Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy

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Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy

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Author : Mainzer Klaus
language : en
Publisher: World Scientific
Release Date : 2017-11-17

Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy written by Mainzer Klaus and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Mathematics categories.

In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy. Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT). Contents: Introduction Basics of Computability Hierarchies of Computability Constructive Proof Theory Computational Mathematics and Digital Information Systems Intuitionistic Mathematics and Human Creativity Proof Mining bridging Logic, Mathematics, and Computer Science Reverse Mathematics Bridging Logic, Mathematics, and Computer Science From Intuitionistic to Homotopy Type Theory — Bridging Logic, Mathematics, and Computer Science Real Computability and Real Analysis Complexity Theory of Real Computing Real Computing and Neural Networks Complexity of Algorithmic Information Complexity of Information Dynamics Digital and Real Physics Digital and Real Computing in the Social World Philosophical Outlook Readership: Undergraduate and graduate students, scientists and readers who are interested in foundational, interdisciplinary, and philosophical questions of mathematics, computer science, and science in general. Keywords: Computability;Complexity;Constructive Mathematics;Proof Mining;Real Computing;Analog Networks;Information System;Digital PhysicsReview: Key Features: Compact introduction into the foundations of modern mathematics and computer science Bridging the gap between digital, real and analog computing by new concepts of information systems Consequences in natural and social sciences with respect to scientific computing

The Digital And The Real World

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Author : Klaus Mainzer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017

The Digital And The Real World written by Klaus Mainzer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.

In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy. Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).

Contemporary Natural Philosophy And Philosophies Part 1

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Author : Gordana Dodig-Crnkovic
language : en
Publisher: MDPI
Release Date : 2019-06-11

Contemporary Natural Philosophy And Philosophies Part 1 written by Gordana Dodig-Crnkovic and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Philosophy categories.

Modern information communication technology eradicates barriers of geographic distances, making the world globally interdependent, but this spatial globalization has not eliminated cultural fragmentation. The Two Cultures of C.P. Snow (that of science–technology and that of humanities) are drifting apart even faster than before, and they themselves crumble into increasingly specialized domains. Disintegrated knowledge has become subservient to the competition in technological and economic race leading in the direction chosen not by the reason, intellect, and shared value-based judgement, but rather by the whims of autocratic leaders or fashion controlled by marketers for the purposes of political or economic dominance. If we want to restore the authority of our best available knowledge and democratic values in guiding humanity, first we have to reintegrate scattered domains of human knowledge and values and offer an evolving and diverse vision of common reality unified by sound methodology. This collection of articles responds to the call from the journal Philosophies to build a new, networked world of knowledge with domain specialists from different disciplines interacting and connecting with other knowledge-and-values-producing and knowledge-and-values-consuming communities in an inclusive, extended, contemporary natural–philosophic manner. In this process of synthesis, scientific and philosophical investigations enrich each other—with sciences informing philosophies about the best current knowledge of the world, both natural and human-made—while philosophies scrutinize the ontological, epistemological, and methodological foundations of sciences, providing scientists with questions and conceptual analyses. This is all directed at extending and deepening our existing comprehension of the world, including ourselves, both as humans and as societies, and humankind.

Proof And Computation Digitization In Mathematics Computer Science And Philosophy

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Author : Mainzer Klaus
language : en
Publisher: World Scientific
Release Date : 2018-05-30

Proof And Computation Digitization In Mathematics Computer Science And Philosophy written by Mainzer Klaus and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-30 with Mathematics categories.

This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields. Contents: Proof and Computation (K Mainzer) Constructive Convex Programming (J Berger and G Svindland) Exploring Predicativity (L Crosilla) Constructive Functional Analysis: An Introduction (H Ishihara) Program Extraction (K Miyamoto) The Data Structures of the Lambda Terms (M Sato) Provable (and Unprovable) Computability (S Wainer) Introduction to Minlog (F Wiesnet) Readership: Graduate students, researchers, and professionals in Mathematics and Computer Science. Keywords: Proof Theory;Computability Theory;Program Extraction;Constructive Analysis;PredicativityReview: Key Features: This book gathers recent contributions of distinguished experts It makes emerging fields accessible to a wider audience, appealing to a broad readership with diverse backgrounds It fills a gap between (under-)graduate level textbooks and state-of-the-art research papers

Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification

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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2021-07-27

Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-27 with Mathematics categories.

