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1031 results in Computational statistics, machine learning and information science

Page 23 of 52

Physical Perspectives on Computation, Computational Perspectives on Physics
  • Edited by Michael E. Cuffaro, Samuel C. Fletcher
  • Published online:
    17 May 2018
    Print publication:
    17 May 2018
  • Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics.

  • 7 - Physics-like Models of Computation

  • Edited by Michael E. Cuffaro, University of Western Ontario, Samuel C. Fletcher
  • Book:
    Physical Perspectives on Computation, Computational Perspectives on Physics
    Published online:
    17 May 2018
    Print publication:
    17 May 2018, pp 153-171

  • Summary

    There are several traditional models of computation such as Church's lambda calculus, Herbrand-Gödel equational calculus and representability in formal systems of arithmetic, that appear unrelated to the general framework of physics. The extreme example in this context is Fenstad's axiomatization of computability. On the other hand, several models that are often more popular with theoretical computer scientists and complexity theorists such as Turing machines, register machines and cellular automata are physics-like in the sense that they are arguably realizable in any plausible model of physics. Of course, all these logical models are equivalent in a certain precise technical sense, but implementations of the latter class are far more direct and they avoid tedious coding issues. The question thus arises whether any insights into the nature of computability can be gained from a careful study of logical versus physical computation. As a case in point we consider discovered rather than constructed universal systems and the old problem of the epistemological status of intermediate recursively enumerable degrees.

  • 5 - How is There a Physics of Information? On Characterizing Physical Evolution as Information Processing

  • Edited by Michael E. Cuffaro, University of Western Ontario, Samuel C. Fletcher
  • Book:
    Physical Perspectives on Computation, Computational Perspectives on Physics
    Published online:
    17 May 2018
    Print publication:
    17 May 2018, pp 103-126

  • Summary

    We have a conundrum. The physical basis of information is clearly a highly active research area. Yet the power of information theory comes precisely from separating it from the detailed problems of building physical systems to perform information-processing tasks. Developments in quantum information over the last two decades seem to have undermined this separation, leading to suggestions that information is itself a physical entity and must be part of our physical theories, with resource-cost implications. We will consider a variety of ways in which physics seems to affect computation, but will ultimately argue to the contrary: rejecting the claims that information is physical provides a better basis for understanding the fertile relationship between information theory and physics. Instead, we will argue that the physical resource costs of information processing are to be understood through the need to consider physically embodied agents for whom information-processing tasks are performed. Doing so sheds light on what it takes for something to be implementing a computational or information-processing task of a given kind.

  • 10 - Intension in the Physics of Computation: Lessons from the Debate about Landauer’s Principle

  • Edited by Michael E. Cuffaro, University of Western Ontario, Samuel C. Fletcher
  • Book:
    Physical Perspectives on Computation, Computational Perspectives on Physics
    Published online:
    17 May 2018
    Print publication:
    17 May 2018, pp 219-239

  • Summary

    In this paper the key issues in the debate about Landauer's Principle are identified, and important lessons are drawn about how our view of computation and physics relates to and is informed by the interpretation of thermal physics. It is argued that there are several respects in which modality, and how processes and systems are represented, are crucial to both Landauer's Principle and the application of thermodynamics. After reviewing the L-machine model of Ladyman, Presnell, Short, and Groisman (2007) as an exemplification of a general account of computation and its physical realization, John Norton's supposed no-go theorem for the thermodynamics of computation, and work by David Wallace (2014) on the nature of the Second Law of thermodynamics and the relationship between thermodynamics and statistical mechanics, it is argued that both computational and thermodynamic states are intensional, but that the modal structure of physical states that represent them can nonetheless be taken to be an objective component of implementation.

  • 6 - Abstraction/Representation Theory and the Natural Science of Computation

  • Edited by Michael E. Cuffaro, University of Western Ontario, Samuel C. Fletcher
  • Book:
    Physical Perspectives on Computation, Computational Perspectives on Physics
    Published online:
    17 May 2018
    Print publication:
    17 May 2018, pp 127-150

  • Summary

    A computer is a physical object, but are all physical objects computers? Computer science, traditionally dealing only with issues of abstract computation, has tended to ignore this question. The lack of formal connection between physical device and abstract theory has given rise both to this type of foundational quandary, and also to difficulties determining the capabilities of new unconventional computing technologies. Recently introduced, Abstraction/Representation (AR) theory fills this gap. AR theory gives a rigorous framework for the interrelation of abstract and physical objects and processes, demonstrating the critical role of representation in both the physical and computational sciences. Amongst other insights, this allows a determination of when a physical system is computing. AR theory foregrounds the deep structural connections between computing and natural science, giving a unifying framework for both the physics of computing, and the computational capabilities of physical systems.

  • 8 - Feasible Computation: Methodological Contributions from Computational Science

  • Edited by Michael E. Cuffaro, University of Western Ontario, Samuel C. Fletcher
  • Book:
    Physical Perspectives on Computation, Computational Perspectives on Physics
    Published online:
    17 May 2018
    Print publication:
    17 May 2018, pp 172-194

  • Summary

    The field of computational science is concerned with generating feasible algorithms to solve mathematical problems, usually those that are important in scientific applications. An important difference between such feasible algorithms and traditional algorithms considered in computability theory is that, in general, they involve various forms of approximation. We will see that there is a common strategy in computational science that can take a problem that is not feasibly computable, and then generate a (more) feasible algorithm to a slightly modified problem. We will see how one, more general, version of this strategy underlies numerical computing, which uses approximations, and how a more restricted version underlies symbolic computing, which is exact. The nature of this feasible computation strategy in these two branches of computational science has some consequences for computability theory. We will also consider its roots in the history of science. It emerges, therefore, that feasible computing is a fundamental part of a great deal of scientific inference, as well as at the core of advanced algorithms for solving problems in computational science.

  • Introduction

  • Edited by Michael E. Cuffaro, University of Western Ontario, Samuel C. Fletcher
  • Book:
    Physical Perspectives on Computation, Computational Perspectives on Physics
    Published online:
    17 May 2018
    Print publication:
    17 May 2018, pp 1-20

  • Summary

    In this introductory chapter, we summarize each of this volume's parts and the particular contributions that fall under them: I) the computability of physical systems and physical systems as computers, II) the implementation of computation in physical systems, III) physical perspectives on computer science, and IV) computational perspectives on physical theory. Before we do so, however, we review some of the basic concepts which will generally be taken for granted in the rest of the book, including those from: I) computability theory, Turing machines, and the Church-Turing thesis, II) computational complexity theory, III) quantum computing, IV) theories of computational implementation and the variety of “physical” Church-Turing theses, and V) Landauer's principle and the thermodynamics of computation.

Page 23 of 52