When Form Becomes Substance

This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams.

Diagrams play a fundamental role in the mathematical visualization and philosophical analysis of forms in space. Some of the most interesting and profound recent developments in contemporary sciences, whether in topology, geometry, dynamic systems theory, quantum field theory or string theory, have been made possible by the introduction of new types of diagrams, which, in addition to their essential role in the discovery of new classes of spaces and phenomena, have contributed to enriching and clarifying the meaning of the operations, structures and properties that are at the heart of these spaces and phenomena.

The volume gives a closer look at the scope and the nature of diagrams as constituents of mathematical and physical thought, their function in contemporary artistic work, and appraise, in particular, the actual importance of the diagrams of knots, of braids, of fields, of interaction, of strings in topology and geometry, in quantum physics and in cosmology, but also in theory of perception, in plastic arts and in philosophy.

The editors carefully curated this volume to be an inspiration to students and researchers in philosophy, phenomenology, mathematics and the sciences, as well as artists, musicians and the general interested audience.

Luciano Boi is a teacher-researcher at the École des Hautes Études en Sciences Sociales, at the Centre de mathématiques and program director at CiPh (Paris). His research interests include various aspects of mathematics and its foundations, theoretical biology, phenomenology of perception and philosophy of science. He has taught in several universities and research institutes abroad. He is a member of the scientific board of various international scientific journals. His work has earned him a research fellowship from the Von Humboldt Foundation and an award from the Guggenheim Foundation. Luciano Boi is the author and editor of numerous books and research articles.

Carlos Lobo is a phenomenologist associated to the Husserl Archives of Paris. After a first monograph on the methodology of transcendental phenomenology, he has published several contributions on phenomenological issues such as intersubjectivity, temporality, individuation, axiology, etc. showing their epistemological importance for the critical understanding and clarification of major current issues in formal logic, probability theory, physics, in ethics and aesthetics. His latest books are Weyl and the problem of Space, From mathematics to philosophy, Springer, 2019 and a translation and introduction to Weyl¿s Philosophie des mathématiques et des sciences de la nature, MétisPresses, Geneva, 2017.

01 Logic, forms and diagrams.- 02 Geometrical spaces and topological knots, old and new.- 03 Diagrams, Graphs and Representation.- 04 Diagrams, physical forces and paths integrals.- 05 Phenomenology in and of Mathematical Diagrams.- 06 Diagrams, Gestures and Subjectivity.- 07 Diagrams, from Mathematics to Aesthetics.- 08 Poetics and politics of diagrams.