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

Author: Klaus Mainzer

Publisher: World Scientific

Published: 2017-11-17

Total Pages: 471

ISBN-13: 9813225505

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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).

The Digital and the Real World
The Digital and the Real World

Author: Klaus Mainzer

Publisher: World Scientific Publishing Company

Published: 2017

Total Pages: 472

ISBN-13: 9789813225480

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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
Contemporary Natural Philosophy and Philosophies - Part 1

Author: Gordana Dodig-Crnkovic

Publisher: MDPI

Published: 2019-06-11

Total Pages: 350

ISBN-13: 3038978221

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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.

Mathesis Universalis, Computability and Proof
Mathesis Universalis, Computability and Proof

Author: Stefania Centrone

Publisher: Springer Nature

Published: 2019-10-25

Total Pages: 375

ISBN-13: 3030204472

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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.

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

Author: Klaus Mainzer

Publisher: World Scientific

Published: 2021-07-27

Total Pages: 425

ISBN-13: 9811236496

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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.

5G, Artificial Intelligence, and Next Generation Internet of Things: Digital Innovation for Green and Sustainable Economies
5G, Artificial Intelligence, and Next Generation Internet of Things: Digital Innovation for Green and Sustainable Economies

Author: Ordóñez de Pablos, Patricia

Publisher: IGI Global

Published: 2023-08-04

Total Pages: 275

ISBN-13: 1668486369

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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
Marketing in Customer Technology Environments

Author: Devanathan Sudharshan

Publisher: Emerald Group Publishing

Published: 2020-04-16

Total Pages: 273

ISBN-13: 1839096004

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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.

Tenth International Conference on Applications and Techniques in Cyber Intelligence (ICATCI 2022)
Tenth International Conference on Applications and Techniques in Cyber Intelligence (ICATCI 2022)

Author: Jemal H. Abawajy

Publisher: Springer Nature

Published: 2023-04-07

Total Pages: 1040

ISBN-13: 3031290976

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This book presents innovative ideas, cutting-edge findings, and novel techniques, methods, and applications in a broad range of cybersecurity and cyberthreat intelligence areas. As our society becomes smarter, there is a corresponding need to secure our cyberfuture. The book describes approaches and findings that are of interest to business professionals and governments seeking to secure our data and underpin infrastructures, as well as to individual users.

Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy
Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy

Author: Klaus Mainzer

Publisher: World Scientific

Published: 2018-05-30

Total Pages: 300

ISBN-13: 9813270950

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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.