Download or read book Undecidability Uncomputability and Unpredictability written by Anthony Aguirre and published by Springer Nature. This book was released on 2021-08-20 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.
Download or read book Foundations of General Relativity written by Klaas Landsman and published by Radboud University Press. This book was released on 2021-10-08 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.
Download or read book Science Music And Mathematics The Deepest Connections Second Edition written by Michael Edgeworth Mcintyre and published by World Scientific. This book was released on 2023-08-02 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. In this book he offers an extraordinary synthesis, revealing the many deep connections between science, music, and mathematics. He avoids equations and technical jargon. The connections are deep in the sense of being embedded in our very nature, rooted in biological evolution over hundreds of millions of years.Michael guides us through biological evolution, perception psychology, and even unconscious science and mathematics, all the way to the scientific uncertainties about the climate crisis.He also has a message of hope for the future. Contrary to popular belief, he holds that biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is far more than a simple competition between selfish genes. Instead, he argues, in some ways it is more like the turbulent, eddying flow in a river or in an atmospheric jet stream, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has long been interested in how different branches of science can better communicate with each other, and with the public. His work harnesses aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication, principles related to the way music works — music of any genre.This Second Edition sharpens the previous discussion of communication skills and their importance for today's great problems, ranging from the widely discussed climate crisis to the need to understand the strengths and weaknesses of artificial intelligence.
Download or read book Sixteenth Marcel Grossmann Meeting The On Recent Developments In Theoretical And Experimental General Relativity Astrophysics And Relativistic Field Theories Proceedings Of The Mg16 Meeting On General Relativity In 4 Volumes written by Remo Ruffini and published by World Scientific. This book was released on 2022-12-15 with total page 4880 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of MG16 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 46 plenary presentations, 3 public lectures, 5 round tables and 81 parallel sessions arranged during the intense six-day online meeting. All talks were recorded and are available on the ICRANet YouTube channel at the following link: www.icranet.org/video_mg16.These proceedings are a representative sample of the very many contributions made at the meeting. They contain 383 papers, among which 14 come from the plenary sessions.The material represented in these proceedings cover the following topics: accretion, active galactic nuclei, alternative theories of gravity, black holes (theory, observations and experiments), binaries, boson stars, cosmic microwave background, cosmic strings, dark energy and large scale structure, dark matter, education, exact solutions, early universe, fundamental interactions and stellar evolution, fast transients, gravitational waves, high energy physics, history of relativity, neutron stars, precision tests, quantum gravity, strong fields, and white dwarf; all of them represented by a large number of contributions.The online e-proceedings are published in an open access format.
Download or read book Information Dynamics written by Thomas Dittrich and published by Springer Nature. This book was released on 2022-11-23 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This wide-ranging book introduces information as a key concept not only in physics, from quantum mechanics to thermodynamics, but also in the neighboring sciences and in the humanities. The central part analyzes dynamical processes as manifestations of information flows between microscopic and macroscopic scales and between systems and their environment. Quantum mechanics is interpreted as a reconstruction of mechanics based on fundamental limitations of information processing on the smallest scales. These become particularly manifest in quantum chaos and in quantum computing. Covering subjects such as causality, prediction, undecidability, chaos, and quantum randomness, the book also provides an information-theoretical view of predictability. More than 180 illustrations visualize the concepts and arguments. The book takes inspiration from the author's graduate-level topical lecture but is also well suited for undergraduate studies and is a valuable resource for researchers and professionals.
Download or read book Quantum Computing For The Brain written by Melanie Swan and published by World Scientific. This book was released on 2022-05-30 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Computing for the Brain argues that the brain is the killer application for quantum computing. No other system is as complex, as multidimensional in time and space, as dynamic, as less well-understood, as of peak interest, and as in need of three-dimensional modeling as it functions in real-life, as the brain.Quantum computing has emerged as a platform suited to contemporary data processing needs, surpassing classical computing and supercomputing. This book shows how quantum computing's increased capacity to model classical data with quantum states and the ability to run more complex permutations of problems can be employed in neuroscience applications such as neural signaling and synaptic integration. State-of-the-art methods are discussed such as quantum machine learning, tensor networks, Born machines, quantum kernel learning, wavelet transforms, Rydberg atom arrays, ion traps, boson sampling, graph-theoretic models, quantum optical machine learning, neuromorphic architectures, spiking neural networks, quantum teleportation, and quantum walks.Quantum Computing for the Brain is a comprehensive one-stop resource for an improved understanding of the converging research frontiers of foundational physics, information theory, and neuroscience in the context of quantum computing.
