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" Mathematics and the natural sciences : "
Francis Bailly, Giuseppe Longo
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BL
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| Record Number
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692889
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b515078
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| Main Entry
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Bailly, Francis
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| Title & Author
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Mathematics and the natural sciences : : the physical singularity of life /\ Francis Bailly, Giuseppe Longo
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| Publication Statement
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London :: Imperial College Press ;Hackensack, N.J. :: distributed by World Scientific,, 2010
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xi, 318 p. ;; 24 cm
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| ISBN
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1848166931
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: 9781848166936
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| Bibliographies/Indexes
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Includes bibliographical references (p. 299-312) and index
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| Contents
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Machine generated contents note: 1.Mathematical Concepts and Physical Objects -- 1.1.On the Foundations of Mathematics. A First Inquiry -- 1.1.1.Terminological issues? -- 1.1.2.The genesis of mathematical structures and of their relationships -- a few conceptual analogies -- 1.1.3.Formalization, calculation, meaning, subjectivity -- 1.1.4.Between cognition and history: Towards new structures of intelligibility -- 1.2.Mathematical Concepts: A Constructive Approach -- 1.2.1.Genealogies of concepts -- 1.2.2.The "transcendent" in physics and in mathematics -- 1.2.3.Laws, structures, and foundations -- 1.2.4.Subject and objectivity -- 1.2.5.From intuitionism to a renewed constructivism -- 1.3.Regarding Mathematical Concepts and Physical Objects -- 1.3.1."Friction" and the determination of physical objects -- 1.3.2.The absolute and the relative in mathematics and in physics -- 1.3.3.On the two functions of language within the process of objectification and the construction of mathematical models in physics -- 1.3.4.From the relativity to reference universes to that of these universes themselves as generators of physical invariances -- 1.3.5.Physical causality and mathematical symmetry -- 1.3.6.Towards the "cognitive subject" -- 2.Incompleteness and Indetermination in Mathematics and Physics -- 2.1.The Cognitive Foundations of Mathematics: Human Gestures in Proofs and Mathematical Incompleteness of Formalisms -- 2.1.1.Introduction -- 2.1.2.Machines, body, and rationality -- 2.1.3.Ameba, motivity, and signification -- 2.1.4.The abstract and the symbolic; the rigor -- 2.1.5.From the Platonist response to action and gesture -- 2.1.6.Intuition, gestures, and the numeric line -- 2.1.7.Mathematical incompleteness of formalisms -- 2.1.8.Iterations and closures on the horizon -- 2.1.9.Intuition -- 2.1.10.Body gestures and the "cogito" -- 2.1.11.Summary and conclusion of part 2.1 -- 2.2.Incompleteness, Uncertainty, and Infinity: Differences and Similarities Between Physics and Mathematics -- 2.2.1.Completeness/incompleteness in physical theories -- 2.2.2.Finite/infinite in mathematics and physics -- 3.Space and Time from Physics to Biology -- 3.1.An Introduction to the Space and Time of Modern Physics -- 3.1.1.Taking leave of Laplace -- 3.1.2.Three types of physical theory: Relativity, quantum physics, and the theory of critical transitions in dynamical systems -- 3.1.3.Some epistemological remarks -- 3.2.Towards Biology: Space and Time in the "Field" of Living Systems -- 3.2.1.The time of life -- 3.2.2.More on Biological time -- 3.2.3.Dynamics of the self-constitution of living systems -- 3.2.4.Morphogenesis -- 3.2.5.Information and geometric structure -- 3.3.Spatiotemporal Determination and Biology -- 3.3.1.Biological aspects -- 3.3.2.Space: Laws of scaling and of critical behavior. The geometry of biological functions -- 3.3.3.Three types of time -- 3.3.4.Epistemological and mathematical aspects -- 3.3.5.Some philosophy, to conclude -- 4.Invariances, Symmetries, and Symmetry Breakings -- 4.1.A Major Structuring Principle of Physics: The Geodesic Principle -- 4.1.1.The physico-mathematical conceptual frame -- 4.2.On the Role of Symmetries and of Their Breakings: From Description to Determination -- 4.2.1.Symmetries, symmetry breaking, and logic -- 4.2.2.Symmetries, symmetry breaking, and determination of physical reality -- 4.3.Invariance and Variability in Biology -- 4.3.1.A few abstract invariances in biology: Homology, analogy, allometry -- 4.3.2.Comments regarding the relationships between invariances and the conditions of possibility for life -- 4.4.About the Possible Recategorizations of the Notions of Space and Time under the Current State of the Natural Sciences -- 5.Causes and Symmetries: The Continuum and the Discrete in Mathematical Modeling -- 5.1.Causal Structures and Symmetries, in Physics -- 5.1.1.Symmetries as starting point for intelligibility -- 5.1.2.Time and causality in physics -- 5.1.3.Symmetry breaking and fabrics of interaction -- 5.2.From the Continuum to the Discrete -- 5.2.1.Computer science and the philosophy of arithmetic -- 5.2.2.Laplace, digital rounding, and iteration -- 5.2.3.Iteration and prediction -- 5.2.4.Rules and the algorithm -- 5.3.Causalities in Biology -- 5.3.1.Basic representation -- 5.3.2.On contingent finality -- 5.3.3."Causal" dynamics: Development, maturity, aging, death -- 5.3.4.Invariants of causal reduction in biology -- 5.3.5.A few comments and comparisons with physics -- 5.4.Synthesis and Conclusion -- 6.Extended Criticality: The Physical Singularity of Life Phenomena -- 6.1.On Singularities and Criticality in Physics -- 6.1.1.From gas to crystal -- 6.1.2.From the local to the global -- 6.1.3.Phase transitions in self-organized criticality and "order for free" -- 6.2.Life as "Extended Critical Situation" -- 6.2.1.Extended critical situations: General approaches -- 6.2.2.The extended critical situation: A few precisions and complements -- 6.2.3.More on the relations to autopoiesis -- 6.2.4.Summary of the characteristics of the extended critical situation -- 6.3.Integration, Regulation, and Causal Regimes -- 6.4.Phase Spaces and Their Trajectories -- 6.5.Another View on Stability and Variability -- 6.5.1.Biolons as attractors and individual trajectories -- 7.Randomness and Determination in the Interplay between the Continuum and the Discrete -- 7.1.Deterministic Chaos and Mathematical Randomness: The Case of Classical Physics -- 7.2.The Objectivity of Quantum Randomness -- 7.2.1.Separability vs non-separability -- 7.2.2.Possible objections -- 7.2.3.Final remarks on quantum randomness -- 7.3.Determination and Continuous Mathematics -- 7.4.Conclusion: Towards Computability -- 8.Conclusion: Unification and Separation of Theories, or the Importance of Negative Results -- 8.1.Foundational Analysis and Knowledge Construction -- 8.2.The Importance of Negative Results -- 8.2.1.Changing frames -- 8.3.Vitalism and Non-Realism -- 8.4.End and Opening
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Biomathematics
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Mathematical models
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Mathematics-- Philosophy
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Physics-- Philosophy
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Space and time
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| Added Entry
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Longo, G., (Giuseppe)
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