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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 |
MARC
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| 100 | 1 | |a Bailly, Francis. | |
| 245 | 1 | 0 | |a Mathematics and the natural sciences : |b the physical singularity of life / |c Francis Bailly, Giuseppe Longo. |
| 260 | |a London : |b Imperial College Press, |c ©2011. | ||
| 300 | |a 1 online resource (xvii, 318 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Advances in computer science and engineering: texts ; |v v. 7 | |
| 504 | |a Includes bibliographical references (pages 299-312) and index. | ||
| 505 | 0 | 0 | |g Machine generated contents note: |g 1. |t Mathematical Concepts and Physical Objects -- |g 1.1. |t On the Foundations of Mathematics. A First Inquiry -- |g 1.1.1. |t Terminological issues? -- |g 1.1.2. |t The genesis of mathematical structures and of their relationships -- a few conceptual analogies -- |g 1.1.3. |t Formalization, calculation, meaning, subjectivity -- |g 1.1.4. |t Between cognition and history: Towards new structures of intelligibility -- |g 1.2. |t Mathematical Concepts: A Constructive Approach -- |g 1.2.1. |t Genealogies of concepts -- |g 1.2.2. |t The "transcendent" in physics and in mathematics -- |g 1.2.3. |t Laws, structures, and foundations -- |g 1.2.4. |t Subject and objectivity -- |g 1.2.5. |t From intuitionism to a renewed constructivism -- |g 1.3. |t Regarding Mathematical Concepts and Physical Objects -- |g 1.3.1. |t "Friction" and the determination of physical objects -- |g 1.3.2. |t The absolute and the relative in mathematics and in physics -- |g 1.3.3. |t On the two functions of language within the process of objectification and the construction of mathematical models in physics. |
| 505 | 0 | 0 | |g 1.3.4. |t From the relativity to reference universes to that of these universes themselves as generators of physical invariances -- |g 1.3.5. |t Physical causality and mathematical symmetry -- |g 1.3.6. |t Towards the "cognitive subject" -- |g 2. |t Incompleteness and Indetermination in Mathematics and Physics -- |g 2.1. |t The Cognitive Foundations of Mathematics: Human Gestures in Proofs and Mathematical Incompleteness of Formalisms -- |g 2.1.1. |t Introduction -- |g 2.1.2. |t Machines, body, and rationality -- |g 2.1.3. |t Ameba, motivity, and signification -- |g 2.1.4. |t The abstract and the symbolic; the rigor -- |g 2.1.5. |t From the Platonist response to action and gesture -- |g 2.1.6. |t Intuition, gestures, and the numeric line -- |g 2.1.7. |t Mathematical incompleteness of formalisms -- |g 2.1.8. |t Iterations and closures on the horizon -- |g 2.1.9. |t Intuition -- |g 2.1.10. |t Body gestures and the "cogito" -- |g 2.1.11. |t Summary and conclusion of part 2.1 -- |g 2.2. |t Incompleteness, Uncertainty, and Infinity: Differences and Similarities Between Physics and Mathematics -- |g 2.2.1. |t Completeness/incompleteness in physical theories -- |g 2.2.2. |t Finite/infinite in mathematics and physics. |
| 505 | 0 | 0 | |g 3. |t Space and Time from Physics to Biology -- |g 3.1. |t An Introduction to the Space and Time of Modern Physics -- |g 3.1.1. |t Taking leave of Laplace -- |g 3.1.2. |t Three types of physical theory: Relativity, quantum physics, and the theory of critical transitions in dynamical systems -- |g 3.1.3. |t Some epistemological remarks -- |g 3.2. |t Towards Biology: Space and Time in the "Field" of Living Systems -- |g 3.2.1. |t The time of life -- |g 3.2.2. |t More on Biological time -- |g 3.2.3. |t Dynamics of the self-constitution of living systems -- |g 3.2.4. |t Morphogenesis -- |g 3.2.5. |t Information and geometric structure -- |g 3.3. |t Spatiotemporal Determination and Biology -- |g 3.3.1. |t Biological aspects -- |g 3.3.2. |t Space: Laws of scaling and of critical behavior. The geometry of biological functions -- |g 3.3.3. |t Three types of time -- |g 3.3.4. |t Epistemological and mathematical aspects -- |g 3.3.5. |t Some philosophy, to conclude -- |g 4. |t Invariances, Symmetries, and Symmetry Breakings -- |g 4.1. |t A Major Structuring Principle of Physics: The Geodesic Principle -- |g 4.1.1. |t The physico-mathematical conceptual frame. |