Download or read book Emergent Quantum Mechanics written by Jan Walleczek and published by MDPI. This book was released on 2019-04-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in "deeper-level" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de Broglie-Bohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeper-level questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and non-classical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.
Download or read book Randomness And Undecidability In Physics written by Karl Svozil and published by World Scientific. This book was released on 1993-10-05 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an “inner description”, a “virtual physics” of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as “randomness” in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the “distant future”. In other words: no “speedup” or “computational shortcut” is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.
Download or read book Randomness and Complexity written by Cristian Calude and published by World Scientific. This book was released on 2007 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.
Download or read book Randomness Through Computation written by Hector Zenil and published by World Scientific. This book was released on 2011 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This review volume consists of an indispensable set of chapters written by leading scholars, scientists and researchers in the field of Randomness, including related subfields specially but not limited to the strong developed connections to the Computability and Recursion Theory. Highly respected, indeed renowned in their areas of specialization, many of these contributors are the founders of their fields. The scope of Randomness Through Computation is novel. Each contributor shares his personal views and anecdotes on the various reasons and motivations which led him to the study of the subject. They share their visions from their vantage and distinctive viewpoints. In summary, this is an opportunity to learn about the topic and its various angles from the leading thinkers.
Download or read book The Theory of Epistemic Fields written by Kofi Kissi Dompere and published by Springer Nature. This book was released on 2024 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about the development of the theory of epistemic fields with the corresponding relational and information fields as a framework for the understanding of strategies and tactics of the theory of knowing as the production of intellectual investment flows and the theory of knowledge accumulation as the production of intellectual capital stocks in systems of factories and departments providing the foundations for the development of open algorithms in the open space of problem-solution dualities. The concepts and the roles of thinking and reasoning with curiosity, creativity, hope, Ill-posed problems, phantom problems, unsolved problems, misinformation, disinformation, fake news, and courage are introduced, defined, and analyzed on the cognitive journeys over the space of ignorance-knowledge dualities, where dualistic-polar conflicts between duals in the space of ignorance-knowledge dualities are resolved with the instruments of fuzzy optimization, the results of which are used to induced the zones of ignorance, the zones of knowledge, and the zones of contentions. A complete development of the set of connecting paths of spaces and sub-spaces is provided, where all varieties, categories, and spaces reside in dualistic-polar structures with knowledge stock viewed as a single tree with the same roots, one trunk, many branches, and a fruit cocktail. The ontological space contains the space of actual-potential dualities as the primary category of knowing, and the epistemological space contains the space of imagination-reality dualities as the derived category of knowing within the space of primary-derived dualities. The space of potentials contains the space of imaginations which contains the sub-spaces of possibility-impossibility, probability-improbability, and possibility-probability dualities with corresponding spaces of necessity-freedom and anticipation-expectation dualities leading to the conception of the possible-world-impossible-world dualities in the space of semantic-non-semantic dualities. This book is also a continuation of the sequence of my works on the theories of paradigms of thought, rationality, info-statics, info-dynamics, entropy, problem-solution dualities in self-contained mathematics and philosophy, and their relational connectivity to information, language, knowing, knowledge, cognitive practices and open maching learning relative to nominalism, and the space of construction-reduction dualities over the spaces of fundamental-applied, production-consumption, input-output, and cost-benefit dualities.
Download or read book Computability in Analysis and Physics written by Marian B. Pour-El and published by Cambridge University Press. This book was released on 2017-03-02 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning.
