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Author: Francis Bailly
Publisher: World Scientific
ISBN: 1908977795
Category : Science
Languages : en
Pages : 336
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Book Description
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. Contents:Mathematical Concepts and Physical ObjectsIncompleteness and Indetermination in Mathematics and PhysicsSpace and Time from Physics to BiologyInvariances, Symmetries, and Symmetry BreakingsCauses and Symmetries: The Continuum and the Discrete in Mathematical ModelingExtended Criticality: The Physical Singularity of Life PhenomenaRandomness and Determination in the Interplay between the Continuum and the DiscreteConclusion: Unification and Separation of Theories, or the Importance of Negative Results Readership: Graduate students and professionals in the fields of natural sciences, biology, computer science, mathematics, and physics. Keywords:Foundations of Mathematics and of Physics;Epistemology;Theoretical BiologyKey Features:This book is an epistemological reflection carried out by two working scientists, a physicist and a mathematician, who focus on biology. They first address a comparative analysis of the founding principles of their own disciplines. On the grounds of a three-fold blend, they then introduce a unique proposal, which does not passively transfer the paradigms of the first two theoretically well-established disciplines, to suggest a novel theoretical framework for the third discipline
Author: Francis Bailly
Publisher: World Scientific
ISBN: 1908977795
Category : Science
Languages : en
Pages : 336
Get Book
Book Description
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. Contents:Mathematical Concepts and Physical ObjectsIncompleteness and Indetermination in Mathematics and PhysicsSpace and Time from Physics to BiologyInvariances, Symmetries, and Symmetry BreakingsCauses and Symmetries: The Continuum and the Discrete in Mathematical ModelingExtended Criticality: The Physical Singularity of Life PhenomenaRandomness and Determination in the Interplay between the Continuum and the DiscreteConclusion: Unification and Separation of Theories, or the Importance of Negative Results Readership: Graduate students and professionals in the fields of natural sciences, biology, computer science, mathematics, and physics. Keywords:Foundations of Mathematics and of Physics;Epistemology;Theoretical BiologyKey Features:This book is an epistemological reflection carried out by two working scientists, a physicist and a mathematician, who focus on biology. They first address a comparative analysis of the founding principles of their own disciplines. On the grounds of a three-fold blend, they then introduce a unique proposal, which does not passively transfer the paradigms of the first two theoretically well-established disciplines, to suggest a novel theoretical framework for the third discipline
Author: Rıdvan Karapınar
Publisher: Livre de Lyon
ISBN: 2382362359
Category : Education
Languages : en
Pages : 104
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Book Description
Mathematics and Natural Sciences Research and Theory
Author: Francis Bailly
Publisher: World Scientific
ISBN: 1848166931
Category : Science
Languages : en
Pages : 337
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Book Description
The book aims at the identification of the organising concepts of some physical and biological phenomena, by means of an analysis of the foundations of mathematics and of physics. This is done in the perspective of unifying phenomena, of bringing different conceptual universes into dialog. The analysis of the role of “order” and of symmetries in the foundations of mathematics is linked to the main invariants and principles, among which the geodesic principle (a consequence of symmetries), which govern and confer unity to the various physical theories. Moreover, we attempt to understand causal structures, a central element of physical intelligibility, in terms of symmetries and their breakings. The importance of the mathematical tool is also highlighted, enabling us to grasp the differences in the models for physics and biology which are proposed by continuous and discrete mathematics, such as computational simulations. A distinction between principles of (conceptual) construction and principles of proofs, both in physics and in mathematics, guides this part of the work.As for biology, being particularly difficult and not as thoroughly examined at a theoretical level, we propose a “unification by concepts”, an attempt which should always precede mathematisation. This constitutes an outline for unification also basing itself upon the highlighting of conceptual differences, of complex points of passage, of technical irreducibilities of one field to another. Indeed, a monist point of view such as ours should not make us blind: we, the living objects, are surely just big bags of molecules or, at least, this is our main metaphysical assumption. The point though is: which theory can help us to better understand these bags of molecules, as they are, indeed, rather “singular”, from the physical point of view. Technically, this singularity is expressed by the notion of “extended criticality”, a notion that logically extends the pointwise critical transitions in physics.
