| Description |
1 online resource (607 p.) |
| Contents |
880-01 Intro -- Introduction -- Topological Visualisation, or How to Apprehend the Invisible -- Feynman Diagrams: A New Way Forward in Theoretical Physics -- Diagrammatics and Invariants in Knot and Braid Theory -- Philosophical and Scientific Implications -- Diagrammatics and Category Theory -- A French Singularity in Epistemological Field: Gilles Châtelet -- Phenomenology of Space (and Time) and Diagrammatic Epistemology -- Towards a "Diagrammatic Critique of Aesthetics" -- Acknowledgments -- Contents -- Part I Logic, Forms and Diagrams -- The Semiotics of Laws of Form -- Introduction |
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880-01/(S La catégorification du polynôme de Jones -- La méthode de catégorification -- La théorie topologique quantique des champs -- Diagrammes et méthode -- Référenes -- Part II Geometrical Spaces and Topological Knots, Old and New -- Which Came First, the Circle or the WheelFrom Idea (δεα) to Concrete Construction -- Introduction -- Geometric Ideas and their Diagrams -- Digital Fabrication -- Geometry in Higher Dimension -- Bibliography -- Sitography -- The Classical Style in Contemporary Geometry: Views from a Person Working in the Field -- Introduction -- Fragments of Basic Algebraic Geometry |
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Finding Distinction -- Finding Primary Arithmetic -- Finding Logic -- Finding Mathematics -- The Arctic Essay -- Epilogue -- References -- Can We "Show" the Correctness of Reasoning? On the Role of Diagrammatic Spatialization in Logical Justification -- Introduction -- The Eulerian Thesis: The Logical Correctness of the Diagrams "Jumps to the Eyes" -- Determining the Logical Framework of Our Research -- The Late Emergence of "Analytical" Logic Diagrams in a Pedagogical Context -- First Section: The Cognitive Advantages of the Diagrammatic Method |
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Second Section: Can Diagrams Be Given the Task of Validating Reasoning? -- Third Section: Can a Diagram Show ("donner à voir") the Nature of a Proposition or the Correctness of a Reasoning? -- Back to Euler -- Showing the Nature of a Proposition -- Showing the Correctness of a Reasoning -- Some Remarks on the Relationship Between the Principles of Logic and Spatiality in Syllogistic (From Aristotle to Hamilton) -- Conclusion: Summary and Discussion -- References -- Articles and Monographs -- Proceedings of International Colloquia -- Catégorification et méthode -- Le polynôme de Jones |
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Sterographic Projections in Dimension 1 and 2 (Figs. 4 and 5) -- Origins of Birational Geometry and Classification -- Cremona Transformations (Fig. 6) -- de Jonquiéres Transformations (Fig. 8) -- Classical Problems and Rational Parametrizations: Curves and Surfaces -- Classical Problems and Rational Parametrizations: Cubics -- The Classical Turn in Algebraic Geometry -- References -- Knots, Diagrams and Kids' Shoelaces. On Space and their Forms -- Introductive Remarks: Shoelaces, Knots, and the Intuition of Space -- Exploring and Visualizing 3-manifols and the Importance of Topology |
| Summary |
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 |
| Notes |
Description based upon print version of record |
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Equivalence of Images and of Forms: Manifolds, Knots and Diagrams |
| Subject |
Science -- Philosophy.
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Phenomenology.
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phenomenology.
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Ciencia -- Filosofía
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Fenomenología
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Phenomenology
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Science -- Philosophy
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Visualització de la informació.
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Diagrames.
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Filosofia de la ciència.
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Fenomenologia.
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| Genre/Form |
Llibres electrònics.
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| Form |
Electronic book
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| Author |
Boi, Luciano
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Lobo, Carlos
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| ISBN |
9783030831257 |
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3030831256 |
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