Jon Williamson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.003.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter describes the central claims of the book. From a philosophical point of view, the book argues for an objective Bayesian interpretation of probability and an epistemic interpretation of ...
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This chapter describes the central claims of the book. From a philosophical point of view, the book argues for an objective Bayesian interpretation of probability and an epistemic interpretation of causality, and claims that these offer a firm foundation for causal modelling. From the computational point of view, the book investigates the relationship between Bayesian nets and maximum entropy methods, and develops a general computational framework for probabilistic and causal reasoning.Less
This chapter describes the central claims of the book. From a philosophical point of view, the book argues for an objective Bayesian interpretation of probability and an epistemic interpretation of causality, and claims that these offer a firm foundation for causal modelling. From the computational point of view, the book investigates the relationship between Bayesian nets and maximum entropy methods, and develops a general computational framework for probabilistic and causal reasoning.
Sander van Smaalen
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570820
- eISBN:
- 9780191718762
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570820.001.0001
- Subject:
- Physics, Crystallography: Physics
Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the ...
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Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the crystal structures, and symmetries of incommensurately modulated crystals and composite crystals. It also gives a brief introduction to quasicrystals, thus providing the necessary background for understanding the distinctive features of aperiodic crystals, and it provides the tools for the application of quantitative methods from the realms of crystallography, solid state chemistry, and solid state physics to aperiodic crystal structures. The second half of the book is devoted to crystallographic methods of structural analysis of incommensurate crystals. Thorough accounts are given of the diffraction by incommensurate crystals, the choice of parameters in structure refinements, and the use of superspace in analysing crystal structures. The presentation of methods of structure determination includes direct methods, Fourier methods, Patterson function methods, the maximum entropy method (MEM), and charge flipping. So-called t-plots are introduced as a versatile method for the crystal chemical analysis of incommensurately modulated structures and composite crystals.Less
Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the crystal structures, and symmetries of incommensurately modulated crystals and composite crystals. It also gives a brief introduction to quasicrystals, thus providing the necessary background for understanding the distinctive features of aperiodic crystals, and it provides the tools for the application of quantitative methods from the realms of crystallography, solid state chemistry, and solid state physics to aperiodic crystal structures. The second half of the book is devoted to crystallographic methods of structural analysis of incommensurate crystals. Thorough accounts are given of the diffraction by incommensurate crystals, the choice of parameters in structure refinements, and the use of superspace in analysing crystal structures. The presentation of methods of structure determination includes direct methods, Fourier methods, Patterson function methods, the maximum entropy method (MEM), and charge flipping. So-called t-plots are introduced as a versatile method for the crystal chemical analysis of incommensurately modulated structures and composite crystals.
Walter T. Grandy, Jr.
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199546176
- eISBN:
- 9780191720161
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546176.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The ...
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This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs — dating from the 19th century and extended considerably over the following 100 years — is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-20th Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.Less
This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs — dating from the 19th century and extended considerably over the following 100 years — is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-20th Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.
Pier A. Mello and Narendra Kumar
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities ...
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This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities and quantum dots) or possessing quenched randomness (e.g., disordered conductors). The emphasis here is on mesoscopic fluctuations of the sample-specific transport. The universal character of the statistical behaviour of these phenomena is revealed in a natural way through a novel maximum-entropy approach (MEA). The latter leads to the most probable distribution for the set of random matrices that describe the ensemble of disordered/chaotic samples, which are macroscopically identical but differ in microscopic details. Here, the Shannon information entropy associated with these random matrices is maximized subject to the symmetries and the constraints which are physically relevant. This non-perturbative information-theoretic approach is reminiscent of, but distinct from, the standard random-matrix theory, and indeed forms the most distinctive feature of the book.Less
This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities and quantum dots) or possessing quenched randomness (e.g., disordered conductors). The emphasis here is on mesoscopic fluctuations of the sample-specific transport. The universal character of the statistical behaviour of these phenomena is revealed in a natural way through a novel maximum-entropy approach (MEA). The latter leads to the most probable distribution for the set of random matrices that describe the ensemble of disordered/chaotic samples, which are macroscopically identical but differ in microscopic details. Here, the Shannon information entropy associated with these random matrices is maximized subject to the symmetries and the constraints which are physically relevant. This non-perturbative information-theoretic approach is reminiscent of, but distinct from, the standard random-matrix theory, and indeed forms the most distinctive feature of the book.