Author: Hermann Weyl
Publisher: Princeton University Press
ISBN: 9780691141206
Category : Mathematics
Languages : en
Pages : 338
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Book Description
History of mathematics.
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309284570
Category : Mathematics
Languages : en
Pages : 223
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Book Description
The mathematical sciences are part of nearly all aspects of everyday life-the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term.
Author: David I. Spivak
Publisher: MIT Press
ISBN: 0262320533
Category : Mathematics
Languages : en
Pages : 495
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Book Description
An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
Author: Ari Ben-Menahem
Publisher: Springer Science & Business Media
ISBN: 3540688315
Category : Education
Languages : en
Pages : 6070
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Book Description
This 5,800-page encyclopedia surveys 100 generations of great thinkers, offering more than 2,000 detailed biographies of scientists, engineers, explorers and inventors who left their mark on the history of science and technology. This six-volume masterwork also includes 380 articles summarizing the time-line of ideas in the leading fields of science, technology, mathematics and philosophy.
Author: Anol Bhattacherjee
Publisher: CreateSpace
ISBN: 9781475146127
Category : Science
Languages : en
Pages : 156
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Book Description
This book is designed to introduce doctoral and graduate students to the process of conducting scientific research in the social sciences, business, education, public health, and related disciplines. It is a one-stop, comprehensive, and compact source for foundational concepts in behavioral research, and can serve as a stand-alone text or as a supplement to research readings in any doctoral seminar or research methods class. This book is currently used as a research text at universities on six continents and will shortly be available in nine different languages.
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309183626
Category : Mathematics
Languages : en
Pages : 134
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Book Description
Over three hundred years ago, Galileo is reported to have said, "The laws of nature are written in the language of mathematics." Often mathematics and science go hand in hand, with one helping develop and improve the other. Discoveries in science, for example, open up new advances in statistics, computer science, operations research, and pure and applied mathematics which in turn enabled new practical technologies and advanced entirely new frontiers of science. Despite the interdependency that exists between these two disciplines, cooperation and collaboration between mathematical scientists and scientists have only occurred by chance. To encourage new collaboration between the mathematical sciences and other fields and to sustain present collaboration, the National Research Council (NRC) formed a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. The goal of the committee was to examine the mechanisms for strengthening interdisciplinary research between mathematical sciences and the sciences, with a strong focus on suggesting the most effective mechanisms of collaboration. Strengthening the Linkages Between the Sciences and the Mathematical Sciences provides the findings and recommendations of the committee as well as case studies of cross-discipline collaboration, the workshop agenda, and federal agencies that provide funding for such collaboration.
Author: Claudio Pellegrini
Publisher: Springer Science & Business Media
ISBN: 1461505917
Category : Technology & Engineering
Languages : en
Pages : 292
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Book Description
The historical and epistemological reflection on the applications of mathematical techniques to the Sciences of Nature - physics, biology, chemistry, and geology - today generates attention and interest because of the increasing use of mathematical models in all sciences and their high level of sophistication. The goal of the meeting and the papers collected in this proceedings volume is to give physicists, biologists, mathematicians, and historians of science the opportunity to share information on their work and reflect on the and mathematical models are used in the natural sciences today and in way mathematics the past. The program of the workshop combines the experience of those working on current scientific research in many different fields with the historical analysis of previous results. We hope that some novel interdisciplinary, philosophical, and epistemological considerations will follow from the two aspects of the workshop, the historical and the scientific· This proceedings includes papers presented at the meeting and some of the results of the discussions that took place during the workshop. We wish to express our gratitude to Sergio Monteiro for all his work, which has been essential for the successful publication of these proceedings. We also want to thank the editors of Kluwer AcademidPlenum Publishers for their patience and constant help, and in particular Beth Kuhne and Roberta Klarreich. Our thanks to the fallowing institutions: -Amministrazione Comunale di Arcidosso -Comunita Montana del Monte Amiata ·Center for the History of Physics, UCLA -Centre F.