This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.

Mathesis Universalis Computability And Proof

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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-10-25

Mathesis Universalis Computability And Proof written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-25 with Philosophy categories.

In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.

5g Artificial Intelligence And Next Generation Internet Of Things Digital Innovation For Green And Sustainable Economies

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Author : Ordóñez de Pablos, Patricia
language : en
Publisher: IGI Global
Release Date : 2023-08-04

5g Artificial Intelligence And Next Generation Internet Of Things Digital Innovation For Green And Sustainable Economies written by Ordóñez de Pablos, Patricia and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-04 with Business & Economics categories.

Key and enabling digital tools and solutions can boost the digital transformation of economies and societies and support achieving the Sustainable Development Goals (SDGs) by 2030. The outcomes of digital innovation must be in line with responsible research and innovation. How can advanced information technologies, including artificial intelligence, blockchain, edge computing, the next generation of the internet of things (NGIoT), IoT, machine learning, and robotics, create digital tools and solutions to build more resilient, climate-neutral, and green economies and societies? 5G, Artificial Intelligence, and Next Generation Internet of Things: Digital Innovation for Green and Sustainable Economies offers innovative conceptual frameworks and theories, case studies, and empirical studies to understand digital innovation and how digital and industrial technologies can accelerate the digital and green transition with multidisciplinary and trans-disciplinary approaches. The book studies how digital tools and solutions can impact the achievement of the Sustainable Development Goals (SDGs) worldwide, focusing on the Asian region. Featuring research on topics such as 5G, artificial intelligence, blockchain, circular economy, green economy, climate-neutral economy, human-centered approach, robotics, geographical focus, and methodologies, this book is ideally designed for academics, researchers, industry players, policymakers, students, academics, experts on IT, CEOs, policymakers, and other relevant stakeholders worldwide.

Marketing In Customer Technology Environments

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Author : Devanathan Sudharshan
language : en
Publisher: Emerald Group Publishing
Release Date : 2020-04-16

Marketing In Customer Technology Environments written by Devanathan Sudharshan and has been published by Emerald Group Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-16 with Business & Economics categories.

With the rise of virtual reality, augmented reality, the internet of things and more, customers are more engaged, more involved, and easier to reach than ever;while being inundated with increasing amounts of marketing material. This straightforward guide takes you through these new technologies and shows how to leverage them to reach new markets.

Limits Of Ai Theoretical Practical Ethical

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Author : Klaus Mainzer
language : en
Publisher: Springer Nature
Release Date :

Limits Of Ai Theoretical Practical Ethical written by Klaus Mainzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Artificial Intelligence When Do Machines Take Over

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Author : Klaus Mainzer
language : en
Publisher: Springer Nature
Release Date : 2019-10-14

Artificial Intelligence When Do Machines Take Over written by Klaus Mainzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-14 with Technology & Engineering categories.

Everybody knows them. Smartphones that talk to us, wristwatches that record our health data, workflows that organize themselves automatically, cars, airplanes and drones that control themselves, traffic and energy systems with autonomous logistics or robots that explore distant planets are technical examples of a networked world of intelligent systems. Machine learning is dramatically changing our civilization. We rely more and more on efficient algorithms, because otherwise we will not be able to cope with the complexity of our civilizing infrastructure. But how secure are AI algorithms? This challenge is taken up in the 2nd edition: Complex neural networks are fed and trained with huge amounts of data (big data). The number of necessary parameters explodes exponentially. Nobody knows exactly what is going on in these "black boxes". In machine learning we need more explainability and accountability of causes and effects in order to be able to decide ethical and legal questions of responsibility (e.g. in autonomous driving or medicine)! Besides causal learning, we also analyze procedures of tests and verification to get certified AI-programs. Since its inception, AI research has been associated with great visions of the future of mankind. It is already a key technology that will decide the global competition of social systems. "Artificial Intelligence and Responsibility" is another central supplement to the 2nd edition: How should we secure our individual liberty rights in the AI world? This book is a plea for technology design: AI must prove itself as a service in society.