The Metamorphic Point
This article presents a radical deconstruction of the static ontology of the point inherited from the Euclidean tradition, through a comparative analysis of the thought of mathematician Gilles Châtelet and visual artist Paul Klee. Against the notion of the point as an inert, partless entity, both th...
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| Publicado no: | URI:https://journals.openedition.org/ejpap, |
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| Autor principal: | |
| Formato: | Article ou chapitre numérique |
| Idioma: | Anglais |
| Publicado em: |
European Journal of Pragmatism and American Philosophy
2026
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| Assuntos: | |
| Acesso em linha: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| Resumo: | This article presents a radical deconstruction of the static ontology of the point inherited from the Euclidean tradition, through a comparative analysis of the thought of mathematician Gilles Châtelet and visual artist Paul Klee. Against the notion of the point as an inert, partless entity, both thinkers conceive of it as a dynamic agent and virtual germ: for Klee, it is an “Agens” imbued with an internal Spannungswille (will to tension), while for Châtelet, it is an “operator” resulting from processes of contraction or dilation. The article identifies three fundamental parallels between them: the point as a site of internal tension and mutual attraction, the line as an oriented arrow actualizing its virtual direction, and the point as a germinal centre of irradiation. The synthesis culminates in Châtelet’s later technical elaborations, where the point becomes, algebraically, a quotient of polynomials (a “germinal matrix”) and, topologically, a becoming-hole. Through gestures of extraction and circumvolution, the point transforms into a relational zone. The diagram thus emerges as the operative field where the point’s virtuality, gesturality, and metamorphic nature are enacted, offering a fertile alternative ontology for both mathematical and artistic practice. |
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