Paul Humphreys
- Published in print:
- 2004
- Published Online:
- February 2006
- ISBN:
- 9780195158700
- eISBN:
- 9780199785964
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195158709.001.0001
- Subject:
- Philosophy, Philosophy of Science
Computational science, especially computer simulations, is now the dominant procedure in many areas of science. This book contains the first systematic philosophical account of this new scientific ...
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Computational science, especially computer simulations, is now the dominant procedure in many areas of science. This book contains the first systematic philosophical account of this new scientific method, and draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access to the empirical world. This expansion forms the basis for a new kind of empiricism better suited to the needs of science than the older anthropocentric forms of empiricism. Human abilities are no longer the ultimate standard of correctness within epistemology. The book includes arguments for the primacy of properties rather than objects, for how technology interacts with scientific methods, and a detailed account of how the path from a computational template or model to a scientific application is constructed and revised. This last feature allows us to hold a form of selective realism in which anti-realist arguments based on abstract reconstructions of theories can be avoided. One important consequence of the rise of computational methods is that the traditional organization of the sciences is being replaced by an organization founded on computational templates.Less
Computational science, especially computer simulations, is now the dominant procedure in many areas of science. This book contains the first systematic philosophical account of this new scientific method, and draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access to the empirical world. This expansion forms the basis for a new kind of empiricism better suited to the needs of science than the older anthropocentric forms of empiricism. Human abilities are no longer the ultimate standard of correctness within epistemology. The book includes arguments for the primacy of properties rather than objects, for how technology interacts with scientific methods, and a detailed account of how the path from a computational template or model to a scientific application is constructed and revised. This last feature allows us to hold a form of selective realism in which anti-realist arguments based on abstract reconstructions of theories can be avoided. One important consequence of the rise of computational methods is that the traditional organization of the sciences is being replaced by an organization founded on computational templates.
Paul Humphreys
- Published in print:
- 2004
- Published Online:
- February 2006
- ISBN:
- 9780195158700
- eISBN:
- 9780199785964
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195158709.003.0003
- Subject:
- Philosophy, Philosophy of Science
Computational science involves a new kind of scientific method. The concepts of a computational template and a computational model are introduced as alternatives to scientific theories and laws, and ...
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Computational science involves a new kind of scientific method. The concepts of a computational template and a computational model are introduced as alternatives to scientific theories and laws, and it is shown how the construction process for templates allows us to hold a selective form of scientific realism. There is an important distinction between the process of construction and the process of adjustment for templates, and the latter is not subject to many conventionalist objections. Templates provide a way of re-organizing the sciences, but subject-specific knowledge is still needed to use them effectively. The important role of syntax in templates argues against the semantic account of theories.Less
Computational science involves a new kind of scientific method. The concepts of a computational template and a computational model are introduced as alternatives to scientific theories and laws, and it is shown how the construction process for templates allows us to hold a selective form of scientific realism. There is an important distinction between the process of construction and the process of adjustment for templates, and the latter is not subject to many conventionalist objections. Templates provide a way of re-organizing the sciences, but subject-specific knowledge is still needed to use them effectively. The important role of syntax in templates argues against the semantic account of theories.
Robert J. Matthews
- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199211258
- eISBN:
- 9780191705724
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211258.001.0001
- Subject:
- Philosophy, Philosophy of Mind
This book provides a sustained critique of a widely held representationalist view of propositional attitudes and their role in the production of thought and behaviour. On this view, having a ...
