Mathematics and the Natural Sciences

Mathematics and the Natural Sciences

Author: Francis Bailly

Publisher: World Scientific

Published: 2011

Total Pages: 337

ISBN-13: 1848166931

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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.


Mathematics And The Natural Sciences: The Physical Singularity Of Life

Mathematics And The Natural Sciences: The Physical Singularity Of Life

Author: Giuseppe Longo

Publisher: World Scientific

Published: 2011-03-04

Total Pages: 337

ISBN-13: 1908977795

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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./a


The Systemic Turn in Human and Natural Sciences

The Systemic Turn in Human and Natural Sciences

Author: Lucia Urbani Ulivi

Publisher: Springer

Published: 2018-12-14

Total Pages: 221

ISBN-13: 3030007251

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This book is dedicated to the consolidation and to the expansion of theoretic systems thinking as a necessary integration of the general reductionist and analytical attitude dominant in our culture. Reductionism and analytical approaches have produced significant results in many fields of contemporary knowledge giving a great contribution to relevant scientific discoveries and to their technological application, but their validity has been improperly universalized as the only and best methods of knowledge in every domain. It is nowadays clear that analytical or mereological approaches are inadequate to solve many problems and that we should introduce – or support the diffusion of - new concepts and different research attitudes. A good candidate to support such a shift is the well known theoretical approach based on the concept of “system” that no more considers the elementary constituents of an object, but the entity emerging from the relations and interactions among its elementary parts. It becomes possible to reconstruct several domains, both philosophical and scientific, from the systemic point of view, introducing fresh ideas in the research in view of a general rational vision of the world on more comprehensive basis. This book contributes to the diffusion and evolution of systemic thinking by focusing on two main objectives: developing and updating the systemic approach in disciplines currently using it and introducing the systemic perspective in humanistic disciplines, where the approach is not widely used. The Systemic Turn in Human and Natural Sciences: A Rock in the Pond is comprised of ten chapters. The chapter authors adopt a trans-disciplinary perspective, consisting in the recognition and harmonization of the special outlooks that together, within the general systemic paradigm, gives an ideal unity to the book.


Ontogenesis Beyond Complexity

Ontogenesis Beyond Complexity

Author: Cary Wolfe

Publisher: Routledge

Published: 2021-12-27

Total Pages: 196

ISBN-13: 1000533611

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This book is based upon the collaborative efforts of the Ontogenetics Process Group (OPG) – an interdisciplinary, multi-institutional, multi-national research group that began meeting in 2017 to explore new and innovative ways of thinking the problem of complexity in living, physical, and social systems outside the algorithmic models that have dominated paradigms of complexity to date. For all the descriptive and predictive power that the complexity sciences offer (the ability to compute feedback systems, recursive networks, emergent dynamics, etc.), they also presume that the living world in all of its modalities (biological, semiotic, economic, affective, social) can be reduced to finite schema of description that delimits in advance all possible outcomes. What is proposed in this volume are conceptual architectures for the living that are not only irreducible to physico-mathematical frames of reference, but that are also as vital as the phenomena they wish to express. In short: life is more complex than complexity. What emerges from this engagement is not the ascendance of a new transcendental principle (or, what amounts to the same thing, a foundational bedrock) derived from the physico-mathematical sciences, but just the opposite: a domain in which the ontological and the epistemological domains enter a zone of strange (and unavoidable) entanglement. The chapters in this book were originally published as a special issue of Angelaki.


Perspectives on Organisms

Perspectives on Organisms

Author: Giuseppe Longo

Publisher: Springer Science & Business Media

Published: 2013-12-13

Total Pages: 293

ISBN-13: 3642359388

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This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould's analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field.


Building Theories

Building Theories

Author: David Danks

Publisher: Springer

Published: 2018-01-18

Total Pages: 282

ISBN-13: 3319727877

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This book explores new findings on the long-neglected topic of theory construction and discovery, and challenges the orthodox, current division of scientific development into discrete stages: the stage of generation of new hypotheses; the stage of collection of relevant data; the stage of justification of possible theories; and the final stage of selection from among equally confirmed theories. The chapters, written by leading researchers, offer an interdisciplinary perspective on various aspects of the processes by which theories rationally should, and descriptively are, built. They address issues such as the role of problem-solving and heuristic reasoning in theory-building; how inferences and models shape the pursuit of scientific knowledge; the relation between problem-solving and scientific discovery; the relative values of the syntactic, semantic, and pragmatic view of theories in understanding theory construction; and the relation between ampliative inferences, heuristic reasoning, and models as a means for building new theories and knowledge. Through detailed arguments and examinations, the volume collectively challenges the orthodox view’s main tenets by characterizing the ways in which the different “stages” are logically, temporally, and psychologically intertwined. As a group, the chapters provide several attempts to answer long-standing questions about the possibility of a unified conceptual framework for building theories and formulating hypotheses.