Download or read book The Theory of Problem Solution Dualities and Polarities written by Kofi Kissi Dompere and published by Springer Nature. This book was released on 2022-04-25 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the development of the understanding of the relational structures of information, knowledge, decision–choice processes of problems and solutions in the theory and practice regarding diversity and unity principles of knowing, science, non-science, and information–knowledge systems through dualistic-polar conditions of variety existence and nonexistence. It is a continuation of the sequence of my epistemic works on the theories on fuzzy rationality, info-statics, info-dynamics, entropy, and their relational connectivity to information, language, knowing, knowledge, cognitive practices relative to variety identification–problem–solution dualities, variety transformation–problem–solution dualities, and variety certainty–uncertainty principle in all areas of knowing and human actions regarding general social transformations. It is also an economic–theoretic approach in understanding the diversity and unity of knowing and science through neuro-decision–choice actions over the space of problem–solution dualities and polarities. The problem–solution dualities are argued to connect all areas of knowing including science and non-science, social science, and non-social-science into unity with diversities under neuro-decision–choice actions to support human existence and nonexistence over the space of static–dynamic dualities. The concepts of diversity and unity are defined and explicated to connect to the tactics and strategies of decision–choice actions over the space of problem–solution dualities. The concepts of problem and solution are defined and explicated not in the space of absoluteness but rather in the space of relativity based on real cost–benefit conditions which are shown to be connected to the general parent–offspring infinite process, where every solution generates new problem(s) which then generates a search for new solutions within the space of minimum–maximum dualities in the decision–choice space under the principle of non-satiation over the space of preference–non-preference dualities with analytical tools drawn from the fuzzy paradigm of thought which connects the conditions of the principle of opposites to the conditions of neuro-decision–choice actions in the zone of variety identifications and transformations. The Monograph would be useful to all areas of Research, Learning and Teaching at Advanced Stages of Knowing and Knowledge Production.
Download or read book Science Music And Mathematics The Deepest Connections written by Michael Edgeworth Mcintyre and published by World Scientific. This book was released on 2021-11-03 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. From a lifetime's thinking, he offers this extraordinary synthesis exposing the deepest connections between science, music, and mathematics, while avoiding equations and technical jargon. He begins with perception psychology and the dichotomization instinct and then takes us through biological evolution, human language, and acausality illusions all the way to the climate crisis and the weaponization of the social media, and beyond that into the deepest parts of theoretical physics — demonstrating our unconscious mathematical abilities.He also has an important message of hope for the future. Contrary to popular belief, biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is more than a simple competition between selfish genes. Rather, he suggests, in some ways it is more like turbulent fluid flow, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has worked on problems as diverse as the Sun's magnetic interior, the Antarctic ozone hole, jet streams in the atmosphere, and the psychophysics of violin sound. He has long been interested in how different branches of science can better communicate with each other and with the public, harnessing aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication.
Download or read book Explanations written by John Cornwell and published by OUP Oxford. This book was released on 2004-04-22 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our lives, states of health, relationships, behaviour, experiences of the natural world, and the technologies that shape our contemporary existence are subject to a superfluity of competing, multi-faceted and sometimes incompatible explanations. Widespread confusion about the nature of 'explanation' and its scope and limits pervades popular exposition of the natural sciences, popular history and philosophy of science. This fascinating and intriguing book explores the way explanations work, why they vary between disciplines, periods, and cultures, and whether they have any necessary boundaries. In other words, Explanations aims to achieve a better understanding of explanation, both within the sciences and the humanities. It features contributions from expert writers from a wide range of disciplines, including science, philosophy, mathematics, and social anthropology.
Download or read book Irreducibility and Computational Equivalence written by Hector Zenil and published by Springer Science & Business Media. This book was released on 2012-12-25 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is clear that computation is playing an increasingly prominent role in the development of mathematics, as well as in the natural and social sciences. The work of Stephen Wolfram over the last several decades has been a salient part in this phenomenon helping founding the field of Complex Systems, with many of his constructs and ideas incorporated in his book A New Kind of Science (ANKS) becoming part of the scientific discourse and general academic knowledge--from the now established Elementary Cellular Automata to the unconventional concept of mining the Computational Universe, from today's widespread Wolfram's Behavioural Classification to his principles of Irreducibility and Computational Equivalence. This volume, with a Foreword by Gregory Chaitin and an Afterword by Cris Calude, covers these and other topics related to or motivated by Wolfram's seminal ideas, reporting on research undertaken in the decade following the publication of Wolfram's NKS book. Featuring 39 authors, its 23 contributions are organized into seven parts: Mechanisms in Programs & Nature Systems Based on Numbers & Simple Programs Social and Biological Systems & Technology Fundamental Physics The Behavior of Systems & the Notion of Computation Irreducibility & Computational Equivalence Reflections and Philosophical Implications.
Download or read book Complexity written by Melanie Mitchell and published by Oxford University Press. This book was released on 2009-04-01 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: What enables individually simple insects like ants to act with such precision and purpose as a group? How do trillions of neurons produce something as extraordinarily complex as consciousness? In this remarkably clear and companionable book, leading complex systems scientist Melanie Mitchell provides an intimate tour of the sciences of complexity, a broad set of efforts that seek to explain how large-scale complex, organized, and adaptive behavior can emerge from simple interactions among myriad individuals. Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. Richly illustrated, Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.