Francesco Calogero
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199535286
- eISBN:
- 9780191715853
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199535286.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
In Chapter 8 five directions of future research are tersely mentioned in order of increasing importance. The investigation of Diophantine relations, such as those reported in Appendix C. The ...
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In Chapter 8 five directions of future research are tersely mentioned in order of increasing importance. The investigation of Diophantine relations, such as those reported in Appendix C. The investigation of the behavior in a quantal context of systems described by isochronous Hamiltonians. The investigation of isochronous systems outside the phase space sectors where they behave isochronously. The investigation of the behavior of the isochronous many-body problems treated in Section 5.5, in particular, when the corresponding unmodified system is a realistic molecular dynamics model characterized by a chaotic evolution yielding—in the context of statistical mechanics and thermodynamics—a steadily increasing entropy—which, however, must eventually decrease when the corresponding Ω-modified system returns to its initial state, as entailed by its isochronous character. And, last but by no means least, the investigation of isochronous systems in an applicative context—be it physics, chemistry, biology, medicine, economy, and so on.Less
In Chapter 8 five directions of future research are tersely mentioned in order of increasing importance. The investigation of Diophantine relations, such as those reported in Appendix C. The investigation of the behavior in a quantal context of systems described by isochronous Hamiltonians. The investigation of isochronous systems outside the phase space sectors where they behave isochronously. The investigation of the behavior of the isochronous many-body problems treated in Section 5.5, in particular, when the corresponding unmodified system is a realistic molecular dynamics model characterized by a chaotic evolution yielding—in the context of statistical mechanics and thermodynamics—a steadily increasing entropy—which, however, must eventually decrease when the corresponding Ω-modified system returns to its initial state, as entailed by its isochronous character. And, last but by no means least, the investigation of isochronous systems in an applicative context—be it physics, chemistry, biology, medicine, economy, and so on.
Peter Main
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199219469
- eISBN:
- 9780191722516
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219469.003.0011
- Subject:
- Physics, Crystallography: Physics
Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy ...
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Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy itself and its relationship to probability and information. They are illustrated by a simple non-scientific example of estimating missing information based on reasonable assumptions.Less
Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy itself and its relationship to probability and information. They are illustrated by a simple non-scientific example of estimating missing information based on reasonable assumptions.
M. Vidyasagar
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691133157
- eISBN:
- 9781400850518
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691133157.003.0002
- Subject:
- Mathematics, Probability / Statistics
This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random ...
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This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random variable (or more precisely, the probability distribution of the random variable). When there are two or more random variables, it is worthwhile to study the conditional entropy of one random variable with respect to another. The last concept is relative entropy, also known as the Kullback–Leibler divergence, which measures the “disparity” between two probability distributions. The chapter first considers convex and concave functions before discussing the properties of the entropy function, conditional entropy, uniqueness of the entropy function, and the Kullback–Leibler divergence.Less
This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random variable (or more precisely, the probability distribution of the random variable). When there are two or more random variables, it is worthwhile to study the conditional entropy of one random variable with respect to another. The last concept is relative entropy, also known as the Kullback–Leibler divergence, which measures the “disparity” between two probability distributions. The chapter first considers convex and concave functions before discussing the properties of the entropy function, conditional entropy, uniqueness of the entropy function, and the Kullback–Leibler divergence.
J. P. Williams
- Published in print:
- 2000
- Published Online:
- October 2011
- ISBN:
- 9780198269991
- eISBN:
- 9780191683855
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198269991.001.0001
- Subject:
- Religion, Theology, World Religions
The classical texts of Christianity and Zen Buddhism contain resources with potent appeal to contemporary spirituality. The ‘apophatic’, or ‘negative’, may offer a means to integrate the conservation ...
