Irreducibility and Computational Equivalence

Irreducibility and Computational Equivalence
Title Irreducibility and Computational Equivalence PDF eBook
Author Hector Zenil
Publisher Springer Science & Business Media
Pages 354
Release 2012-12-25
Genre Technology & Engineering
ISBN 3642354823

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It is clear that computation is playing an increasingly prominent role in the development of mathematics, as well as in the natural and social sciences. The work of Stephen Wolfram over the last several decades has been a salient part in this phenomenon helping founding the field of Complex Systems, with many of his constructs and ideas incorporated in his book A New Kind of Science (ANKS) becoming part of the scientific discourse and general academic knowledge--from the now established Elementary Cellular Automata to the unconventional concept of mining the Computational Universe, from today's widespread Wolfram's Behavioural Classification to his principles of Irreducibility and Computational Equivalence. This volume, with a Foreword by Gregory Chaitin and an Afterword by Cris Calude, covers these and other topics related to or motivated by Wolfram's seminal ideas, reporting on research undertaken in the decade following the publication of Wolfram's NKS book. Featuring 39 authors, its 23 contributions are organized into seven parts: Mechanisms in Programs & Nature Systems Based on Numbers & Simple Programs Social and Biological Systems & Technology Fundamental Physics The Behavior of Systems & the Notion of Computation Irreducibility & Computational Equivalence Reflections and Philosophical Implications.

A New Kind of Science

A New Kind of Science
Title A New Kind of Science PDF eBook
Author Stephen Wolfram
Publisher
Pages 1197
Release 2002
Genre Cellular automata
ISBN 9780713991161

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This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.

Symmetry And Complexity: The Spirit And Beauty Of Nonlinear Science

Symmetry And Complexity: The Spirit And Beauty Of Nonlinear Science
Title Symmetry And Complexity: The Spirit And Beauty Of Nonlinear Science PDF eBook
Author Klaus Mainzer
Publisher World Scientific
Pages 448
Release 2005-06-10
Genre Science
ISBN 9814480819

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Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity.

A Project to Find the Fundamental Theory of Physics

A Project to Find the Fundamental Theory of Physics
Title A Project to Find the Fundamental Theory of Physics PDF eBook
Author Stephen Wolfram
Publisher Wolfram Media
Pages 0
Release 2020
Genre Science
ISBN 9781579550356

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The Wolfram Physics Project is a bold effort to find the fundamental theory of physics. It combines new ideas with the latest research in physics, mathematics and computation in the push to achieve this ultimate goal of science. Written with Stephen Wolfram's characteristic expository flair, this book provides a unique opportunity to learn about a historic initiative in science right as it is happening. A Project to Find the Fundamental Theory of Physics includes an accessible introduction to the project as well as core technical exposition and rich, never-before-seen visualizations.

Partial Derivatives in Arithmetic Complexity and Beyond

Partial Derivatives in Arithmetic Complexity and Beyond
Title Partial Derivatives in Arithmetic Complexity and Beyond PDF eBook
Author Xi Chen
Publisher Now Publishers Inc
Pages 157
Release 2011
Genre Computers
ISBN 1601984804

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Partial Derivatives in Arithmetic Complexity and Beyond is devoted mainly to the study of polynomials from a computational perspective. The main point of this book is that one can learn a great deal about the structure and complexity of polynomials by studying (some of) their partial derivatives.

A Course in Computational Algebraic Number Theory

A Course in Computational Algebraic Number Theory
Title A Course in Computational Algebraic Number Theory PDF eBook
Author Henri Cohen
Publisher Springer Science & Business Media
Pages 556
Release 2013-04-17
Genre Mathematics
ISBN 3662029456

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A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

The End of Theory

The End of Theory
Title The End of Theory PDF eBook
Author Richard Bookstaber
Publisher Princeton University Press
Pages 236
Release 2019-04-02
Genre Business & Economics
ISBN 0691191859

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An in-depth look at how to account for the human complexities at the heart of today’s financial system Our economy may have recovered from the Great Recession—but not our economics. The End of Theory discusses why the human condition and the radical uncertainty of our world renders the standard economic model—and the theory behind it—useless for dealing with financial crises. What model should replace it? None. At least not any version we’ve been using for the past two hundred years. Richard Bookstaber argues for a new approach called agent-based economics, one that takes as a starting point the fact that we are humans, not the optimizing automatons that standard economics assumes we are. Sweeping aside the historic failure of twentieth-century economics, The End of Theory offers a novel perspective and more realistic framework to help prevent today's financial system from blowing up again.