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This book provides a sustained critique of a widely held representationalist view of propositional attitudes and their role in the production of thought and behaviour. On this view, having a propositional attitude is a matter of having an explicit representation that plays a particular causal/computational role in the production of thought and behaviour. The book argues that this view does not enjoy the theoretical or the empirical support that proponents claim for it; moreover, the view misconstrues the role of propositional attitude attributions in cognitive scientific theorizing. This book develops an alternative measurement-theoretic account of propositional attitudes and the sentences by which we attribute them. On this account, the sentences by which we attribute propositional attitudes function semantically like the sentences by which we attribute a quantity of some physical magnitude (e.g., having a mass of 80 kilos). That is, in much the same way that we specify a quantity of some physical magnitude by means of its numerical representative on a measurement scale, we specify propositional attitude of a given type by means of its measurement space. Propositional attitudes turn out to be causally efficacious aptitudes for thought and behaviour, not semantically evaluable mental particulars of some sort. This book's measurement-theoretic account provides a plausible view of the explanatorily relevant properties of propositional attitudes, the semantics of propositional attitude attributions, and the role of such attributions in computational cognitive scientific theorizing.Less
This book provides a sustained critique of a widely held representationalist view of propositional attitudes and their role in the production of thought and behaviour. On this view, having a propositional attitude is a matter of having an explicit representation that plays a particular causal/computational role in the production of thought and behaviour. The book argues that this view does not enjoy the theoretical or the empirical support that proponents claim for it; moreover, the view misconstrues the role of propositional attitude attributions in cognitive scientific theorizing. This book develops an alternative measurement-theoretic account of propositional attitudes and the sentences by which we attribute them. On this account, the sentences by which we attribute propositional attitudes function semantically like the sentences by which we attribute a quantity of some physical magnitude (e.g., having a mass of 80 kilos). That is, in much the same way that we specify a quantity of some physical magnitude by means of its numerical representative on a measurement scale, we specify propositional attitude of a given type by means of its measurement space. Propositional attitudes turn out to be causally efficacious aptitudes for thought and behaviour, not semantically evaluable mental particulars of some sort. This book's measurement-theoretic account provides a plausible view of the explanatorily relevant properties of propositional attitudes, the semantics of propositional attitude attributions, and the role of such attributions in computational cognitive scientific theorizing.
Stefan Helmreich
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164809
- eISBN:
- 9781400873869
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164809.001.0001
- Subject:
- Anthropology, Social and Cultural Anthropology
What is life? What is water? What is sound? This book investigates how contemporary scientists—biologists, oceanographers, and audio engineers—are redefining these crucial concepts. Life, water, and ...
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What is life? What is water? What is sound? This book investigates how contemporary scientists—biologists, oceanographers, and audio engineers—are redefining these crucial concepts. Life, water, and sound are phenomena at once empirical and abstract, material and formal, scientific and social. In the age of synthetic biology, rising sea levels, and new technologies of listening, these phenomena stretch toward their conceptual snapping points, breaching the boundaries between the natural, cultural, and virtual. Through examinations of the computational life sciences, marine biology, astrobiology, acoustics, and more, the book follows scientists to the limits of these categories. Along the way, it offers critical accounts of such other-than-human entities as digital life forms, microbes, coral reefs, whales, seawater, extraterrestrials, tsunamis, seashells, and bionic cochlea. It develops a new notion of “sounding”—as investigating, fathoming, listening—to describe the form of inquiry appropriate for tracking meanings and practices of the biological, aquatic, and sonic in a time of global change and climate crisis. The book shows that life, water, and sound no longer mean what they once did, and that what count as their essential natures are under dynamic revision.Less
What is life? What is water? What is sound? This book investigates how contemporary scientists—biologists, oceanographers, and audio engineers—are redefining these crucial concepts. Life, water, and sound are phenomena at once empirical and abstract, material and formal, scientific and social. In the age of synthetic biology, rising sea levels, and new technologies of listening, these phenomena stretch toward their conceptual snapping points, breaching the boundaries between the natural, cultural, and virtual. Through examinations of the computational life sciences, marine biology, astrobiology, acoustics, and more, the book follows scientists to the limits of these categories. Along the way, it offers critical accounts of such other-than-human entities as digital life forms, microbes, coral reefs, whales, seawater, extraterrestrials, tsunamis, seashells, and bionic cochlea. It develops a new notion of “sounding”—as investigating, fathoming, listening—to describe the form of inquiry appropriate for tracking meanings and practices of the biological, aquatic, and sonic in a time of global change and climate crisis. The book shows that life, water, and sound no longer mean what they once did, and that what count as their essential natures are under dynamic revision.