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The classical texts of Christianity and Zen Buddhism contain resources with potent appeal to contemporary spirituality. The ‘apophatic’, or ‘negative’, may offer a means to integrate the conservation of traditional religious practices and beliefs with an openness to experience beyond the limits of doctrine and of rational thought. This book argues for a new understanding of what is meant by apophatic theology, supported by extensive analysis of the texts of Dionysius the Areopagite, St Maximus the Confessor, and Zen Master Dogen. It demonstrates how an apophatic spirituality might inform personal and communal spiritual development, and sketches out the contribution it can offer to modern debate on theology and postmodernism, entropy, and interfaith dialogue, and to development of an active theological commitment to humanity.Less
The classical texts of Christianity and Zen Buddhism contain resources with potent appeal to contemporary spirituality. The ‘apophatic’, or ‘negative’, may offer a means to integrate the conservation of traditional religious practices and beliefs with an openness to experience beyond the limits of doctrine and of rational thought. This book argues for a new understanding of what is meant by apophatic theology, supported by extensive analysis of the texts of Dionysius the Areopagite, St Maximus the Confessor, and Zen Master Dogen. It demonstrates how an apophatic spirituality might inform personal and communal spiritual development, and sketches out the contribution it can offer to modern debate on theology and postmodernism, entropy, and interfaith dialogue, and to development of an active theological commitment to humanity.
Paul Bloomfield
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780195137132
- eISBN:
- 9780199833092
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195137132.001.0001
- Subject:
- Philosophy, Moral Philosophy
The book is a work in metaethics, constituting a defense of moral realism. The book begins with what I call a “modest transcendental argument” for the existence of the property of moral goodness ...
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The book is a work in metaethics, constituting a defense of moral realism. The book begins with what I call a “modest transcendental argument” for the existence of the property of moral goodness based on an acknowledgment of the possibility that personal moral failing may go forever undetected; as such this is an argument from error. The property of physical health, understood in terms of proper function, is used as a model for moral goodness. This anchors the moral ontology on foundations as solid as those found in the physical sciences. A moral epistemology is developed in which we may learn about goodness much in the way doctors and scientists may learn about healthiness. The semantics that emerges from this picture is multifaceted and nuanced enough to preserve complicated common sense semantic intuitions about how the word “good” is used in moral contexts. The position also implies a defense of an externalist theory about the relationship between the recognition of a moral consideration and motivation. The book closes with an appendix in which the reduction of thermodynamics to statistical mechanics is questioned, and a nonreducible ontology for entropy is considered as an ontological model for both physical health and moral goodness.Less
The book is a work in metaethics, constituting a defense of moral realism. The book begins with what I call a “modest transcendental argument” for the existence of the property of moral goodness based on an acknowledgment of the possibility that personal moral failing may go forever undetected; as such this is an argument from error. The property of physical health, understood in terms of proper function, is used as a model for moral goodness. This anchors the moral ontology on foundations as solid as those found in the physical sciences. A moral epistemology is developed in which we may learn about goodness much in the way doctors and scientists may learn about healthiness. The semantics that emerges from this picture is multifaceted and nuanced enough to preserve complicated common sense semantic intuitions about how the word “good” is used in moral contexts. The position also implies a defense of an externalist theory about the relationship between the recognition of a moral consideration and motivation. The book closes with an appendix in which the reduction of thermodynamics to statistical mechanics is questioned, and a nonreducible ontology for entropy is considered as an ontological model for both physical health and moral goodness.
Jon Williamson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.003.0005
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
Objective Bayesianism imposes two norms on degrees of belief: degrees of belief should be constrained by empirical information and they should otherwise be as equivocal as possible. The origins of ...