| 505 | 0 | 0 | |g 4.2. |t On the Role of Symmetries and of Their Breakings: From Description to Determination -- |g 4.2.1. |t Symmetries, symmetry breaking, and logic -- |g 4.2.2. |t Symmetries, symmetry breaking, and determination of physical reality -- |g 4.3. |t Invariance and Variability in Biology -- |g 4.3.1. |t A few abstract invariances in biology: Homology, analogy, allometry -- |g 4.3.2. |t Comments regarding the relationships between invariances and the conditions of possibility for life -- |g 4.4. |t About the Possible Recategorizations of the Notions of Space and Time under the Current State of the Natural Sciences -- |g 5. |t Causes and Symmetries: The Continuum and the Discrete in Mathematical Modeling -- |g 5.1. |t Causal Structures and Symmetries, in Physics -- |g 5.1.1. |t Symmetries as starting point for intelligibility -- |g 5.1.2. |t Time and causality in physics -- |g 5.1.3. |t Symmetry breaking and fabrics of interaction -- |g 5.2. |t From the Continuum to the Discrete -- |g 5.2.1. |t Computer science and the philosophy of arithmetic -- |g 5.2.2. |t Laplace, digital rounding, and iteration. |
| 505 | 0 | 0 | |g 5.2.3. |t Iteration and prediction -- |g 5.2.4. |t Rules and the algorithm -- |g 5.3. |t Causalities in Biology -- |g 5.3.1. |t Basic representation -- |g 5.3.2. |t On contingent finality -- |g 5.3.3. |t "Causal" dynamics: Development, maturity, aging, death -- |g 5.3.4. |t Invariants of causal reduction in biology -- |g 5.3.5. |t A few comments and comparisons with physics -- |g 5.4. |t Synthesis and Conclusion -- |g 6. |t Extended Criticality: The Physical Singularity of Life Phenomena -- |g 6.1. |t On Singularities and Criticality in Physics -- |g 6.1.1. |t From gas to crystal -- |g 6.1.2. |t From the local to the global -- |g 6.1.3. |t Phase transitions in self-organized criticality and "order for free" -- |g 6.2. |t Life as "Extended Critical Situation" -- |g 6.2.1. |t Extended critical situations: General approaches -- |g 6.2.2. |t The extended critical situation: A few precisions and complements -- |g 6.2.3. |t More on the relations to autopoiesis -- |g 6.2.4. |t Summary of the characteristics of the extended critical situation -- |g 6.3. |t Integration, Regulation, and Causal Regimes -- |g 6.4. |t Phase Spaces and Their Trajectories. |
| 505 | 0 | 0 | |g 6.5. |t Another View on Stability and Variability -- |g 6.5.1. |t Biolons as attractors and individual trajectories -- |g 7. |t Randomness and Determination in the Interplay between the Continuum and the Discrete -- |g 7.1. |t Deterministic Chaos and Mathematical Randomness: The Case of Classical Physics -- |g 7.2. |t The Objectivity of Quantum Randomness -- |g 7.2.1. |t Separability vs non-separability -- |g 7.2.2. |t Possible objections -- |g 7.2.3. |t Final remarks on quantum randomness -- |g 7.3. |t Determination and Continuous Mathematics -- |g 7.4. |t Conclusion: Towards Computability -- |g 8. |t Conclusion: Unification and Separation of Theories, or the Importance of Negative Results -- |g 8.1. |t Foundational Analysis and Knowledge Construction -- |g 8.2. |t The Importance of Negative Results -- |g 8.2.1. |t Changing frames -- |g 8.3. |t Vitalism and Non-Realism -- |g 8.4. |t End and Opening. |
| 588 | 0 | |a Print version record. | |
| 520 | |a 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 symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics guides most of the work. The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations. Since biology is particularly complex and not as well understood at a theoretical level, we propose a "unification by concepts" which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are "big bags of molecules". The main question though is to understand which "theory" can help better understand these bags of molecules. They are, indeed, rather "singular", from the physical point of view. Technically, we express this singularity through the concept of "extended criticality", which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level. | ||
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| 700 | 1 | |a Longo, G. |q (Giuseppe) | |
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| 830 | 0 | |a Advances in computer science and engineering. |p Texts ; |v v. 7. | |
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