A Critical Reflection on Automated Science

A Critical Reflection on Automated Science

Author: Marta Bertolaso

Publisher: Springer Nature

Published: 2020-02-05

Total Pages: 302

ISBN-13: 3030250016

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This book provides a critical reflection on automated science and addresses the question whether the computational tools we developed in last decades are changing the way we humans do science. More concretely: Can machines replace scientists in crucial aspects of scientific practice? The contributors to this book re-think and refine some of the main concepts by which science is understood, drawing a fascinating picture of the developments we expect over the next decades of human-machine co-evolution. The volume covers examples from various fields and areas, such as molecular biology, climate modeling, clinical medicine, and artificial intelligence. The explosion of technological tools and drivers for scientific research calls for a renewed understanding of the human character of science. This book aims precisely to contribute to such a renewed understanding of science.


Quantitative Semiotic Analysis

Quantitative Semiotic Analysis

Author: Dario Compagno

Publisher: Springer

Published: 2018-01-16

Total Pages: 193

ISBN-13: 3319615939

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​This contributed volume gives access to semiotic researches adopting a quantitative stance. European semiotics is traditionally based on immanent methodologies: meaning is seen as an autonomous dimension of human existence, whose laws can be investigated via purely qualitative analytical and reflexive analysis. Today, researches crossing disciplinary boundaries reveal the limitations of such an homogeneous practice. In particular, two families of quantitative research strategies can be identified. On the one hand, researchers wish to naturalize meaning, by making semiotic results interact with those coming from Neurophysiological and psychological sciences. On the other hand, statistical and computational tools are adopted to work on linguistic and multimedia corpora. The book acts to put the two approaches into dialogue.


Einstein vs. Bergson

Einstein vs. Bergson

Author: Alessandra Campo

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-11-08

Total Pages: 467

ISBN-13: 3110753707

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This book brings together papers from a conference that took place in the city of L'Aquila, 4–6 April 2019, to commemorate the 10th anniversary of the earthquake that struck on 6 April 2009. Philosophers and scientists from diverse fields of research debated the problem that, on 6 April 1922, divided Einstein and Bergson: the nature of time. For Einstein, scientific time is the only time that matters and the only time we can rely on. Bergson, however, believes that scientific time is derived by abstraction, even in the sense of extraction, from a more fundamental time. The plurality of times envisaged by the theory of Relativity does not, for him, contradict the philosophical intuition of the existence of a single time. But how do things stand today? What can we say about the relationship between the quantitative and qualitative dimensions of time in the light of contemporary science? What do quantum mechanics, biology and neuroscience teach us about the nature of time? The essays collected here take up the question that pitted Einstein against Bergson, science against philosophy, in an attempt to reverse the outcome of their monologue in two voices, with a multilogue in several voices.


Biosemiotics and Evolution

Biosemiotics and Evolution

Author: Elena Pagni

Publisher: Springer Nature

Published: 2022-01-03

Total Pages: 268

ISBN-13: 3030852652

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This book reviews the evolution of Biosemiotics and gives an outlook on the future of this interdisciplinary new discipline. In this volume, the foundations of symbolism are transformed into a phenomenological, technological, philosophical and psychological discussion enriching the readers’ knowledge of these foundations. It offers the opportunity to rethink the impact that evolution theory and the confirmations about evolution as a historical and natural fact, has had and continues to have today. The book is divided into three parts: Part I Life, Meaning, and Information Part II Semiosis and Evolution Part III Physics, medicine, and bioenergetics It starts by laying out a general historical, philosophical, and scientific framework for the collection of studies that will follow. In the following some of the main reference models of evolutionary theories are revisited: Extended Synthesis, Formal Darwinism and Biosemiotics. The authors shed new light on how to rethink the processes underlying the origins and evolution of knowledge, the boundary between teleonomic and teleological paradigms of evolution and their possible integration, the relationship between linguistics and biological sciences, especially with reference to the concept of causality, biological information and the mechanisms of its transmission, the difference between physical and biosemiotic intentionality, as well as an examination of the results offered or deriving from the application in the economics and the engineering of design, of biosemiotic models for the transmission of culture, digitalization and proto-design. This volume is of fundamental scientific and philosophical interest, and seen as a possibility for a dialogue based on theoretical and methodological pluralism. The international nature of the publication, with contributions from all over the world, will allow a further development of academic relations, at the service of the international scientific and humanistic heritage.