In contrast to the aisled plans, multistoried elevations, and ribbed vaults of early Gothic architecture in the north of France, church design in Languedoc in the second half of the twelfth century tended to favor wide and aisleless two-storied basilicas with flat expanses of uninterrupted wall. The interior of Saint-Pons-de-Thomières, for example, is a large, unified volume nearly 15 meters wide (see Fig. 51). The surface of the walls encasing the interior space is interrupted only sparingly. Each bay is defined by the linear organization of vertical pilasters that carry transverse arches. Within each bay, small nave windows signal an otherwise undifferentiated second story. Round-headed windows originally opened into the nave to mark the presence of the lower gallery level, but the skeletal support of the building is otherwise unarticulated. The slightly pointed barrel vault, like the nave walls, features large flat areas of undecorated surface masonry.

Wide spans and planar surfaces seem to have been a feature of architecture in the Midi as early as the ninth century. These elements continued to dominate southern Gothic architecture of the mid-twelfth and thirteenth centuries. In this sense, the division between Romanesque and Gothic is less clearly defined in southern French architecture, or perhaps it is better to observe that the terms “Romanesque” and “Gothic” are less useful in describing the architectural history of Languedoc.

The student of any fortified enclosure must keep two groups in careful perspective: those who are inside, and those who aspire to that coveted position. The “included” and “excluded” normally comprised competing groups of people, but valued possessions, livestock, and even supernatural protectors could form part of the medieval equation. Fortress-churches also participated in the competition between “inside” and “outside” groups. With the fortified abbeys of Maguelone, Agde, and Saint-Pons-de-Thomières, the “outsiders,” identified textually, were “Saracens,” pirates, brigands, and heretics. The principal “insider” was the bishop or abbot. The cathedral chapters of Maguelone and Agde and the monastic community of Saint-Pons were normally “inside” with the bishop. The relationship of the chapter to the bishop could, however, become strained. The cartulary for Maguelone preserves evidence of conflicts between the bishop and chapter, especially in the second half of the twelfth century. At Agde, the bishop and chapter were in direct conflict during much of the eleventh and twelfth centuries.

Disputes often arose from the designation of certain groups as “insiders.” In 1168, the provost of Maguelone brought a complaint to Jean de Montlaur, bishop of Maguelone. The provost alleged that the bishop's knights entered areas of the monastery that should remain closed to them and that they stole some of the abbey's table knives. At Saint-Pons, the arbitrated agreement between Abbot Raymond of Saint-Pons and the viscount Roger Trencavel stipulated that, in addition to the bishop and monks, only the abbey's serfs were permitted in the cloister (Appendix 32).

The culture of medieval France was undoubtedly as complex and contradictory as our own. One of the primary tasks of the historian is to create a framework for keeping track of innumerable events, forms, and people and for mapping the complex interactions among these elements. This framework provides a structure by which we organize and – we hope – make sense of a past that can be similar to our own experience but that can also be quite alien. The frame, however, can also become a limit to vision. For example, the failure of past historians of Western medieval Europe to consider aspects of the medieval East, the place of women, or the evidence of material culture have produced views of the Middle Ages we now see as flawed. Similarly, the conventional frame of architectural history has marginalized buildings in Languedoc that are unusual according to standards more appropriate to the north than to the south of France.

A close reading of the uses and meanings of the fortified church in Languedoc has forced us to reevaluate some of the canons of architectural history. The fortress-church has demanded that we integrate the study of military and ecclesiastical architecture, reconsider the motivations for a host of architectural forms, rescue Languedoc from its position as a provincial backwater, reexamine the links between medieval East and West and between the North and South, and reevaluate the stylistic concepts of Romanesque and Gothic.

The previous chapter dealt with a general spatial accounting model which can be applied to many systems. In this chapter the particular application to the location and interaction of activities in the urban or regional space is discussed. It begins by describing the general dynamic structure of the activity system, identifying three main elements: activity allocation and land market, the dynamic relationship between activities and floorspace, and the dynamic relationship between activities and transport. Reference is also made to section 1.5 where general model dynamics were discussed.

General urban–regional dynamics

In the previous chapter, when discussing the issue of abnormal prices, a particular way of representing supply–demand dynamics was proposed when there are short–term restrictions in the capacity of production in particular sectors and regions. If demand for such goods in certain places exceeds capacity, short-term prices rise, generating abnormal profits or rent. Different levels of profit in particular sectors and regions constitute the determining factor in the distribution of investment in a following time period; given a total amount of money available for investment, an investment allocation model can be constructed to distribute money to sectors and regions. This, in turn, will determine increments in the capacity of production for the next time period, thus generating new demand/supply relationships.

In the case of the location and interaction of activities in space, the system can be viewed as people performing activities in particular places in what can be termed the activity system. In such a system, whether at the urban or regional scale, the main restrictions that generate abnormal costs are labour, land/floorspace and transport.

