From modelling to experiment

Abstract

Mathematical models applied to urban and regional planning have been widely developed during the sixties. Since that time the scientific and technologic developments have deeply transformed the field of spatial modelling. There has been a reaction against the idea that reality could be reduced to deterministic models. The paradigms of complexity, chaos, self-organisation, fractal geometry have made obvious the unpredictability of complex socio-economic systems. At the same time the progress of computation has led to the substitution of simulation methods to analytic solutions of mathematical models. In such a context, models are loosing in generality and reproducibility what they earn in adaptation to empirical situations. An important challenge is also to confirm the pertinence and specificity of the geographical approach. In that respect the spatial analysis programs must prove the evidence of a common methodology dealing either with physical or human and economic domain. We are working, for instance, on cellular automata programs applied to the historical evolution of an urban space and also to the run-off process in an elementary basin. The spatial structure of the models may be slightly different: rectangular or hexagonal tessellations in the “Human Geography” program, TIN structure, closer to the physical reality, in the other. The relations between the cells may also differ: they are often defined by a distance matrix for the socio-economic models, but a contiguity matrix is of course needed for the streaming process. But, beyond these technical differences, it appears that the geographical programs are developed on a macro-level, that is on aggregate statistical units. The elementary particle is always (or should be for a geographer...) a material, spatial unit, unlike the drop of water of the hydrologists, or the individual “agents” of the sociologists' multi-agents systems. The difference between the micro and macro level is not a question of scale, but a difference of logic. The simulation approach has a requisite, which is a need of systematic validation by a permanent comparison with the actual situation, but the objective is not prediction. The scientific concern is, before all, a precise understanding of the past and recent evolutions, more than a forecasting, which escapes to the specific field of scientific research. What is scientific is what can be measured. The possible prediction may rely on the scientific research, but belongs strictly to the domain of intellectual and personal thinking.