Masao Ito, Yasushi Miyashita, and Edmund T. Rolls (eds)
- Published in print:
- 1997
- Published Online:
- March 2012
- ISBN:
- 9780198524144
- eISBN:
- 9780191689147
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198524144.001.0001
- Subject:
- Psychology, Cognitive Psychology
The topic of consciousness is truly multidisciplinary, attracting researchers and theorists from diverse backgrounds. It is now widely accepted that previously disparate areas all have contributions ...
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The topic of consciousness is truly multidisciplinary, attracting researchers and theorists from diverse backgrounds. It is now widely accepted that previously disparate areas all have contributions to make to the understanding of the nature of consciousness. Thus, we now have computational scientists, neuroscientists, and philosophers all engaged in the same effort. This book illustrates these three approaches. The first section is concerned with philosophical approaches to consciousness. One of the fundamental issues here is that of subjective feeling or qualia. The second section focuses on approaches from cognitive neuroscience. Patients with different types of neurological problems, and new imaging techniques, provide rich sources of data for studying how consciousness relates to brain function. The third section includes computational approaches looking at the quantitative relationship between brain processes and conscious experience.Less
The topic of consciousness is truly multidisciplinary, attracting researchers and theorists from diverse backgrounds. It is now widely accepted that previously disparate areas all have contributions to make to the understanding of the nature of consciousness. Thus, we now have computational scientists, neuroscientists, and philosophers all engaged in the same effort. This book illustrates these three approaches. The first section is concerned with philosophical approaches to consciousness. One of the fundamental issues here is that of subjective feeling or qualia. The second section focuses on approaches from cognitive neuroscience. Patients with different types of neurological problems, and new imaging techniques, provide rich sources of data for studying how consciousness relates to brain function. The third section includes computational approaches looking at the quantitative relationship between brain processes and conscious experience.
Paul Humphreys
- Published in print:
- 2019
- Published Online:
- May 2019
- ISBN:
- 9780199334872
- eISBN:
- 9780190219710
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199334872.003.0003
- Subject:
- Philosophy, Philosophy of Science
A new kind of scientific revolution is described, one called an emplacement revolution. Emplacement revolutions are contrasted with Kuhnian revolutions and Hacking revolutions. The concept of the ...
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A new kind of scientific revolution is described, one called an emplacement revolution. Emplacement revolutions are contrasted with Kuhnian revolutions and Hacking revolutions. The concept of the anthropocentric predicament is introduced and the associated concept of the interface problem. Each provides a challenge in understanding the world from the perspective of computational science. The central concept of epistemic opacity is described and connected to the interface problem. Some reasons why computational science is new are given, arguments are provided for why philosophy of science should not restrict itself to in principle results, and the fact that contemporary science is inextricably entwined with technological advances is explored.Less
A new kind of scientific revolution is described, one called an emplacement revolution. Emplacement revolutions are contrasted with Kuhnian revolutions and Hacking revolutions. The concept of the anthropocentric predicament is introduced and the associated concept of the interface problem. Each provides a challenge in understanding the world from the perspective of computational science. The central concept of epistemic opacity is described and connected to the interface problem. Some reasons why computational science is new are given, arguments are provided for why philosophy of science should not restrict itself to in principle results, and the fact that contemporary science is inextricably entwined with technological advances is explored.
Paul Humphreys
- Published in print:
- 2019
- Published Online:
- May 2019
- ISBN:
- 9780199334872
- eISBN:
- 9780190219710
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199334872.003.0004
- Subject:
- Philosophy, Philosophy of Science
Reasons are given to justify the claim that computer simulations and computational science constitute a distinctively new set of scientific methods as compared to traditional analytic methods and ...
