When Form Becomes Substance: Power of Gestures, Diagrammatical Intuition and Phenomenology of Space

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
		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
		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
		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 Wheel? From 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
			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
		Equivalence of Images and of Forms: Manifolds, Knots and Diagrams
		Embeddings and Isotopies
		Mathematical Propaedeutic for the Understanding of Knots
		Knots and Links: Equivalence, Invariants and the Knot Complement
		The Alexander and Jones Polynomials
		Crossing Changes of Knots
		Back to Classical Invariants of Knots and Links
		Historical Note on Knots and their Diagrams
		Equivalence of Knots and Links
		From the Alexander Polynomial to Seifert Surfaces for Knots
		Reidemeister Moves and Classical Knot Invariants
		Dehn Surgery of Knots and his Work on Knot Theory and 3-dimensional Manifolds
		The Fundamental Group of Knots and Links
		Invariants of 3-manifolds and Hyperbolic Knots
		The Importance of the Linking Number in Molecular Biology
		Geometrical and Topological Properties of the Double Helix and Supercoiling
		Knots, Links, and Topological Quantum Field Theories: An Overview
		Knots and Dynamics Systems
		The Energy of Knots
		References
Part III Diagrams, Graphs and Representation
	Diagrammes planaires qui représentent des objets de dimension 1, 2, 3 et 4
		Problème de classification
		Approche combinatoire
		Noeuds (dimension 1)
		Surfaces (dimension 2)
		Codage planaire des surfaces
		Variétés de dimension 3
		Polyèdres spéciaux
		Polyèdres spéciaux épaississable
		Reconstruction
		Codage graphique
		Mouvements locaux
		Calcul graphique
		Variétés de dimension 4
		Codage graphique des ombres
		References
	From Singularities to Graphs
		Introduction
		What Is the Meaning of Such Graphs?
		What Does it Mean to Resolve the Singularities of an Algebraic Surface?
		Representations of Surface Singularities Around 1900
		Du Val's Singularities, Coxeter's Diagrams and the Birth of Dual Graphs
		Mumford's Paper on the Links of Surface Singularities
		Waldhausen's Graph Manifolds and Neumann's Calculus with Graphs
		Conclusion
		References
Part IV Diagrams, Physical Forces and Path Integrals
	Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections
		Introduction
		The Case of Quantum Fields
		Divergences and Diagrams
		Some Conclusions, Philosophical Remarks and Reflections
		References
	Some Remarks on Penrose Diagrams
		Introduction
		Reflexions on the Different Notions of Dimensions
		The Notion of a Function
		A Second Kind of Diagram
		The Introduction of Infinity
		Some Complements to Conformal Geometry and General Relativity
		Cosmology and Conformal Diagrams
		Philosophical Comments
		Final Complements
		References
Part V Phenomenology in and of Mathematical Diagrams
	Phénoménologie, représentations, combinatoire
		Représentations géométriques: une approche classique
		Représentations géométriques: l'approche mathématique
		Représentations géométriques: l'approche phénoménologique
		Partitions non croisées
		Représentations graphiques
		De l'usage des représentations diagrammatiques.
		De la portée des représentations diagrammatiques
		Références
	Husserl, Intentionality and Mathematics: Geometry and Category Theory
		Intentionality and Space
		The Idea of a Mannigfaltigkeitslehre
		Space and Time in Phenomenology
		Issues of Foundation in Phenomenology through Category Theory
		References
	Diagrams of Time and Syntaxes of Consciousness: A Contribution to the Phenomenology of Visualization
		The Time Diagram Has Been Touched Upon (Varela, Weyl)
			Phenomenological Elucidation of the Subjective Resources of the Mathematical Construction of Linear Time
			The Specious Time of Neurophenomenology
		Phenomenology of the Use of Diagrams in Science Including Phenomenology
			Diagrammatic Underpinnings of Scientific Knowledge
			The Use of Diagrams in Phenomenology
			A Second Example: Intersubjective Constitution and Relativisation of the Original Coordinate System
		Symbolisation and Formal Writing in Phenomenology
			Symbolisation and Diagrammatisation of Intentional Analysis
			Intentionality as a System of Modification and Its Symbolism
			Analysis of the System of Continuous, i.e. Temporal Changes in 1913
			An Example of Moving from an Analysis to a Mathematical Model
		Phenomenology and Diagrammatic of Lived Time
			The Dialectic of Phenomenological Reflection, Symbolisation and Diagram Construction Between 1905 and 1918
				Diagrams of Retentions and Drafts of a Chronometry
				From Infinitesimal Analysis to Complex Analysis of Phenomenological Time
			Gaps in the 1905 Diagrams
			An Important Gap in the Initial Retention Diagram: The Meaning of the Zero
			Diagrams of the on-in-the-Other (or Nesting) and Intertwining of Retentions and Protentions
			Diagrams in Reflection
		Conclusion: Perspectives for a General Theory of Possible Times
		References
Part VI Diagrams, Gestures and Subjectivity
	A Topological Analysis of Space-Time-Consciousness: Self, Self-Self, Self-Other
		Knot Logic: Linking as Mutuality
		Belongingness: Not-I, Knot-I
		Self-Mutuality as Mutuality: Mutuality as Self-Mutuality
		Plurality of Now's
		Music
		Kauffman's Universe and HYK's Self
		References
	Gestes, diagrammes et subjectivité
		Un exemple de diagramme social (et ses gestes)
		Prendre sur soi, le 0-milieu
		Rapport à soi, la verticale
		Tourner autour de soi, le trou
		Le virtuel-Temps événementiel
	Some Prolegomena for a Contemporary “Critique of Imagination”
		Six Guiding Theses
		Imagination: Common Sense Notions
		Imagination: Philosophic Insights from Leibniz, Hume, Kant and Husserl
		Imagination: Hints from Neuroscience
		Bibliography
	Le langage diagrammatique au-delà de la différencephénoménologique
		Introduction
		La première forme canonique de notre rapport au monde : la signifiance
		De la signifiance au calcul : brève histoire de la différence phénoménologique
		Conclusion
Part VII Diagrams: from Mathematics to Aesthetics
	Ars diagrammaticae
		Le phénomène de compactification
		Du diagramme comme preuve par l'image
			Quelques précisions maintenant concernant la désintrication des concepts d'Image, de Figure & de Diagramme.
	Grid Diagram: Deleuze's Aesthetics Applied to Maggs's Photographs
		Grid as Diagram in Portraits
		Faciality of Portraits
		Grid and Virtuality
		Dada Diagrams/Dada Portraits
		Routes of Reference: Technical Diagrams as Art
		Nomenclature as Poetic Potential
		Conclusion
	Les jeux de l'unilatère
		L'invariant, Persée (8 = 8). 8, par exemple
		A Plat
	Le diagramme à l'œuvre
Part VIII Poetics and Politics of Diagrams
	Diagrammes du possible : de l'espace des phases au sujet politique
		L'espace des phases: exemple des diagrammes qui ne sont pas représentation
		Faute de programmes on trace des diagrammes
		La crise du sujet politique
	La dimension diagrammatique de l'écriture littéraire : un formalisme dynamique inscrit dans la sensorialité du langage
		DE DIAGRAMME EN DIAGRAMME
		LA DIMENSION DIAGRAMMATIQUE DE L'ECRITURE LITTERAIRE
		SPÉCIFICITÉ DE L'ÉCRITURE LITTÉRAIRE
			Une autre langue dans la langue
			Iconicité et abstraction
			Diagrammatisation de l'écriture ; « sensorialisation » d'une nouvelle logique
			Avec Charles Baudelaire et Emily Dickinson