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Objective Bayesianism imposes two norms on degrees of belief: degrees of belief should be constrained by empirical information and they should otherwise be as equivocal as possible. The origins of objective Bayesianism are explained, with the work of Jakob Bernoulli and Laplace presented at some length. A contemporary reading of the two norms is developed in detail. Then, it is shown how Bayesian nets can be used to represent objective Bayesian degrees of belief (this leads to what are now called objective Bayesian nets).Less
Objective Bayesianism imposes two norms on degrees of belief: degrees of belief should be constrained by empirical information and they should otherwise be as equivocal as possible. The origins of objective Bayesianism are explained, with the work of Jakob Bernoulli and Laplace presented at some length. A contemporary reading of the two norms is developed in detail. Then, it is shown how Bayesian nets can be used to represent objective Bayesian degrees of belief (this leads to what are now called objective Bayesian nets).
Paul F. Lurquin and Linda Stone
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780195315387
- eISBN:
- 9780199785674
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195315387.003.0005
- Subject:
- Religion, Religion and Society
This chapter demonstrates that the origin of the universe was probabilistic, not preordained, because Heisenberg's uncertainty principle would have been violated at the level of the Big Bang. The ...
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This chapter demonstrates that the origin of the universe was probabilistic, not preordained, because Heisenberg's uncertainty principle would have been violated at the level of the Big Bang. The appearance of structure in the universe was made possible by the decoupling of matter and radiation about 400,000 years after the Big Bang. Structure appeared — and continues to appear — without violating the second law of thermodynamics because entropy is not increasing as fast as it could, and this keeps the universe in a state of disequilibrium, not equilibrium. Life appeared as a consequence of this disequilibrium, possibly involving a sequence of events such as formation of an organic prebiotic soup (or synthesis of organic compounds in hydrothermal vents), the appearance of an RNA world, and the formation of lipid-bound hypercycles.Less
This chapter demonstrates that the origin of the universe was probabilistic, not preordained, because Heisenberg's uncertainty principle would have been violated at the level of the Big Bang. The appearance of structure in the universe was made possible by the decoupling of matter and radiation about 400,000 years after the Big Bang. Structure appeared — and continues to appear — without violating the second law of thermodynamics because entropy is not increasing as fast as it could, and this keeps the universe in a state of disequilibrium, not equilibrium. Life appeared as a consequence of this disequilibrium, possibly involving a sequence of events such as formation of an organic prebiotic soup (or synthesis of organic compounds in hydrothermal vents), the appearance of an RNA world, and the formation of lipid-bound hypercycles.
Jon Williamson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.003.0012
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter discusses the situation in which an agent's language or domain may change. It is argued — against a principle of language invariance — that language contains implicit knowledge and so ...
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This chapter discusses the situation in which an agent's language or domain may change. It is argued — against a principle of language invariance — that language contains implicit knowledge and so degrees of belief should be expected to change when language changes. A conservativity principle, which demands that new degrees of belief be as close as possible to old degrees of belief, is rejected. An overview is given of formal methods for revising beliefs as language changes, and maximum entropy methods are advocated.Less
This chapter discusses the situation in which an agent's language or domain may change. It is argued — against a principle of language invariance — that language contains implicit knowledge and so degrees of belief should be expected to change when language changes. A conservativity principle, which demands that new degrees of belief be as close as possible to old degrees of belief, is rejected. An overview is given of formal methods for revising beliefs as language changes, and maximum entropy methods are advocated.
David M. Wilkinson
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568469
- eISBN:
- 9780191717611
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568469.003.0002
- Subject:
- Biology, Ecology
The second law of thermodynamics is central to understanding ecology, although it is ignored by most ecology text books. It follows from the second law that all organisms must draw free energy from ...
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The second law of thermodynamics is central to understanding ecology, although it is ignored by most ecology text books. It follows from the second law that all organisms must draw free energy from their environment and return waste products back to their environment. Microorganisms often play a central role in decomposition of these waste products, but in spite of their importance are ignored by most food web studies. The possible relevance of developing ideas on maximum entropy production (MEP) to global ecology is also discussed.Less
The second law of thermodynamics is central to understanding ecology, although it is ignored by most ecology text books. It follows from the second law that all organisms must draw free energy from their environment and return waste products back to their environment. Microorganisms often play a central role in decomposition of these waste products, but in spite of their importance are ignored by most food web studies. The possible relevance of developing ideas on maximum entropy production (MEP) to global ecology is also discussed.