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Reasons are given to justify the claim that computer simulations and computational science constitute a distinctively new set of scientific methods as compared to traditional analytic methods and that these computational methods introduce new issues in the philosophy of science. These issues are both epistemological and methodological in kind. Definitions of epistemic opacity and essential epistemic opacity are given, the syntactic and semantic accounts of theories are shown to address different problems than those addressed by computational science, the important role of concrete dynamics in simulations is stressed, and differences between in principle approaches and in practice approaches to philosophy of science are explored.Less
Reasons are given to justify the claim that computer simulations and computational science constitute a distinctively new set of scientific methods as compared to traditional analytic methods and that these computational methods introduce new issues in the philosophy of science. These issues are both epistemological and methodological in kind. Definitions of epistemic opacity and essential epistemic opacity are given, the syntactic and semantic accounts of theories are shown to address different problems than those addressed by computational science, the important role of concrete dynamics in simulations is stressed, and differences between in principle approaches and in practice approaches to philosophy of science are explored.
Jonathan Gratch and Stacy Marsella (eds)
- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780195387643
- eISBN:
- 9780199369195
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195387643.001.0001
- Subject:
- Psychology, Cognitive Models and Architectures, Cognitive Psychology
Motion profoundly shapes human social interactions. Researchers across a surprising diversity of scientific and technical fields are attempting to measure, understand and possibly harness the impact ...
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Motion profoundly shapes human social interactions. Researchers across a surprising diversity of scientific and technical fields are attempting to measure, understand and possibly harness the impact emotion’s role in shaping interactions between people and between people and technology. Concepts like rapport, emotional contagion or emergent emotions presuppose people rapidly detect nonverbal affective cues, make inferences about the other party’s mental state, and respond in ways that jointly shape the success or failure of social interactions. Recent advances in artificial intelligence are allowing computer systems to engage in this nonverbal dance, on the one hand opening a wealth of possibilities for human-machine systems, and on the other, creating powerful new tools for behavioral science research. This book reports on the state-of-the-art in both social science theory and computational methods, and illustrates how these two fields, together, can both facilitate and illuminate human social processes. The book has several aims: • Present current social science theories of social emotions from cognitive, biological, social and developmental perspectives • Strengthen the theoretical foundation for building computational systems that co-construct emotional trajectories with human participants • Discuss computational models of social cognition that can represent and reason about the evolving relationship between interaction partners • Present the current and future potential of sensing technology to reliably detect and classify affective nonverbal cues • Discuss the potential of computational methods as tools for empirical research into human transactional processes • Consider methodological approaches for assessing the social consequences of socio-emotional systems Less
Motion profoundly shapes human social interactions. Researchers across a surprising diversity of scientific and technical fields are attempting to measure, understand and possibly harness the impact emotion’s role in shaping interactions between people and between people and technology. Concepts like rapport, emotional contagion or emergent emotions presuppose people rapidly detect nonverbal affective cues, make inferences about the other party’s mental state, and respond in ways that jointly shape the success or failure of social interactions. Recent advances in artificial intelligence are allowing computer systems to engage in this nonverbal dance, on the one hand opening a wealth of possibilities for human-machine systems, and on the other, creating powerful new tools for behavioral science research. This book reports on the state-of-the-art in both social science theory and computational methods, and illustrates how these two fields, together, can both facilitate and illuminate human social processes. The book has several aims: • Present current social science theories of social emotions from cognitive, biological, social and developmental perspectives • Strengthen the theoretical foundation for building computational systems that co-construct emotional trajectories with human participants • Discuss computational models of social cognition that can represent and reason about the evolving relationship between interaction partners • Present the current and future potential of sensing technology to reliably detect and classify affective nonverbal cues • Discuss the potential of computational methods as tools for empirical research into human transactional processes • Consider methodological approaches for assessing the social consequences of socio-emotional systems
Maurice S. Lee
- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691192925
- eISBN:
- 9780691194219
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691192925.003.0001
- Subject:
- Literature, 19th-century Literature and Romanticism
This chapter provides an understanding of information that is productive for literary critics at a time of methodological instability and professional insecurity. It reflects on knowledge as the ...
