CATASTROPHE TEACHER

Une introduction à la Théorie des catastrophes pour les expérimentateurs


Qu'est-ce qu'un modèle mathématique?

Nous voulons faire un modèle, c'est-à-dire proposer une analogie... Selon le schéma proposé par R. Thom, nous sommes en train de regarder un être enigmatique et nous nous posons des questions à son propos ; ces questions doivent être traduites à l'aide d'une analogie pour pouvoir être posées au modèle. Ensuite on fait fonctionner le modèle qui fournit une réponse, laquelle est traduite par l'analogie fonctionnant en retour. Cette réponse traduite sera comparée avec les résultats expérimentaux.

Cette figure est reprise d'après Thom (Thom R. - Modélisation et scientificité in Delattre P. & Tellier M. - Elaboration et justification des modèles. Maloine S.A. , Paris, 1979).


Aller à: "Cette applet comme une boîte noire: comment interpréter son comportement ?"

Aller à: "La fronce comme modèle du comportement de l'applet"


BLACK BOX METHOD (from Web Dictionary of Cybernetics and Systems)

A strategy for investigating a complex object without knowledge or assumptions about its internal make-up, STRUCTURE or parts. The method aims at either a formal description of the TRANSFORMATION RULEs linking INPUTs and OUTPUTs or the CONSTRUCTion of a MODEL exhibiting a BEHAVIOR that approximates what is observable from the outside of the "black box". Initially, the method codified the experiments an engineer would have to perform with a sealed piece of equipment in order to deduce what it does or how it could have been wired. The method is quite general, however. E.g., the linguist who can not utilize available knowledge of brain tissue for understanding linguistic production find himself in a similar situation. The resulting model of a black box is considered "grey" inasmuch as its STRUCTURE is known, save for the knowledge of the internal make-up of that model's parts. The black box method applies to an extreme case. In practice an investigator may find and should utilize clues to the internal processes by non-experimental means. So, the engineer may conclude from the absence of a wire that a particular switch has nothing to do with a certain component just as the linguist may obtain insights about the use of language by being competent in that language himself. The ISOMORPHISM between the black box and its model, which the method aims to establish, does not imply structural correspondences between the two. One may be a mechanical device, a chemical process or human organ, the other may be a mathematical formula, an ALGORITHM or electronic piece of equipment. However, the ORGANIZATION of such a model often leads to fruitful hypotheses concerning the structure of the black box. (Krippendorff)



Retourner à: "Nous allons maintenant considérer l'applet comme une "boîte noire"..."


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