LEADER 05804nam 2200709 a 450 001 9910826406603321 005 20240516111037.0 010 $a1-283-23454-8 010 $a9786613234544 010 $a1-84816-694-X 035 $a(CKB)3400000000016054 035 $a(EBL)840535 035 $a(OCoLC)858227748 035 $a(SSID)ssj0000538992 035 $a(PQKBManifestationID)12177382 035 $a(PQKBTitleCode)TC0000538992 035 $a(PQKBWorkID)10569420 035 $a(PQKB)11749772 035 $a(MiAaPQ)EBC840535 035 $a(WSP)0000P774 035 $a(Au-PeEL)EBL840535 035 $a(CaPaEBR)ebr10493543 035 $a(CaONFJC)MIL323454 035 $a(EXLCZ)993400000000016054 100 $a20110624d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematics and the natural sciences $ethe physical singularity of life /$fFrancis Bailly, Giuseppe Longo 205 $a1st ed. 210 $aLondon $cImperial College Press ;$aHackensack, N.J. $cDistributed by World Scientific Pub. Co. Pte. Ltd.$dc2011 215 $a1 online resource (337 p.) 225 1 $aAdvances in computer science and engineering: Texts ;$vv. 7 300 $aEnglish translation of the revised version of: F. Bailly and G. Longo, Mathe?matiques et sciences de la nature. La singularite? physique du vivant, Hermann, Paris (2006). 311 $a1-84816-693-1 320 $aIncludes bibliographical references (p. 299-312) and index. 327 $aPreface; Contents; Chapter 1 Mathematical Concepts and Physical Objects; Introduction; 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 327 $a1.2.4 Subject and objectivity1.2.5 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 327 $a1.3.6 Towards the "cognitive subject"Chapter 2 Incompleteness and Indetermination in Mathematics and Physics; Introduction; 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 327 $a2.1.9 Intuition2.1.10 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; Chapter 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 327 $a3.1.3 Some epistemological remarks3.2 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 327 $aChapter 4 Invariances, Symmetries, and Symmetry Breakings 330 $aThis book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of "order" and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical int 410 0$aAdvances in computer science and engineering.$pTexts ;$vv. 7. 606 $aMathematics$xPhilosophy 606 $aPhysics$xPhilosophy 606 $aBiomathematics 615 0$aMathematics$xPhilosophy. 615 0$aPhysics$xPhilosophy. 615 0$aBiomathematics. 676 $a510.1 700 $aBailly$b Francis$0947087 701 $aLongo$b G$g(Giuseppe)$026352 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910826406603321 996 $aMathematics and the natural sciences$94057658 997 $aUNINA