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This chapter provides an understanding of information that is productive for literary critics at a time of methodological instability and professional insecurity. It reflects on knowledge as the subject of epistemology, while information—a more recent and less disciplined concept—seems more the stuff of numbers, facts, classification, computational science, and media technology. To study information in these terms is to pivot away from philosophical questions about correlations between subjects and objects or the accuracy of language, and to focus instead on the possibilities of navigating the world through algorithmic processes, bureaucratic protocols, and data-based analysis. The chapter also claims that informational concepts and practices shape not only the internal thematics of literature but also the ways in which meanings are made from texts. It explains how writers and readers, including literary critics, have frequently been inclined to resist the rise of information.Less
This chapter provides an understanding of information that is productive for literary critics at a time of methodological instability and professional insecurity. It reflects on knowledge as the subject of epistemology, while information—a more recent and less disciplined concept—seems more the stuff of numbers, facts, classification, computational science, and media technology. To study information in these terms is to pivot away from philosophical questions about correlations between subjects and objects or the accuracy of language, and to focus instead on the possibilities of navigating the world through algorithmic processes, bureaucratic protocols, and data-based analysis. The chapter also claims that informational concepts and practices shape not only the internal thematics of literature but also the ways in which meanings are made from texts. It explains how writers and readers, including literary critics, have frequently been inclined to resist the rise of information.
Tony Hey and Anne Trefethen
- Published in print:
- 2008
- Published Online:
- August 2013
- ISBN:
- 9780262151207
- eISBN:
- 9780262281041
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262151207.003.0002
- Subject:
- Society and Culture, Media Studies
This chapter finds that computational science has evolved into a more scientific methodology. Computer science professionals are developing software tools and applications to develop a ...
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This chapter finds that computational science has evolved into a more scientific methodology. Computer science professionals are developing software tools and applications to develop a cyberinfrastructure necessary for carrying out scientific research in collaboration with the global research network. The efforts of these professionals have resulted in associating science with computational science and creating a new field known as e-science. E-science involves increasing collaboration between computational science professionals and scientists, enabling scientists to use the latest software and communication tools to undertake respective research projects.Less
This chapter finds that computational science has evolved into a more scientific methodology. Computer science professionals are developing software tools and applications to develop a cyberinfrastructure necessary for carrying out scientific research in collaboration with the global research network. The efforts of these professionals have resulted in associating science with computational science and creating a new field known as e-science. E-science involves increasing collaboration between computational science professionals and scientists, enabling scientists to use the latest software and communication tools to undertake respective research projects.
Paul Humphreys
- Published in print:
- 2019
- Published Online:
- May 2019
- ISBN:
- 9780199334872
- eISBN:
- 9780190219710
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199334872.003.0005
- Subject:
- Philosophy, Philosophy of Science
I argue here that the computational models of numerical experimentation constitute a distinctively new kind of scientific method, intermediate in kind between empirical experimentation and analytic ...
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I argue here that the computational models of numerical experimentation constitute a distinctively new kind of scientific method, intermediate in kind between empirical experimentation and analytic theory. A parallel is also drawn between extending our senses with scientific instruments and extending our mathematical powers by using computational instruments. A specific application of these methods to Ising Models using the Metropolis algorithm is described in detail. Finally, it is argued that what counts as observable, or what counts as computable, is doubly contingent and is not fixed, being dependent upon the current state of technology and the way the world is.Less
I argue here that the computational models of numerical experimentation constitute a distinctively new kind of scientific method, intermediate in kind between empirical experimentation and analytic theory. A parallel is also drawn between extending our senses with scientific instruments and extending our mathematical powers by using computational instruments. A specific application of these methods to Ising Models using the Metropolis algorithm is described in detail. Finally, it is argued that what counts as observable, or what counts as computable, is doubly contingent and is not fixed, being dependent upon the current state of technology and the way the world is.
John Mayfield
- Published in print:
- 2013
- Published Online:
- November 2015
- ISBN:
- 9780231163040
- eISBN:
- 9780231535281
- Item type:
- book
- Publisher:
- Columbia University Press
- DOI:
- 10.7312/columbia/9780231163040.001.0001
- Subject:
- Biology, Evolutionary Biology / Genetics
The concepts of evolution and complexity theory have become part of the intellectual ether permeating the life sciences, the social and behavioral sciences, and, more recently, management science and ...