Paul Nunez
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195340716
- eISBN:
- 9780199776269
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195340716.001.0001
- Subject:
- Neuroscience, Development
Does the brain create the mind, or is some external entity involved? In addressing this hard problem of consciousness, we face a central human challenge: what do we really know and how do we know it? ...
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Does the brain create the mind, or is some external entity involved? In addressing this hard problem of consciousness, we face a central human challenge: what do we really know and how do we know it? Tentative answers in this book follow from a synthesis of profound ideas, borrowed from philosophy, religion, politics, economics, neuroscience, physics, mathematics, and cosmology, the knowledge structures supporting our meager grasp of reality. This search for new links in the web of human knowledge extends in many directions: the shadows of our thought processes revealed by brain imagining, brains treated as complex adaptive systems that reveal fractal-like behavior in the brain's nested hierarchy, resonant interactions facilitating functional connections in brain tissue, probability and entropy as measures of human ignorance, fundamental limits on human knowledge, and the central role played by information in both brains and physical systems. The author discusses the possibility of deep connections between relativity, quantum mechanics, thermodynamics, and consciousness; all entities involved with fundamental information barriers. This study elaborates on possible new links in this nested web of human knowledge that may tell us something new about the nature and origins of consciousness. In the end, does the brain create the mind? Or is the mind already out there?Less
Does the brain create the mind, or is some external entity involved? In addressing this hard problem of consciousness, we face a central human challenge: what do we really know and how do we know it? Tentative answers in this book follow from a synthesis of profound ideas, borrowed from philosophy, religion, politics, economics, neuroscience, physics, mathematics, and cosmology, the knowledge structures supporting our meager grasp of reality. This search for new links in the web of human knowledge extends in many directions: the shadows of our thought processes revealed by brain imagining, brains treated as complex adaptive systems that reveal fractal-like behavior in the brain's nested hierarchy, resonant interactions facilitating functional connections in brain tissue, probability and entropy as measures of human ignorance, fundamental limits on human knowledge, and the central role played by information in both brains and physical systems. The author discusses the possibility of deep connections between relativity, quantum mechanics, thermodynamics, and consciousness; all entities involved with fundamental information barriers. This study elaborates on possible new links in this nested web of human knowledge that may tell us something new about the nature and origins of consciousness. In the end, does the brain create the mind? Or is the mind already out there?
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the ...
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This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.Less
This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.
Robert Alicki and Mark Fannes
- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198504009
- eISBN:
- 9780191708503
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504009.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter presents some theories relating quantum dynamical entropy and the open problem of a rigorous description of transport phenomena in macroscopic bodies.
This chapter presents some theories relating quantum dynamical entropy and the open problem of a rigorous description of transport phenomena in macroscopic bodies.
Paull Nunez
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195340716
- eISBN:
- 9780199776269
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195340716.003.0008
- Subject:
- Neuroscience, Development
This chapter considers the general limits of scientific knowledge, and identifies probability and entropy as important measures of human ignorance; scientific predictions are shown to be severely ...
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This chapter considers the general limits of scientific knowledge, and identifies probability and entropy as important measures of human ignorance; scientific predictions are shown to be severely limited in complex systems. It argues that fundamental limits on computer power may preclude the creation of artificial consciousness, even if natural brains actually do create minds, as assumed by most contemporary scientists.Less
This chapter considers the general limits of scientific knowledge, and identifies probability and entropy as important measures of human ignorance; scientific predictions are shown to be severely limited in complex systems. It argues that fundamental limits on computer power may preclude the creation of artificial consciousness, even if natural brains actually do create minds, as assumed by most contemporary scientists.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0012
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter examines the effects of large variations in density with depth, that is, density stratification. It first describes anelastic models for 2D cartesian box and 2D cylindrical annulus ...