The earliest models which sought to explain the spatial distribution of activities were based on micro-economic theory. They took as their central concern two related questions: what is the rationale that regulates the location of activities, and how does land rent or land values emerge from this process? The models which evolved from this microeconomic approach started by adopting the conceptual framework of classical and neo-classical economics.

In this approach, the location of activities is seen as the outcome of a combined market mechanism involving three basic elements: commodities, land and transport. On the one hand, land is required to perform productive operations, or for the satisfaction of residential needs. On the other hand, transport is required in order to move surplus production or labour. A farmer, for instance, wants to sell his surplus in the market-place, and the resident of a city wants to sell his labour where there is a demand for it. The process of exchange involves transportation, either of commodities to the market, or of residents to their place of work.

Land is considered to be a large featureless plain and infinitely available, so that in principle there would be no need to pay for it. What gives land a differential quality is the cost of travel or accessibility, which is the main factor in the generation of land values.

This book has a dual character. On the one hand, it is structured in the form of a textbook. Subjects are treated in a sequence such that the reader can follow from basics to more elaborate formulations; most of the elements required for its proper comprehension are given, making it self sufficient; references are deliberately kept to a minimum. On the other hand, the book is the result of extensive research, and the knowledgeable reader will find many stimulating propositions, some more novel than others, and some probably more pertinent than others.

Integrated land use and transport modelling is an area of research that reached a high peak in Britain in the early seventies, mainly with an academic interest. Real:world applications in industrialised nations, however, have been limited mainly because of the slow rate of growth of the cities of Europe. The second half of the seventies and the first half of the eighties have seen considerable advances in the development of theories and operational models in the area of transport. Most cities in Europe and the USA regularly use stand:alone transport models for their everyday planning practice, considering the location of activities and other socio:economic variables as a relatively stable set of given inputs. The situation in third world countries, however, is quite different; since cities grow so rapidly, the interaction between the location of activities and the transport system becomes a dominant issue. It is not surprising, then, that the research contained in this book is supported by applications mostly carried out in Venezuela.

The Micro-economic models described in the previous chapter can be defined as belonging to a disaggregated approach, because the analysis centres around the behaviour of individual units. The approach taken by spatial interaction models, by contrast, can be defined as aggregate, because both space and activities are grouped into discrete categories. Instead of analysing particular points in space, zones containing a large number of activities are defined. Activities, on the other hand, are aggregated into groups, and it is assumed that all the individual members of a group have similar characteristics.

Origins and development of spatial interaction models

There is a considerable amount of literature on spatial interaction models, so that only a brief review is presented in this section. Excellent reviews are contained in Lee (1973), Batty (1975, 1976), and Baxter (1976). In spite of earlier work by Reilly (1931), Hoyt (1939), Stewart (1948), Zipf (1949), Converse (1949), Clark (1951), Isard (1956), and others, most authors agree on placing the origins of modern spatial interaction models in 1959 with the work of Hansen. After this, a flurry of research activity took place.

There are many factors which led to the rapid growth of this area of research, but perhaps the most important one is that spatial interaction models are easy to apply to real cases, producing useful and realistic results. Another factor is that the spatial interaction approach is particularly relevant to transportation analysis.

The view that social sciences are very different from other forms of science is common, hence the need to develop special methods. In section 1.1 it is argued that, although there are some important differences, modern developments both in social sciences and in what are called here natural sciences tend to reduce them, pointing towards a common methodological framework. This idea serves as an introduction to further sections where the scientific method for the social sciences is outlined, and then is shown the role that models play in it.

Natural and social sciences: the hypothesis of convergency

Traditionally, social sciences have been considered a very special form of science, different from biology, physics or natural sciences in general. Many arguments are put forward to support this distinction. By contrast, social phenomena are considered to be ever:changing. It may well be that in natural sciences theories themselves change and old ones are replaced by new ones, but once adopted, they are considered as permanent. If social phenomena are ever:changing, social theories may be valid only for a short period of time; that is, they have a particular historical reference.

Because it is generally assumed that natural phenomena are permanent, theories that successfully explain their past behaviour have strong predictive power. In social sciences, even if a theory has been very successful in explaining a phenomenon that occurred in the past, it can only provide predictions as long as the historical conditions prevail.

Another difference that is commonly pointed out is that natural phenomena can be reproduced in the controlled conditions of a laboratory, which isolates them from unwanted externalities. The use of experiments has become a key element in the creation of knowledge in natural sciences.

The relationship between the location of activities and the transport system has been discussed extensively in the literature for many years, but it is only recently that it has been established more formally. This is due perhaps to the historical development of theories related to the use of space and those related to the use of transport, and to the fact that both evolved in relative isolation.

It was pointed out in previous chapters that the majority of land use theories considered the transportation system as having a definite effect on the location of activities; this is a common element in the works of Von Thünen (1826), Christaller (1933), Hansen (1959), Wingo (1961), Alonso (1964) and Lowry (1964), as well as most of the land use research that took place in the late 1960s and early 1970s. All of this work, though, considered accessibility or transport costs in an ambiguous way, and basically as exogenous. Even in the work of Wingo, which could be considered to have pioneered the field because it developed both transport and land use to considerable extent, the two remained in separate compartments, and the transport variables that go into the land use model were restricted to the concept of ‘distance to the centre’.

