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This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

Computer science. --- Computers. --- Computer science --- Mathematical logic. --- Computer Science. --- Theory of Computation. --- Mathematics of Computing. --- Mathematical Logic and Foundations. --- Mathematics. --- Computable functions. --- Unsolvability (Mathematical logic) --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Degrees of unsolvability --- Turing degrees of unsolvability --- Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Constructive mathematics --- Decidability (Mathematical logic) --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Recursive functions --- Information theory. --- Informatics --- Science --- Communication theory --- Communication --- Cybernetics --- Computer science—Mathematics. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace

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Complex analysis --- Biomathematics. Biometry. Biostatistics --- Computer science --- Programming --- Information systems --- Computer. Automation --- toegepaste informatica --- complexe analyse (wiskunde) --- bio-informatica --- informatica --- biometrie --- systeemontwikkeling (informatica) --- wiskunde --- algoritmen --- methodologieën --- Europe

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Mathematical logic --- Logic --- Complex analysis --- Computer science --- Information systems --- Computer. Automation --- toegepaste informatica --- cryptologie --- complexe analyse (wiskunde) --- informatica --- ontwerpen --- programmeren (informatica) --- wiskunde --- programmatielogica

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This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

Mathematical logic --- Mathematical control systems --- Computer science --- Computer. Automation --- toegepaste informatica --- computers --- informatica --- wiskunde --- logica --- computerkunde --- informatietheorie

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CiE 2005: New Computational Paradigms http://www. illc. uva. nl/CiE/ ThecooperationComputabilityinEurope (CiE)isaninformalEuropeannetwork covering computability in theoretical computer science and mathematical logic, ranging from application of novel approaches to computation to set-theoretic analysesofin?nitarycomputingmodels. Thecooperationconsistsofelevenmain nodesandincludesover400researchers;itiscoordinatedfromLeeds(UK). More information about CiE can be found in Barry Cooper's introductory paper to this volume (p. 1) and at http://www. amsta. leeds. ac. uk/pure/staff/cooper/cie. html CiE 2005 was a conference on the special topic New Computational Pa- digms  and was held in Amsterdam in June 2005. It was initiated by and served as a focus point for the informal cooperation CiE. The topic of New Com- tational Paradigms  covers connections between computation and physical s- tems (e. g. , quantum computation, neural nets, molecular computation) but also higher mathematical models of computation (e. g. , in?nitary computation or real computation). Computability theory is central to large areas of theoretical computer science and mathematical logic. Traditionally, the computational model of the Turing machine (or mathematically equivalent models) has been used to reason about computation or computability. For general computability inquiries (with - bounded resources), the choice of the model of computation hardly matters (this fact is encapsulated in the so-called Church-Turing thesis ); this could change as soon as questions of e?ciency are investigated.

Computers. --- Algorithms. --- Computer science—Mathematics. --- Artificial intelligence. --- Bioinformatics. --- Theory of Computation. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Computing. --- Artificial Intelligence. --- Bioinformatics. --- Algorithms.