Exploring Randomness

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Exploring Randomness

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Author : Gregory J. Chaitin
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-07-30

Exploring Randomness written by Gregory J. Chaitin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-30 with Computers categories.

This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything hes seen. Don miss it." John Casti, Santa Fe Institute, Author of Goedel: A Life of Logic.'

The Art Of Randomness

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Author : Ronald T. Kneusel
language : en
Publisher: No Starch Press
Release Date : 2024-03-05

The Art Of Randomness written by Ronald T. Kneusel and has been published by No Starch Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-05 with Computers categories.

Harness the power of randomness (and Python code) to solve real-world problems in fun, hands-on experiments—from simulating evolution to encrypting messages to making machine-learning algorithms! The Art of Randomness is a hands-on guide to mastering the many ways you can use randomized algorithms to solve real programming and scientific problems. You’ll learn how to use randomness to run simulations, hide information, design experiments, and even create art and music. All you need is some Python, basic high school math, and a roll of the dice. Author Ronald T. Kneusel focuses on helping you build your intuition so that you’ll know when and how to use random processes to get things done. You’ll develop a randomness engine (a Python class that supplies random values from your chosen source), then explore how to leverage randomness to: Simulate Darwinian evolution and optimize with swarm-based search algorithms Design scientific experiments to produce more meaningful results by making them truly random Implement machine learning algorithms like neural networks and random forests Use Markov Chain Monte Carlo methods to sample from complex distributions Hide information in audio files and images, generate art, and create music Reconstruct original signals and images from only randomly sampled data Scientific anecdotes and code examples throughout illustrate how randomness plays into areas like optimization, machine learning, and audio signals. End-of-chapter exercises encourage further exploration. Whether you’re a programmer, scientist, engineer, mathematician, or artist, you’ll find The Art of Randomness to be your ticket to discovering the hidden power of applied randomness and the ways it can transform your approach to solving problems, from the technical to the artistic.

Randomness And Complexity

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Author : Cristian Calude
language : en
Publisher: World Scientific
Release Date : 2007

Randomness And Complexity written by Cristian Calude and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.

The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.

Thinking About G Del And Turing

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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 2007

Thinking About G Del And Turing written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable ê number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as G”del and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of G”del and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.

Sortition

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Author : Gil Delannoi
language : en
Publisher: Andrews UK Limited
Release Date : 2016-10-05

Sortition written by Gil Delannoi and has been published by Andrews UK Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-05 with Political Science categories.

This volume reflects the up-and-coming academic interest in sortition. It is based on contributions to the first international conference dedicated to the subject held at the University of Political Science (Sciences-Po) in Paris in November 2008. The papers explore important theoretical questions such as how we should recognise and define differing lottery forms; the relationship between sortition and different aspects and forms of democracy; and its potential benefits to current political and commercial practice. Contributors include: Hubertus Buchstein, Gil Delannoi, Oliver Dowlen, Gerhard Göhler, Barbara Goodwin, Michael Hein, Yves Sintomer, Peter Stone and Antoine Vergne.

Goedel S Way

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Author : Gregory Chaitin
language : en
Publisher: CRC Press
Release Date : 2011-10-14

Goedel S Way written by Gregory Chaitin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Consciousness As Complex Event

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Author : Craig Delancey
language : en
Publisher: Taylor & Francis
Release Date : 2022-09-09

Consciousness As Complex Event written by Craig Delancey and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-09 with Philosophy categories.

Consciousness as Complex Event: Towards a New Physicalism provides a new approach to the study of consciousness. The author argues that what makes phenomenal experiences mysterious is that these experiences are extremely complex brain events. The text provides an accessible introduction to descriptive complexity (also known as Kolmogorov Complexity) and then applies this to show that the most influential arguments against physicalism about consciousness are unsound. The text also offers an accessible review of the current debates about consciousness and introduces a rigorous new conception of physicalism. It concludes with a positive program for the future study of phenomenal experience. It is readable and compact and will be of interest to philosophers and cognitive scientists, and of value to advanced students of philosophy. Key Features Provides a new approach to the study of consciousness, using information theory. Offers a valuable discussion of physicalism, of use in other disciplines. Contains an introduction to the main literature and arguments in the debate about consciousness. Includes an accessible overview of how to apply descriptive complexity to philosophical problems.

Uncertainty

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Author : William Briggs
language : en
Publisher: Springer
Release Date : 2016-07-15

Uncertainty written by William Briggs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-15 with Mathematics categories.

This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance." The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, such as out-of-the-box regression, cannot help in discovering cause. This new way of looking at uncertainty ties together disparate fields — probability, physics, biology, the “soft” sciences, computer science — because each aims at discovering cause (of effects). It broadens the understanding beyond frequentist and Bayesian methods to propose a Third Way of modeling.

Aspects Of Kolmogorov Complexity The Physics Of Information

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Author : Bradley S. Tice
language : en
Publisher: CRC Press
Release Date : 2022-09-01

Aspects Of Kolmogorov Complexity The Physics Of Information written by Bradley S. Tice and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Science categories.

The research presented in Aspects of Kolmogorov Complexity addresses the fundamental standard of defining randomness as measured by a Martin-Lof level of randomness as found in random sequential binary strings. A classical study of statistics that addresses both a fundamental standard of statistics as well as an applied measure for statistical communication theory. The research points to compression levels in a random state that are greater than is found in current literature. A historical overview of the field of Kolmogorov Complexity and Algorithmic Information Theory, a subfield of Information Theory, is given as well as examples using a radix 3, radix 4, and radix 5 base numbers for both random and non-random sequential strings. The text also examines monochromatic and chromatic symbols and both theoretical and applied aspects of data compression as they relate to the transmission and storage of information. The appendix contains papers on the subject given at conferences and the references are current.ContentsTechnical topics addressed in Aspects of Kolmogorov Complexity include:• Statistical Communication Theory• Algorithmic Information Theory• Kolmogorov Complexity• Martin-Lof Randomness• Compression, Transmission and Storage of Information

Contagious Architecture

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Author : Luciana Parisi
language : en
Publisher: MIT Press
Release Date : 2022-11-01

Contagious Architecture written by Luciana Parisi and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-01 with Social Science categories.

A proposal that algorithms are not simply instructions to be performed but thinking entities that construct digital spatio-temporalities. In Contagious Architecture, Luciana Parisi offers a philosophical inquiry into the status of the algorithm in architectural and interaction design. Her thesis is that algorithmic computation is not simply an abstract mathematical tool but constitutes a mode of thought in its own right, in that its operation extends into forms of abstraction that lie beyond direct human cognition and control. These include modes of infinity, contingency, and indeterminacy, as well as incomputable quantities underlying the iterative process of algorithmic processing. The main philosophical source for the project is Alfred North Whitehead, whose process philosophy is specifically designed to provide a vocabulary for “modes of thought” exhibiting various degrees of autonomy from human agency even as they are mobilized by it. Because algorithmic processing lies at the heart of the design practices now reshaping our world—from the physical spaces of our built environment to the networked spaces of digital culture—the nature of algorithmic thought is a topic of pressing importance that reraises questions of control and, ultimately, power. Contagious Architecture revisits cybernetic theories of control and information theory's notion of the incomputable in light of this rethinking of the role of algorithmic thought. Informed by recent debates in political and cultural theory around the changing landscape of power, it links the nature of abstraction to a new theory of power adequate to the complexities of the digital world.