Throughout this book, reference has been made to a number of computer programs that are intended to help the understanding of particular topics. They can be used by the interested reader for his own benefit, or they can be used for computer aided teaching.

All programs have been written for the MS–DOS operating system and require modest resources, so that they should work on many popular personal computers. There are English and Spanish versions. In some cases, there are programs that require graphic screens, but there is always an alternative version without them. Each program is accompanied with a document file to explain its use, and one or more example data-files.

Users interested in acquiring these programs should post two DSDD 5¼″ diskettes with a covering letter explaining the intended use (for the purpose of keeping a record) to the following address:

What follows is a short description of each of the programs referred to in the book. All programs have been written by the author. In many cases they are representations of models proposed or developed by others, and they have been written on the basis of published material. Hence, there might be conceptual differences between these versions and the originals, not always involuntary.

DIAL

This program contains a simplified version of Dial's assignment algorithm, with a fixed number of trips from a given pair of origin and destination nodes.

In chapter 2 the micro-economic approach for representing a spatial system was presented and discussed. Although the models that can be derived have a strong theoretical content, the nature of the simplifying assumptions, their mathematical representation and their operational difficulties, forces them to stay as theoretical propositions only, providing no useful analytical tools for the practitioner. The main shortcomings of this approach can be summarised as follows:

1. (a) Both users and suppliers are assumed to have perfect information about market conditions. Limited information would be a more realistic assumption.

2. (b) Bidders or suppliers are assumed to have deterministic utility functions. Faced with the same options, they will always make the same choices. Variations in individual behaviour should be considered instead.

3. (c) Bidders or suppliers have frictionless mobility, and they can even appear or disappear at no cost. Restricted dynamics would produce more realistic results.

4. (d) There is no way to aggregate demand or supply functions. With a large population, the resulting models are impractical. If, in order to solve this, the analyst applies the same models to socioeconomic and spatial aggregates, the results would be unreal, because it would imply large groups showing identical behaviour.

Spatial interaction models, as explained in chapter 3, were derived by maximising an entropy function, subject to some known constraints. The resulting distributions, as has been pointed out, are the least prejudiced statements about the system being modelled, that is, they are the distributions that make the weakest assumptions about the system apart from what is known and reflected in the constraints.

In this chapter, a number of case studies are presented where a specific modelling package, TRANUS, has been applied. The package is based on much of the theoretical framework described in the previous chapters. The purpose of presenting these applications is to illustrate particular instances in which the proposed theories and methods can be helpful in the solution of many real planning problems.

The chapter begins with a brief description of the modelling package, followed by a case:by:case explanation of each application. The case studies described are not the only ones where the package has been applied; they have been selected as the most representative cases in each of the following areas: urban land use planning, urban transport planning and regional transport planning. A final example related to energy evaluation is also included. The author has been involved in all case studies described here together with colleagues, particularly with B. Perez, A. Morais, M. E. Botero and P. A. Rickaby.

Brief description of the TRANUS system

TRANUS is an integrated land use and transport model that can be applied at an urban or a regional scale. The program suite has a double purpose: firstly, simulation of the probable effects of applying or implementing particular land use and transport policies and projects, and secondly, the evaluation of these effects from social, economic and financial points of view.

The TRANUS system has been developed by de la Barra and B. Perez since 1982. It is based on many of the theoretical proposals that have been presented and discussed in the previous chapters.

In the preceding chapters, Micro-economic theories of the use of space were reviewed, followed by spatial interaction and entropy maximising models, and finally random utility theory was described. This chapter concludes the general theoretical framework by describing another important development from macro-economics: the input–output model. This introduces a new dimension to the problem, that of production and its relation to the urban and regional structure.

In very broad terms, the first generation of input–output models were intended as nationwide global economic accounting frameworks; the second generation of i–o models attempted a regional disaggregation; a third generation, currently in progress, attempts a more general description of the structure of a nation, and consequently these models have been defined as social accounting models. The intention of this chapter is to derive a general model to represent a spatial-economic system at any scale, capitalising on the teachings of random utility theory. Since spatial aspects become so closely linked to the economic accounting ones, the results have been termed spatial accounting models.

Keynes' theory of production and the multiplier is briefly reviewed as a starting point for later developments of regional theories such as the theory of regional rent and the study of the economic base of a region. Then the elements of the input–output model are presented and its regional disaggregation. At this point, the presentation diverts from the main stream by re-introducing random utility concepts, with related decision chains, variable costs, elasticities and hierarchies.

The theory of production and the multiplier

Keynes (1936) begins by introducing the principle of effective demand, whereby the process of production is mainly determined by consumption. According to this principle, producers determine the level of their activity according to their estimates of future demand.