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Mathematics and the natural sciences : the physical singularity of life /
This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of "order" and symm...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Imperial College Press,
©2011.
|
| Colección: | Advances in computer science and engineering. Texts ;
v. 7. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.