Non Diophantine Arithmetics In Mathematics Physics And Psychology
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Non Diophantine Arithmetics In Mathematics Physics And Psychology
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Author : Mark Burgin
language : en
Publisher: World Scientific
Release Date : 2020-11-04
Non Diophantine Arithmetics In Mathematics Physics And Psychology written by Mark Burgin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-04 with Mathematics categories.
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 mathematical research and applications of mathematics.A similar event happened in arithmetic in the 20th century. Even longer than with geometry, all thought there was only one conventional arithmetic of natural numbers — the Diophantine arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the conventional arithmetic by the name Diophantine arithmetic due to the important contributions to arithmetic by Diophantus. Nevertheless, in the 20th century, many non-Diophantine arithmetics were discovered, in some of which 2+2=5 or 1+1=3. It took more than two millennia to do this. This discovery has even more implications than the discovery of new geometries because all people use arithmetic.This book provides a detailed exposition of the theory of non-Diophantine arithmetics and its various applications. Reading this book, the reader will see that on the one hand, non-Diophantine arithmetics continue the ancient tradition of operating with numbers while on the other hand, they introduce extremely original and innovative ideas.
Trilogy Of Numbers And Arithmetic Book 1 History Of Numbers And Arithmetic An Information Perspective
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Author : Mark Burgin
language : en
Publisher: World Scientific
Release Date : 2022-04-22
Trilogy Of Numbers And Arithmetic Book 1 History Of Numbers And Arithmetic An Information Perspective written by Mark Burgin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-22 with Mathematics categories.
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, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.
Local Mathematics For Local Physics From Number Scaling To Guage Theory And Cosmology
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Author : Paul Benioff
language : en
Publisher: World Scientific
Release Date : 2024-01-19
Local Mathematics For Local Physics From Number Scaling To Guage Theory And Cosmology written by Paul Benioff and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-19 with Mathematics categories.
The language of the universe is mathematics, but how exactly do you know that all parts of the universe 'speak' the same language? Benioff builds on the idea that the entity that gives substance to both mathematics and physics is the fundamental field, called the 'value field'. While exploring this idea, he notices the similarities that the value field shares with several mysterious phenomena in modern physics: the Higgs field, and dark energy.The author first introduces the concept of the value field and uses it to reformulate the basic framework of number theory, calculus, and vector spaces and bundles. The book moves on to find applications to classical field theory, quantum mechanics and gauge theory. The last two chapters address the relationship between theory and experiment, and the possible physical consequences of both the existence and non-existence of the value field. The book is open-ended, and the list of open questions is certainly longer than the set of proposed answers.Paul Benioff, a pioneer in the field of quantum computing and the author of the first quantum-mechanical description of the Turing machine, devoted the last few years of his life to developing a universal description in which mathematics and physics would be on equal footing. He died on March 29, 2022, his work nearly finished. The final editing was undertaken by Marek Czachor who, in the editorial afterword, attempts to place the author's work in the context of a shift in the scientific paradigm looming on the horizon.
Non Newtonian Calculus
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Author : Michael Grossman
language : en
Publisher: Non-Newtonian Calculus
Release Date : 1972
Non Newtonian Calculus written by Michael Grossman and has been published by Non-Newtonian Calculus this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
The non-Newtonian calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. It may well be that these calculi can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Information Studies And The Quest For Transdisciplinarity Unity Through Diversity
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Author : Mark Burgin
language : en
Publisher: World Scientific
Release Date : 2017-03-27
Information Studies And The Quest For Transdisciplinarity Unity Through Diversity written by Mark Burgin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-27 with Computers categories.
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 most recent achievements, ideas and opinions of leading researchers in this domain reflecting their quest for advancing information science and technology. With the goal of building a better society, in which social and technological innovations help make information key to the flourishing of humanity, we dispense with the bleak view of the dark side of information society.It is aimed at readers that conduct research into any aspect of information, information society and information technology, who develop or implement social or technological applications. It is also for those who have an interest in participating in setting the goals for the sciences of information and the social applications of technological achievements and the scientific results.
Future Information Society The Social And Technological Problems
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Author : Wolfgang Hofkirchner
language : en
Publisher: World Scientific
Release Date : 2017-01-24
Future Information Society The Social And Technological Problems written by Wolfgang Hofkirchner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Computers categories.
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 better society, in which social and technological innovations help make information key to the flourishing of humanity and dispense with the bleak view of the dark side of information society.It is aimed at readers that conduct research into any aspect of information, information society and information technology, who develop or implement social or technological applications. It is also for those who have an interest in participating in setting the goals for sciences of information and social applications of technological achievements and scientific results.
Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Computers categories.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Semitopological Vector Spaces
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Author : Mark Burgin
language : en
Publisher: CRC Press
Release Date : 2017-06-26
Semitopological Vector Spaces written by Mark Burgin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-26 with Mathematics categories.
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 hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. Exploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory. To make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader.
Laws Of Form A Fiftieth Anniversary
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Author : Louis H Kauffman
language : en
Publisher: World Scientific
Release Date : 2023-01-09
Laws Of Form A Fiftieth Anniversary written by Louis H Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-09 with Mathematics categories.
Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8-10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.
Chaos Information And The Future Of Physics The Seaman Rossler Dialogue With Information Perspectives By Burgin And Seaman
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Author : William Seaman
language : en
Publisher: World Scientific
Release Date : 2023-06-22
Chaos Information And The Future Of Physics The Seaman Rossler Dialogue With Information Perspectives By Burgin And Seaman written by William Seaman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-22 with Mathematics categories.
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 of papers and books published by Rössler and other related collaborative researchers. The goal is to delineate an intellectual directory for future researchers. The discussed topics being transdisciplinary in nature cross many fields in science and technology. A comprehensive historical bibliography is also included. The work explores many fields germane to theoretical science as Rössler was often quite early in developing these fields and interacting with many famous scientists. This work pertains to information theory, which has often been left out of the historical literature.Burgin as an expert in information theory is providing an information perspective on this dialogue adding historical discussion and relevant scientific and mathematical underpinnings of the discussed ideas. His observations are complemented by Seaman, who presents the synthesis of artistic and scientific outlook.Addendum contains articles describing Rössler's relationships to colleagues from multiple fields, a parable by Rössler and papers related to Rössler's research and theoretical models of processes in the universe.