Search results

Ce texte présente le contexte politico-symbolique qui a imprégné la jeunesse de l'auteur au Liban et qui a vu naître sa passion des mathématiques. Il décrit la révolution de ses modes de représentations provoquée par l'éclatement de la guerre civile libanaise, et cela, au contact du milieu intellectuel et politique français. Cela donna corps à son engagement dans un domaine particulier des mathématiques, la « théorie des jeux ». Il introduit brièvement le cadre conceptuel de cette théorie en vue de l'analyse du conflit, et la façon dont il fut étendu pour y inclure les configurations politiques instables. Il livre enfin des lignes directrices pour une modélisation applicable à la condition particulière du Liban et à la récurrence de ses crises structurelles.

We view political activity as an interaction between forces seeking to achieve a political agenda. The viability of a situation depends on the compatibility of such agendas. However even in a conflictual situation a compromise may be possible. Mathematically a political structure is modeled as a simplicial complex and a viable configuration as a simplex. A represented compromise is a viable configuration obtained by the withdrawal of some agents in favor of some friendly representatives. A delegated compromise is a sophisticated version of a compromise obtained by the iteration of the withdrawal process. Existence of such solutions depends on the discrete topology of the simplicial complex. In particular we prove that the existence of a delegated compromise is equivalent to the strong contractibility of the simplicial complex.

We view political activity as an interaction between forces seeking to achieve a political agenda. The viability of a situation depends on the compatibility of such agendas. However even in a conflictual situation a compromise may be possible. Mathematically a political structure is modeled as a simplicial complex and a viable configuration as a simplex. A represented compromise is a viable configuration obtained by the withdrawal of some agents in favor of some friendly representatives. A delegated compromise is a sophisticated version of a compromise obtained by the iteration of the withdrawal process. Existence of such solutions depends on the discrete topology of the simplicial complex. In particular we prove that the existence of a delegated compromise is equivalent to the strong contractibility of the simplicial complex.

We view political activity as an interaction between forces seeking to achieve a political agenda. The viability of a situation depends on the compatibility of such agendas. However even in a conflictual situation a compromise may be possible. Mathematically a political structure is modeled as a simplicial complex and a viable configuration as a simplex. A represented compromise is a viable configuration obtained by the withdrawal of some agents in favor of some friendly representatives. A delegated compromise is a sophisticated version of a compromise obtained by the iteration of the withdrawal process. Existence of such solutions depends on the discrete topology of the simplicial complex. In particular we prove that the existence of a delegated compromise is equivalent to the strong contractibility of the simplicial complex.