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  • Non-diophantine Arithmetics In Mathematics, Physics And Psychology

    For a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for ... En savoir plus

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  • Hypernumbers and Extrafunctions

    Extending the Classical Calculus

    par Mark Burgin ...
    Collections series Mathematics and Statistics (R0)
    “Hypernumbers and Extrafunctions” presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a ... En savoir plus

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  • Semitopological Vector Spaces

    Hypernorms, Hyperseminorms, and Operators

    par Mark Burgin ...
    This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and ... En savoir plus

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  • Chaos, Information, and the Future of Physics

    The Seaman-Rössler Dialogue with Information Perspectives by Burgin and Seaman

    Collections Livre 15 - World Scientific Series in Information Studies
    The main part of the book consists of the dialogue between physicist Otto Rössler, and artist and AI researcher Bill Seaman with the commentaries disclosing information perspective by information scientist Mark Burgin and Bill Seaman. In this dialogue, Rössler and Seaman discuss concepts surrounding Rössler's major research over his lifetime. Additionally, each research topic is linked to the set ... En savoir plus

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  • Trilogy of Numbers and Arithmetic

    Book 1: History of Numbers and Arithmetic: An Information Perspective

    par Mark Burgin ...
    Collections Livre 12 - World Scientific Series in Information Studies
    The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, ... En savoir plus

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  • Philosophy And Methodology Of Information: The Study Of Information In The Transdisciplinary Perspective

    Collections Livre 10 - World Scientific Series In Information Studies
    The book gives up-to-date, multi-aspect exposition of the philosophy and methodology of information, and related areas within the nascent field of the study of information. It presents the most recent achievements, ideas and opinions of leading researchers in this domain, as well as from physicists, biologists and social scientists. Collaboration of researchers from different areas and fields ... En savoir plus

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  • Information And Complexity

    Collections Livre 6 - World Scientific Series In Information Studies
    The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and processes. There are intrinsic relations between information and complexity.The research in information theory, the theory of complexity and their interrelations is very active. The book will expand ... En savoir plus

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  • Theoretical Information Studies: Information In The World

    Collections Livre 11 - World Scientific Series In Information Studies
    This is the first attempt to delineate the synthetic field of the theoretical study of information, treating information as the basic phenomenon on the fundamental level of the world, encompassing nature, technology, individuals and society. The exploration of information is done within Info-computational approaches, to natural and social phenomena such as Bioinformatics, Information Physics, ... En savoir plus

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  • Theory Of Knowledge: Structures And Processes

    par Mark Burgin ...
    Collections Livre 5 - World Scientific Series In Information Studies
    This book aims to synthesize different directions in knowledge studies into a unified theory of knowledge and knowledge processes. It explicates important relations between knowledge and information. It provides the readers with understanding of the essence and structure of knowledge, explicating operations and process that are based on knowledge and vital for society.The book also highlights how ... En savoir plus

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  • Information Studies And The Quest For Transdisciplinarity: Unity Through Diversity

    Collections Livre 9 - World Scientific Series In Information Studies
    This book is the second volume of a two-volume edition based on the International Society for Information Studies Summit Vienna 2015 on 'The Information Society at the Crossroads. Response and Responsibility of the Sciences of Information' (see summit.is4is.org).The book gives an up-to-date multiaspect exposition of contemporary studies in the field of information and related areas. It presents ... En savoir plus

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  • Future Information Society, The: Social And Technological Problems

    Collections Livre 8 - World Scientific Series In Information Studies
    This book is the first volume of a two-volume edition based on the International Society for Information Studies Summit Vienna 2015 on 'The Information Society at the Crossroads. Response and Responsibility of the Sciences of Information' (see summit.is4is.org).The book represents a trans-disciplinary endeavor of the leading experts in the field of information studies posing the question for a ... En savoir plus

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    The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results ... En savoir plus

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