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This chapter examines the effects of large variations in density with depth, that is, density stratification. It first describes anelastic models for 2D cartesian box and 2D cylindrical annulus geometries, using entropy and pressure as working thermodynamic variables or using temperature and pressure, for both convectively unstable and stable regions. In particular, it considers anelastic approximation and how to formulate the anelastic equations, as well as the anelastic form of mass conservation, momentum conservation with entropy as a variable, internal energy conservation with entropy as a variable, and temperature as a variable. It also discusses possible choices for a reference state, focusing on polytropes, before explaining modifications to the numerical method and presenting the numerical simulations using the anelastic model.Less
This chapter examines the effects of large variations in density with depth, that is, density stratification. It first describes anelastic models for 2D cartesian box and 2D cylindrical annulus geometries, using entropy and pressure as working thermodynamic variables or using temperature and pressure, for both convectively unstable and stable regions. In particular, it considers anelastic approximation and how to formulate the anelastic equations, as well as the anelastic form of mass conservation, momentum conservation with entropy as a variable, internal energy conservation with entropy as a variable, and temperature as a variable. It also discusses possible choices for a reference state, focusing on polytropes, before explaining modifications to the numerical method and presenting the numerical simulations using the anelastic model.
Kenneth C. Calman
- Published in print:
- 1998
- Published Online:
- September 2009
- ISBN:
- 9780192629449
- eISBN:
- 9780191723674
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780192629449.003.0015
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
This short end piece provides a personal view on the importance of health and what is needed to change it. It emphasises public and patient participation, and returns to the title and the word ...
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This short end piece provides a personal view on the importance of health and what is needed to change it. It emphasises public and patient participation, and returns to the title and the word ‘potential’. It can variously be defined to include energy and the power to do work, and it uses the term entropy as the power to restore order. The world is a remarkable place. With the goodwill of people, wanting to improve the common weal, then health can, and will be improved.Less
This short end piece provides a personal view on the importance of health and what is needed to change it. It emphasises public and patient participation, and returns to the title and the word ‘potential’. It can variously be defined to include energy and the power to do work, and it uses the term entropy as the power to restore order. The world is a remarkable place. With the goodwill of people, wanting to improve the common weal, then health can, and will be improved.
William P. Brown
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199730797
- eISBN:
- 9780199777075
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199730797.003.0008
- Subject:
- Religion, Biblical Studies, Theology
Though not a creation account per se, Ecclesiastes 1:2-11 features a portrait of creation that is entirely unique in the biblical corpus. Qoheleth, the ostensible author of most of Ecclesiastes, ...
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Though not a creation account per se, Ecclesiastes 1:2-11 features a portrait of creation that is entirely unique in the biblical corpus. Qoheleth, the ostensible author of most of Ecclesiastes, describes creation in terms of wearying, ever-repeating cycles, from wind and water to life and death. Qoheleth’s world is devoid of anything “new,” a creation without pause and effect with human life beset by uninterrupted toil. The final chapter of Ecclesiastes, moreover, alludes to the eventual dissipation of creation. All is “vanity” (hebel); creation is a static, closed whole. Science, too, points to the ultimate dissolution of the universe, death by entropy. At the same time, science reveals that the cycles of nature Qoheleth so disparaged are in fact life-sustaining. Science both underscores and reorients Qoheleth’s “empirical” view of the world. Though creation seems pointless, it nevertheless provides sustaining moments of joy for human well-being.Less
Though not a creation account per se, Ecclesiastes 1:2-11 features a portrait of creation that is entirely unique in the biblical corpus. Qoheleth, the ostensible author of most of Ecclesiastes, describes creation in terms of wearying, ever-repeating cycles, from wind and water to life and death. Qoheleth’s world is devoid of anything “new,” a creation without pause and effect with human life beset by uninterrupted toil. The final chapter of Ecclesiastes, moreover, alludes to the eventual dissipation of creation. All is “vanity” (hebel); creation is a static, closed whole. Science, too, points to the ultimate dissolution of the universe, death by entropy. At the same time, science reveals that the cycles of nature Qoheleth so disparaged are in fact life-sustaining. Science both underscores and reorients Qoheleth’s “empirical” view of the world. Though creation seems pointless, it nevertheless provides sustaining moments of joy for human well-being.
