1965, published at the CNRS in 1967), but at a time when my position on the subject was far from clear; a special issue of the Revue géographique des Pyrénées et du Sud-Ouest 1969 ("Quartiers ruraux du Midi toulousain") based on research conducted in 1964-1966; and in the first issue of L’Espace géographique in 1972 ("Les villes du Massif central").

37(3) Of various debates, let us recall at least the summary published in 1988 by C. Kesteloot: The Use of Models in Belgian Geography.

38(4) See A. Berque, Etre humains sur la terre, principes d’éthique de l’écoumène, Paris: Gallimard, 1996 and Écoumène: introduction à l’étude des milieux humains, Paris: Belin, 2000.

39(5) I have already emphasised a lattice of European networks and a ring of centres of finance and power in North-Western Europe: see Territoires de France et d’Europe, Paris: Belin, 1997 ("L’Europe des réseaux", p.41 et seq.) and "Le Ring", l’Espace géographique 1998 n° 4, p.369.

40(6) The frequently used term "graphic model" seems rather infelicitous. Grapho means "I write", and writing implies a text. There is also confusion with "graph", commonly used to refer to a diagram.

41(7) A useful experience in this regard with specialists from the French ministry of industry on an "applied" research project (Le Redéploiement industriel, Montpellier: Reclus,(1986).

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