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The concepts of evolution and complexity theory have become part of the intellectual ether permeating the life sciences, the social and behavioral sciences, and, more recently, management science and economics. This book synthesizes core concepts from multiple disciplines to offer a new approach to understanding how evolution works and how complex organisms, structures, organizations, and social orders can and do arise based on information theory and computational science. This book challenges readers with a nuanced understanding of evolution and complexity that offers consistent, durable, and coherent explanations for major aspects of our life experiences. Numerous examples throughout the book illustrate evolution and complexity formation in action and highlight the core function of computation lying at the work's heart.Less
The concepts of evolution and complexity theory have become part of the intellectual ether permeating the life sciences, the social and behavioral sciences, and, more recently, management science and economics. This book synthesizes core concepts from multiple disciplines to offer a new approach to understanding how evolution works and how complex organisms, structures, organizations, and social orders can and do arise based on information theory and computational science. This book challenges readers with a nuanced understanding of evolution and complexity that offers consistent, durable, and coherent explanations for major aspects of our life experiences. Numerous examples throughout the book illustrate evolution and complexity formation in action and highlight the core function of computation lying at the work's heart.
Joshua M. Epstein and Julia Chelen
- Published in print:
- 2016
- Published Online:
- May 2017
- ISBN:
- 9780262035385
- eISBN:
- 9780262337717
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262035385.003.0016
- Subject:
- Economics and Finance, History of Economic Thought
Agent_Zero is a mathematical and computational individual that can generate important, but insufficiently understood, social dynamics from the bottom up. First published by Epstein (2013), this new ...
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Agent_Zero is a mathematical and computational individual that can generate important, but insufficiently understood, social dynamics from the bottom up. First published by Epstein (2013), this new theoretical entity possesses emotional, deliberative, and social modules, each grounded in contemporary neuroscience. Agent_Zero’s observable behavior results from the interaction of these internal modules. When multiple Agent_Zeros interact with one another, a wide range of important, even disturbing, collective dynamics emerge. These dynamics are not straightforwardly generated using the canonical rational actor which has dominated mathematical social science since the 1940s. Following a concise exposition of the Agent_Zero model, this chapter offers a range of fertile research directions, including the use of realistic geographies and population levels, the exploration of new internal modules and new interactions among them, the development of formal axioms for modular agents, empirical testing, the replication of historical episodes, and practical applications. These may all serve to advance the Agent_Zero research program.Less
Agent_Zero is a mathematical and computational individual that can generate important, but insufficiently understood, social dynamics from the bottom up. First published by Epstein (2013), this new theoretical entity possesses emotional, deliberative, and social modules, each grounded in contemporary neuroscience. Agent_Zero’s observable behavior results from the interaction of these internal modules. When multiple Agent_Zeros interact with one another, a wide range of important, even disturbing, collective dynamics emerge. These dynamics are not straightforwardly generated using the canonical rational actor which has dominated mathematical social science since the 1940s. Following a concise exposition of the Agent_Zero model, this chapter offers a range of fertile research directions, including the use of realistic geographies and population levels, the exploration of new internal modules and new interactions among them, the development of formal axioms for modular agents, empirical testing, the replication of historical episodes, and practical applications. These may all serve to advance the Agent_Zero research program.
I. S. Duff, A. M. Erisman, and J. K. Reid
- Published in print:
- 2017
- Published Online:
- April 2017
- ISBN:
- 9780198508380
- eISBN:
- 9780191746420
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508380.001.0001
- Subject:
- Mathematics, Numerical Analysis
Direct Methods for Sparse Matrices, second edition, is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and ...
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Direct Methods for Sparse Matrices, second edition, is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all our examples were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done since the first edition, some of it by the authors. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.Less
Direct Methods for Sparse Matrices, second edition, is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all our examples were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done since the first edition, some of it by the authors. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.